TSTP Solution File: ITP250^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP250^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:26:01 EDT 2023
% Result : Timeout 299.91s 300.16s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.72/2.79 % Problem : ITP250^3 : TPTP v8.1.2. Released v8.1.0.
% 2.72/2.79 % Command : do_cvc5 %s %d
% 2.84/3.01 % Computer : n013.cluster.edu
% 2.84/3.01 % Model : x86_64 x86_64
% 2.84/3.01 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.84/3.01 % Memory : 8042.1875MB
% 2.84/3.01 % OS : Linux 3.10.0-693.el7.x86_64
% 2.84/3.01 % CPULimit : 300
% 2.84/3.01 % WCLimit : 300
% 2.84/3.01 % DateTime : Sun Aug 27 11:02:05 EDT 2023
% 2.84/3.01 % CPUTime :
% 5.42/5.61 %----Proving TH0
% 5.42/5.62 %------------------------------------------------------------------------------
% 5.42/5.62 % File : ITP250^3 : TPTP v8.1.2. Released v8.1.0.
% 5.42/5.62 % Domain : Interactive Theorem Proving
% 5.42/5.62 % Problem : Sledgehammer problem VEBT_Bounds 00802_043357
% 5.42/5.62 % Version : [Des22] axioms.
% 5.42/5.62 % English :
% 5.42/5.62
% 5.42/5.62 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.42/5.62 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.42/5.62 % Source : [Des22]
% 5.42/5.62 % Names : 0071_VEBT_Bounds_00802_043357 [Des22]
% 5.42/5.62
% 5.42/5.62 % Status : Theorem
% 5.42/5.62 % Rating : 1.00 v8.1.0
% 5.42/5.62 % Syntax : Number of formulae : 11296 (5983 unt;1039 typ; 0 def)
% 5.42/5.62 % Number of atoms : 27928 (12544 equ; 0 cnn)
% 5.42/5.62 % Maximal formula atoms : 71 ( 2 avg)
% 5.42/5.62 % Number of connectives : 116338 (2779 ~; 481 |;1781 &;100927 @)
% 5.42/5.62 % ( 0 <=>;10370 =>; 0 <=; 0 <~>)
% 5.42/5.62 % Maximal formula depth : 39 ( 6 avg)
% 5.42/5.62 % Number of types : 92 ( 91 usr)
% 5.42/5.62 % Number of type conns : 3967 (3967 >; 0 *; 0 +; 0 <<)
% 5.42/5.62 % Number of symbols : 951 ( 948 usr; 60 con; 0-8 aty)
% 5.42/5.62 % Number of variables : 25395 (1831 ^;22734 !; 830 ?;25395 :)
% 5.42/5.62 % SPC : TH0_THM_EQU_NAR
% 5.42/5.62
% 5.42/5.62 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.42/5.62 % from the van Emde Boas Trees session in the Archive of Formal
% 5.42/5.62 % proofs -
% 5.42/5.62 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.42/5.62 % 2022-02-18 02:50:20.033
% 5.42/5.62 %------------------------------------------------------------------------------
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% 5.42/5.62 thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
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% 5.42/5.62 thf(ty_n_t__VEBT____Definitions__OVEBT,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Code____Numeral__Ointeger,type,
% 5.42/5.62 code_integer: $tType ).
% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Extended____Nat__Oenat,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__List__Olist_I_Eo_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Complex__Ocomplex,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Set__Oset_I_Eo_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__String__Ochar,type,
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% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Real__Oreal,type,
% 5.42/5.62 real: $tType ).
% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Rat__Orat,type,
% 5.42/5.62 rat: $tType ).
% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Num__Onum,type,
% 5.42/5.62 num: $tType ).
% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Nat__Onat,type,
% 5.42/5.62 nat: $tType ).
% 5.42/5.62
% 5.42/5.62 thf(ty_n_t__Int__Oint,type,
% 5.42/5.62 int: $tType ).
% 5.42/5.62
% 5.42/5.62 % Explicit typings (948)
% 5.42/5.62 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 5.42/5.62 archim2889992004027027881ng_rat: rat > int ).
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% 5.42/5.62 thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
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% 5.42/5.62 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_Eo_001_Eo,type,
% 5.42/5.62 bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Binomial_Obinomial,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Oand__int__rel,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Oand__not__num,type,
% 5.42/5.62 bit_and_not_num: num > num > option_num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
% 5.42/5.62 bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 5.42/5.62 bit_concat_bit: nat > int > int > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
% 5.42/5.62 bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
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% 5.42/5.62 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
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% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
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% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
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% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
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% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Code____Numeral__Ointeger,type,
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% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
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% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Ointeger,type,
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% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Nat__Onat,type,
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% 5.42/5.62
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Otake__bit__num,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations_Oand__num,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Oadjust__mod,type,
% 5.42/5.62 adjust_mod: int > int > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Odivmod__nat,type,
% 5.42/5.62 divmod_nat: nat > nat > product_prod_nat_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Oeucl__rel__int,type,
% 5.42/5.62 eucl_rel_int: int > int > product_prod_int_int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
% 5.42/5.62 unique6319869463603278526ux_int: product_prod_int_int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 5.42/5.62 unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 5.42/5.62 unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
% 5.42/5.62 unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 5.42/5.62 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 5.42/5.62 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 comm_s8582702949713902594nteger: code_integer > nat > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Complex__Ocomplex,type,
% 5.42/5.62 comm_s2602460028002588243omplex: complex > nat > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Int__Oint,type,
% 5.42/5.62 comm_s4660882817536571857er_int: int > nat > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Nat__Onat,type,
% 5.42/5.62 comm_s4663373288045622133er_nat: nat > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Rat__Orat,type,
% 5.42/5.62 comm_s4028243227959126397er_rat: rat > nat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Real__Oreal,type,
% 5.42/5.62 comm_s7457072308508201937r_real: real > nat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 semiri3624122377584611663nteger: nat > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
% 5.42/5.62 semiri5044797733671781792omplex: nat > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint,type,
% 5.42/5.62 semiri1406184849735516958ct_int: nat > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 5.42/5.62 semiri1408675320244567234ct_nat: nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Rat__Orat,type,
% 5.42/5.62 semiri773545260158071498ct_rat: nat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 5.42/5.62 semiri2265585572941072030t_real: nat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 5.42/5.62 invers8013647133539491842omplex: complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 5.42/5.62 inverse_inverse_rat: rat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 5.42/5.62 inverse_inverse_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 5.42/5.62 at_bot_real: filter_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 5.42/5.62 at_top_nat: filter_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 5.42/5.62 at_top_real: filter_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 5.42/5.62 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 5.42/5.62 eventually_real: ( real > $o ) > filter_real > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.42/5.62 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.42/5.62 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.42/5.62 filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.42/5.62 princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.42/5.62 princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 5.42/5.62 finite_card_o: set_o > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 5.42/5.62 finite_card_complex: set_complex > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 5.42/5.62 finite_card_int: set_int > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
% 5.42/5.62 finite_card_list_nat: set_list_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 5.42/5.62 finite_card_nat: set_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 5.42/5.62 finite410649719033368117t_unit: set_Product_unit > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 5.42/5.62 finite_card_char: set_char > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
% 5.42/5.62 finite_finite_o: set_o > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 5.42/5.62 finite3207457112153483333omplex: set_complex > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 5.42/5.62 finite_finite_int: set_int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
% 5.42/5.62 finite_finite_list_o: set_list_o > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.42/5.62 finite8712137658972009173omplex: set_list_complex > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Int__Oint_J,type,
% 5.42/5.62 finite3922522038869484883st_int: set_list_int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
% 5.42/5.62 finite8100373058378681591st_nat: set_list_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.42/5.62 finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 5.42/5.62 finite_finite_nat: set_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Num__Onum,type,
% 5.42/5.62 finite_finite_num: set_num > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
% 5.42/5.62 finite_finite_rat: set_rat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 5.42/5.62 finite_finite_real: set_real > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.42/5.62 finite1152437895449049373et_nat: set_set_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Finite__Set_Ofinite_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.42/5.62 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.42/5.62 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 5.42/5.62 comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.42/5.62 comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Oid_001_Eo,type,
% 5.42/5.62 id_o: $o > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 5.42/5.62 id_nat: nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 5.42/5.62 inj_on_nat_char: ( nat > char ) > set_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.42/5.62 inj_on_real_real: ( real > real ) > set_real > $o ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 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 ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 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 ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 5.42/5.62 map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.42/5.62 map_fu1532550112467129777l_real: ( real > nat > rat ) > ( ( ( nat > rat ) > nat > rat ) > real > real ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > real > real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.42/5.62 map_fu7146612038024189824t_real: ( real > nat > rat ) > ( ( nat > rat ) > real ) > ( ( nat > rat ) > nat > rat ) > real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_Eo_001_Eo,type,
% 5.42/5.62 map_fu1856342031159181835at_o_o: ( real > nat > rat ) > ( $o > $o ) > ( ( nat > rat ) > $o ) > real > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 5.42/5.62
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% 5.42/5.62 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.42/5.62 set_o2: list_o > set_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.42/5.62 set_complex2: list_complex > set_complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.42/5.62 set_int2: list_int > set_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.42/5.62 set_nat2: list_nat > set_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.42/5.62 set_real2: list_real > set_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 5.42/5.62 tl_nat: list_nat > list_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.42/5.62 list_update_o: list_o > nat > $o > list_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 5.42/5.62 list_update_complex: list_complex > nat > complex > list_complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.42/5.62 list_update_int: list_int > nat > int > list_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.42/5.62 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.42/5.62 list_update_real: list_real > nat > real > list_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001_Eo,type,
% 5.42/5.62 nth_o: list_o > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.42/5.62 nth_complex: list_complex > nat > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.42/5.62 nth_int: list_int > nat > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.42/5.62 nth_nat: list_nat > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.42/5.62 nth_num: list_num > nat > num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.42/5.62 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 5.42/5.62 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.42/5.62 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.42/5.62 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.42/5.62 nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.42/5.62 nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.42/5.62 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.42/5.62 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.42/5.62 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.42/5.62 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.42/5.62 nth_real: list_real > nat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.42/5.62 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.42/5.62 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 5.42/5.62 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.42/5.62 produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.42/5.62 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 5.42/5.62 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.42/5.62 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.42/5.62 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.42/5.62 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.42/5.62 replicate_o: nat > $o > list_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.42/5.62 replicate_complex: nat > complex > list_complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.42/5.62 replicate_int: nat > int > list_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.42/5.62 replicate_nat: nat > nat > list_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.42/5.62 replicate_real: nat > real > list_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.42/5.62 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.42/5.62 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.42/5.62 take_nat: nat > list_nat > list_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oupt,type,
% 5.42/5.62 upt: nat > nat > list_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oupto,type,
% 5.42/5.62 upto: int > int > list_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_List_Oupto__aux,type,
% 5.42/5.62 upto_aux: int > int > list_int > list_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_OSuc,type,
% 5.42/5.62 suc: nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.42/5.62 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.42/5.62 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.42/5.62 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Onat_Opred,type,
% 5.42/5.62 pred: nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 semiri4939895301339042750nteger: nat > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.42/5.62 semiri8010041392384452111omplex: nat > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.42/5.62 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.42/5.62 semiri1314217659103216013at_int: nat > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.42/5.62 semiri1316708129612266289at_nat: nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.42/5.62 semiri681578069525770553at_rat: nat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.42/5.62 semiri5074537144036343181t_real: nat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.42/5.62 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.42/5.62 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.42/5.62 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.42/5.62 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 5.42/5.62 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.42/5.62 size_size_list_o: list_o > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 5.42/5.62 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.42/5.62 size_s3451745648224563538omplex: list_complex > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.42/5.62 size_size_list_int: list_int > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.42/5.62 size_size_list_nat: list_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.42/5.62 size_size_list_num: list_num > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.42/5.62 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.42/5.62 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 5.42/5.62 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.42/5.62 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 5.42/5.62 size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.42/5.62 size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.42/5.62 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.42/5.62 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.42/5.62 size_size_list_real: list_real > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.42/5.62 size_size_num: num > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.42/5.62 size_size_option_nat: option_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
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% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 5.42/5.62 size_size_char: char > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.42/5.62 nat_list_encode: list_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.42/5.62 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.42/5.62 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.42/5.62 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.42/5.62 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.42/5.62 nat_set_decode: nat > set_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.42/5.62 nat_set_encode: set_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.42/5.62 nat_triangle: nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_NthRoot_Oroot,type,
% 5.42/5.62 root: nat > real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_NthRoot_Osqrt,type,
% 5.42/5.62 sqrt: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_OBitM,type,
% 5.42/5.62 bitM: num > num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oinc,type,
% 5.42/5.62 inc: num > num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.42/5.62 neg_numeral_dbl_int: int > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
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% 5.42/5.62
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% 5.42/5.62 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.42/5.62 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.42/5.62 neg_nu8557863876264182079omplex: complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onum_OBit0,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onum_OBit1,type,
% 5.42/5.62 bit1: num > num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onum_OOne,type,
% 5.42/5.62 one: num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onum_Osize__num,type,
% 5.42/5.62 size_num: num > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onum__of__nat,type,
% 5.42/5.62 num_of_nat: nat > num ).
% 5.42/5.62
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% 5.42/5.62 numera6620942414471956472nteger: num > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.42/5.62 numera6690914467698888265omplex: num > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 5.42/5.62 numera1916890842035813515d_enat: num > extended_enat ).
% 5.42/5.62
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
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% 5.42/5.62
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Option_Ooption_Osize__option_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
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% 5.42/5.62 thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
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% 5.42/5.62 thf(sy_c_Order__Relation_OunderS_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.42/5.62 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 5.42/5.62 produc7828578312038201481er_o_o: ( code_integer > $o > $o ) > produc6271795597528267376eger_o > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.42/5.62 produc1043322548047392435omplex: ( code_integer > $o > set_complex ) > produc6271795597528267376eger_o > set_complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
% 5.42/5.62 produc1253318751659547953et_int: ( code_integer > $o > set_int ) > produc6271795597528267376eger_o > set_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.42/5.62 produc5431169771168744661et_nat: ( code_integer > $o > set_nat ) > produc6271795597528267376eger_o > set_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.42/5.62 produc242741666403216561t_real: ( code_integer > $o > set_real ) > produc6271795597528267376eger_o > set_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.42/5.62 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.42/5.62 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.42/5.62 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.42/5.62 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.42/5.62 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 5.42/5.62 produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.42/5.62 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.42/5.62 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.42/5.62 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.42/5.62 produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 5.42/5.62 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.42/5.62
% 5.42/5.62 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,
% 5.42/5.62 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.42/5.62 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.42/5.62 produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001_Eo,type,
% 5.42/5.62 produc4927758841916487424_num_o: ( nat > num > $o ) > product_prod_nat_num > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.42/5.62 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.42/5.62 produc6231982587499038204omplex: ( nat > num > set_complex ) > product_prod_nat_num > set_complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.42/5.62 produc1435849484188172666t_real: ( nat > num > set_real ) > product_prod_nat_num > set_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001_Eo,type,
% 5.42/5.62 produc5703948589228662326_num_o: ( num > num > $o ) > product_prod_num_num > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.42/5.62 produc2866383454006189126omplex: ( num > num > set_complex ) > product_prod_num_num > set_complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Int__Oint_J,type,
% 5.42/5.62 produc6406642877701697732et_int: ( num > num > set_int ) > product_prod_num_num > set_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.42/5.62 produc1361121860356118632et_nat: ( num > num > set_nat ) > product_prod_num_num > set_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.42/5.62 produc8296048397933160132t_real: ( num > num > set_real ) > product_prod_num_num > set_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 5.42/5.62 produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ofst_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.42/5.62 product_fst_int_int: product_prod_int_int > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.42/5.62 product_snd_int_int: product_prod_int_int > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rat_OFract,type,
% 5.42/5.62 fract: int > int > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rat_OFrct,type,
% 5.42/5.62 frct: product_prod_int_int > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rat_ORep__Rat,type,
% 5.42/5.62 rep_Rat: rat > product_prod_int_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.42/5.62 field_5140801741446780682s_real: set_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 5.42/5.62 field_7254667332652039916t_real: rat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rat_Onormalize,type,
% 5.42/5.62 normalize: product_prod_int_int > product_prod_int_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rat_Opositive,type,
% 5.42/5.62 positive: rat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rat_Oquotient__of,type,
% 5.42/5.62 quotient_of: rat > product_prod_int_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real_OReal,type,
% 5.42/5.62 real2: ( nat > rat ) > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real_Ocauchy,type,
% 5.42/5.62 cauchy: ( nat > rat ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real_Opositive,type,
% 5.42/5.62 positive2: real > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real_Orealrel,type,
% 5.42/5.62 realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real_Orep__real,type,
% 5.42/5.62 rep_real: real > nat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real_Ovanishes,type,
% 5.42/5.62 vanishes: ( nat > rat ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.42/5.62 real_V2521375963428798218omplex: set_complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.42/5.62 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 5.42/5.62 real_V3694042436643373181omplex: complex > complex > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 5.42/5.62 real_V975177566351809787t_real: real > real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.42/5.62 real_V1022390504157884413omplex: complex > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.42/5.62 real_V7735802525324610683m_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.42/5.62 real_V4546457046886955230omplex: real > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 5.42/5.62 real_V1803761363581548252l_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 5.42/5.62 real_V2046097035970521341omplex: real > complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 5.42/5.62 real_V1485227260804924795R_real: real > real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Relation_OField_001t__Nat__Onat,type,
% 5.42/5.62 field_nat: set_Pr1261947904930325089at_nat > set_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Relation_OId_001t__Nat__Onat,type,
% 5.42/5.62 id_nat2: set_Pr1261947904930325089at_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
% 5.42/5.62 algebr932160517623751201me_int: int > int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
% 5.42/5.62 algebr934650988132801477me_nat: nat > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.42/5.62 divide1717551699836669952omplex: complex > complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.42/5.62 divide_divide_int: int > int > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.42/5.62 divide_divide_nat: nat > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.42/5.62 divide_divide_rat: rat > rat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.42/5.62 divide_divide_real: real > real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.42/5.62 dvd_dvd_complex: complex > complex > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.42/5.62 dvd_dvd_int: int > int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.42/5.62 dvd_dvd_nat: nat > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.42/5.62 dvd_dvd_rat: rat > rat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.42/5.62 dvd_dvd_real: real > real > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.42/5.62 modulo_modulo_int: int > int > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.42/5.62 modulo_modulo_nat: nat > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 zero_n356916108424825756nteger: $o > code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.42/5.62 zero_n1201886186963655149omplex: $o > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.42/5.62 zero_n2684676970156552555ol_int: $o > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.42/5.62 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.42/5.62 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.42/5.62 zero_n3304061248610475627l_real: $o > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.42/5.62 suminf_complex: ( nat > complex ) > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 5.42/5.62 suminf_int: ( nat > int ) > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 5.42/5.62 suminf_nat: ( nat > nat ) > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.42/5.62 suminf_real: ( nat > real ) > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 5.42/5.62 summable_complex: ( nat > complex ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 5.42/5.62 summable_int: ( nat > int ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 5.42/5.62 summable_nat: ( nat > nat ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.42/5.62 summable_real: ( nat > real ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 5.42/5.62 sums_complex: ( nat > complex ) > complex > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 5.42/5.62 sums_int: ( nat > int ) > int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 5.42/5.62 sums_nat: ( nat > nat ) > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.42/5.62 sums_real: ( nat > real ) > real > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 5.42/5.62 collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.42/5.62 collect_complex: ( complex > $o ) > set_complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 5.42/5.62 collect_int: ( int > $o ) > set_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 5.42/5.62 collect_list_o: ( list_o > $o ) > set_list_o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.42/5.62 collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 5.42/5.62 collect_list_int: ( list_int > $o ) > set_list_int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.42/5.62 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.42/5.62 collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 5.42/5.62 collect_nat: ( nat > $o ) > set_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Num__Onum,type,
% 5.42/5.62 collect_num: ( num > $o ) > set_num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.42/5.62 collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).
% 5.42/5.62
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% 5.42/5.62 collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
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% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 5.42/5.62 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.42/5.62 vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
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% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
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% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
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% 5.42/5.62 thf(sy_c_String_Ochar_OChar,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
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% 5.42/5.62
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% 5.42/5.62 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
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% 5.42/5.62 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
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% 5.42/5.62
% 5.42/5.62 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.42/5.62 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 5.42/5.62 topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 5.42/5.62 topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Oarccos,type,
% 5.42/5.62 arccos: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.42/5.62 arcosh_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Oarcsin,type,
% 5.42/5.62 arcsin: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Oarctan,type,
% 5.42/5.62 arctan: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.42/5.62 arsinh_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.42/5.62 artanh_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.42/5.62 cos_complex: complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.42/5.62 cos_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.42/5.62 cos_coeff: nat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.42/5.62 cosh_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.42/5.62 cot_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.42/5.62 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.42/5.62 diffs_int: ( nat > int ) > nat > int ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Odiffs_001t__Rat__Orat,type,
% 5.42/5.62 diffs_rat: ( nat > rat ) > nat > rat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.42/5.62 diffs_real: ( nat > real ) > nat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.42/5.62 exp_complex: complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.42/5.62 exp_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.42/5.62 ln_ln_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Olog,type,
% 5.42/5.62 log: real > real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Opi,type,
% 5.42/5.62 pi: real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.42/5.62 powr_real: real > real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.42/5.62 sin_complex: complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.42/5.62 sin_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.42/5.62 sin_coeff: nat > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.42/5.62 sinh_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.42/5.62 tan_complex: complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.42/5.62 tan_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.42/5.62 tanh_complex: complex > complex ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.42/5.62 tanh_real: real > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.42/5.62 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.42/5.62 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t,type,
% 5.42/5.62 vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H,type,
% 5.42/5.62 vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H__rel,type,
% 5.42/5.62 vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t__rel,type,
% 5.42/5.62 vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 5.42/5.62 vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t__rel,type,
% 5.42/5.62 vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 5.42/5.62 vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 5.42/5.62 vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 5.42/5.62 vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 5.42/5.62 vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l,type,
% 5.42/5.62 vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l__rel,type,
% 5.42/5.62 vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 5.42/5.62 vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 5.42/5.62 vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.42/5.62 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.42/5.62 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.42/5.62 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.42/5.62 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.42/5.62 vEBT_VEBT_high: nat > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.42/5.62 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.42/5.62 vEBT_VEBT_low: nat > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.42/5.62 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.42/5.62 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.42/5.62 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.42/5.62 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.42/5.62 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.42/5.62 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.42/5.62 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.42/5.62 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.42/5.62 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.42/5.62 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 5.42/5.62 vEBT_VEBT_height: vEBT_VEBT > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 5.42/5.62 vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.42/5.62 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.42/5.62 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.42/5.62 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.42/5.62 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.42/5.62 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.42/5.62 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.42/5.62 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.42/5.62 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.42/5.62 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.42/5.62 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.42/5.62 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.42/5.62 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.42/5.62 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.42/5.62 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.42/5.62 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.42/5.62 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.42/5.62 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.42/5.62 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.42/5.62 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.42/5.62 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.42/5.62 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.42/5.62 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.42/5.62 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.42/5.62 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.42/5.62 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 5.42/5.62 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 5.42/5.62 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 5.42/5.62 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.42/5.62 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.42/5.62 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.42/5.62 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.42/5.62 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.42/5.62 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.42/5.62 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 5.42/5.62 wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.42/5.62 fChoice_real: ( real > $o ) > real ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001_Eo,type,
% 5.42/5.62 member_o: $o > set_o > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.42/5.62 member_complex: complex > set_complex > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__Int__Oint,type,
% 5.42/5.62 member_int: int > set_int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.42/5.62 member_list_o: list_o > set_list_o > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.42/5.62 member_list_int: list_int > set_list_int > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.42/5.62 member_list_nat: list_nat > set_list_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.42/5.62 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__Nat__Onat,type,
% 5.42/5.62 member_nat: nat > set_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__Num__Onum,type,
% 5.42/5.62 member_num: num > set_num > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.42/5.62 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__Rat__Orat,type,
% 5.42/5.62 member_rat: rat > set_rat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__Real__Oreal,type,
% 5.42/5.62 member_real: real > set_real > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.42/5.62 member_set_nat: set_nat > set_set_nat > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.42/5.62 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.42/5.62
% 5.42/5.62 thf(sy_v_deg____,type,
% 5.42/5.62 deg: nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_v_m____,type,
% 5.42/5.62 m: nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_v_ma____,type,
% 5.42/5.62 ma: nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_v_mi____,type,
% 5.42/5.62 mi: nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_v_na____,type,
% 5.42/5.62 na: nat ).
% 5.42/5.62
% 5.42/5.62 thf(sy_v_summary____,type,
% 5.42/5.62 summary: vEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_v_treeList____,type,
% 5.42/5.62 treeList: list_VEBT_VEBT ).
% 5.42/5.62
% 5.42/5.62 thf(sy_v_xa____,type,
% 5.42/5.62 xa: nat ).
% 5.42/5.62
% 5.42/5.62 % Relevant facts (10212)
% 5.42/5.62 thf(fact_0_False,axiom,
% 5.42/5.62 ~ ( ord_less_nat @ xa @ mi ) ).
% 5.42/5.62
% 5.42/5.62 % False
% 5.42/5.62 thf(fact_1__C5_Ohyps_C_I7_J,axiom,
% 5.42/5.62 ord_less_eq_nat @ mi @ ma ).
% 5.42/5.62
% 5.42/5.62 % "5.hyps"(7)
% 5.42/5.62 thf(fact_2_max__in__set__def,axiom,
% 5.42/5.62 ( vEBT_VEBT_max_in_set
% 5.42/5.62 = ( ^ [Xs: set_nat,X: nat] :
% 5.42/5.62 ( ( member_nat @ X @ Xs )
% 5.42/5.62 & ! [Y: nat] :
% 5.42/5.62 ( ( member_nat @ Y @ Xs )
% 5.42/5.62 => ( ord_less_eq_nat @ Y @ X ) ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % max_in_set_def
% 5.42/5.62 thf(fact_3_min__in__set__def,axiom,
% 5.42/5.62 ( vEBT_VEBT_min_in_set
% 5.42/5.62 = ( ^ [Xs: set_nat,X: nat] :
% 5.42/5.62 ( ( member_nat @ X @ Xs )
% 5.42/5.62 & ! [Y: nat] :
% 5.42/5.62 ( ( member_nat @ Y @ Xs )
% 5.42/5.62 => ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % min_in_set_def
% 5.42/5.62 thf(fact_4__C5_OIH_C_I2_J,axiom,
% 5.42/5.62 ! [X2: nat] : ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ summary @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ summary ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % "5.IH"(2)
% 5.42/5.62 thf(fact_5_height__compose__summary,axiom,
% 5.42/5.62 ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % height_compose_summary
% 5.42/5.62 thf(fact_6__092_060open_0622_A_092_060le_062_Adeg_092_060close_062,axiom,
% 5.42/5.62 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.42/5.62
% 5.42/5.62 % \<open>2 \<le> deg\<close>
% 5.42/5.62 thf(fact_7__092_060open_062T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ax_A_092_060le_062_A23_A_L_AT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Asummary_A_Ihigh_A_Iif_Ax_A_060_Ami_Athen_Ami_Aelse_Ax_J_A_Ideg_Adiv_A2_J_J_092_060close_062,axiom,
% 5.42/5.62 ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % \<open>T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t (Node (Some (mi, ma)) deg treeList summary) x \<le> 23 + T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t summary (high (if x < mi then mi else x) (deg div 2))\<close>
% 5.42/5.62 thf(fact_8__C5_Ohyps_C_I8_J,axiom,
% 5.42/5.62 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.42/5.62
% 5.42/5.62 % "5.hyps"(8)
% 5.42/5.62 thf(fact_9_insert__simp__mima,axiom,
% 5.42/5.62 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.42/5.62 ( ( ( X2 = Mi )
% 5.42/5.62 | ( X2 = Ma ) )
% 5.42/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.62 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % insert_simp_mima
% 5.42/5.62 thf(fact_10_one__add__one,axiom,
% 5.42/5.62 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.42/5.62 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_add_one
% 5.42/5.62 thf(fact_11_one__add__one,axiom,
% 5.42/5.62 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.42/5.62 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_add_one
% 5.42/5.62 thf(fact_12_one__add__one,axiom,
% 5.42/5.62 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.42/5.62 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_add_one
% 5.42/5.62 thf(fact_13_one__add__one,axiom,
% 5.42/5.62 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.42/5.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_add_one
% 5.42/5.62 thf(fact_14_one__add__one,axiom,
% 5.42/5.62 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.42/5.62 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_add_one
% 5.42/5.62 thf(fact_15_numeral__plus__one,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.42/5.62 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_one
% 5.42/5.62 thf(fact_16_numeral__plus__one,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.42/5.62 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_one
% 5.42/5.62 thf(fact_17_numeral__plus__one,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.42/5.62 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_one
% 5.42/5.62 thf(fact_18_numeral__plus__one,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.42/5.62 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_one
% 5.42/5.62 thf(fact_19_numeral__plus__one,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.42/5.62 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_one
% 5.42/5.62 thf(fact_20_one__plus__numeral,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.42/5.62 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral
% 5.42/5.62 thf(fact_21_one__plus__numeral,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.42/5.62 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral
% 5.42/5.62 thf(fact_22_one__plus__numeral,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.42/5.62 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral
% 5.42/5.62 thf(fact_23_one__plus__numeral,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral
% 5.42/5.62 thf(fact_24_one__plus__numeral,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.42/5.62 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral
% 5.42/5.62 thf(fact_25_numeral__le__one__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.42/5.62 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_le_one_iff
% 5.42/5.62 thf(fact_26_numeral__le__one__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.42/5.62 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_le_one_iff
% 5.42/5.62 thf(fact_27_numeral__le__one__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.42/5.62 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_le_one_iff
% 5.42/5.62 thf(fact_28_numeral__le__one__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.42/5.62 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_le_one_iff
% 5.42/5.62 thf(fact_29_numeral__eq__one__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ( numera6690914467698888265omplex @ N )
% 5.42/5.62 = one_one_complex )
% 5.42/5.62 = ( N = one ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_one_iff
% 5.42/5.62 thf(fact_30_numeral__eq__one__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ( numeral_numeral_real @ N )
% 5.42/5.62 = one_one_real )
% 5.42/5.62 = ( N = one ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_one_iff
% 5.42/5.62 thf(fact_31_numeral__eq__one__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ( numeral_numeral_rat @ N )
% 5.42/5.62 = one_one_rat )
% 5.42/5.62 = ( N = one ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_one_iff
% 5.42/5.62 thf(fact_32_numeral__eq__one__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ( numeral_numeral_nat @ N )
% 5.42/5.62 = one_one_nat )
% 5.42/5.62 = ( N = one ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_one_iff
% 5.42/5.62 thf(fact_33_numeral__eq__one__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ( numeral_numeral_int @ N )
% 5.42/5.62 = one_one_int )
% 5.42/5.62 = ( N = one ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_one_iff
% 5.42/5.62 thf(fact_34_one__eq__numeral__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( one_one_complex
% 5.42/5.62 = ( numera6690914467698888265omplex @ N ) )
% 5.42/5.62 = ( one = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_eq_numeral_iff
% 5.42/5.62 thf(fact_35_one__eq__numeral__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( one_one_real
% 5.42/5.62 = ( numeral_numeral_real @ N ) )
% 5.42/5.62 = ( one = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_eq_numeral_iff
% 5.42/5.62 thf(fact_36_one__eq__numeral__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( one_one_rat
% 5.42/5.62 = ( numeral_numeral_rat @ N ) )
% 5.42/5.62 = ( one = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_eq_numeral_iff
% 5.42/5.62 thf(fact_37_one__eq__numeral__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( one_one_nat
% 5.42/5.62 = ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( one = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_eq_numeral_iff
% 5.42/5.62 thf(fact_38_one__eq__numeral__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( one_one_int
% 5.42/5.62 = ( numeral_numeral_int @ N ) )
% 5.42/5.62 = ( one = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_eq_numeral_iff
% 5.42/5.62 thf(fact_39_distrib__left__numeral,axiom,
% 5.42/5.62 ! [V: num,B: complex,C: complex] :
% 5.42/5.62 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.42/5.62 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_left_numeral
% 5.42/5.62 thf(fact_40_distrib__left__numeral,axiom,
% 5.42/5.62 ! [V: num,B: real,C: real] :
% 5.42/5.62 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.42/5.62 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_left_numeral
% 5.42/5.62 thf(fact_41_distrib__left__numeral,axiom,
% 5.42/5.62 ! [V: num,B: rat,C: rat] :
% 5.42/5.62 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.42/5.62 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_left_numeral
% 5.42/5.62 thf(fact_42_distrib__left__numeral,axiom,
% 5.42/5.62 ! [V: num,B: nat,C: nat] :
% 5.42/5.62 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.42/5.62 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_left_numeral
% 5.42/5.62 thf(fact_43_distrib__left__numeral,axiom,
% 5.42/5.62 ! [V: num,B: int,C: int] :
% 5.42/5.62 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.42/5.62 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_left_numeral
% 5.42/5.62 thf(fact_44_distrib__right__numeral,axiom,
% 5.42/5.62 ! [A: complex,B: complex,V: num] :
% 5.42/5.62 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.42/5.62 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_right_numeral
% 5.42/5.62 thf(fact_45_distrib__right__numeral,axiom,
% 5.42/5.62 ! [A: real,B: real,V: num] :
% 5.42/5.62 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.42/5.62 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_right_numeral
% 5.42/5.62 thf(fact_46_distrib__right__numeral,axiom,
% 5.42/5.62 ! [A: rat,B: rat,V: num] :
% 5.42/5.62 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.42/5.62 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_right_numeral
% 5.42/5.62 thf(fact_47_distrib__right__numeral,axiom,
% 5.42/5.62 ! [A: nat,B: nat,V: num] :
% 5.42/5.62 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.42/5.62 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_right_numeral
% 5.42/5.62 thf(fact_48_distrib__right__numeral,axiom,
% 5.42/5.62 ! [A: int,B: int,V: num] :
% 5.42/5.62 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.42/5.62 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % distrib_right_numeral
% 5.42/5.62 thf(fact_49_nat__1__eq__mult__iff,axiom,
% 5.42/5.62 ! [M: nat,N: nat] :
% 5.42/5.62 ( ( one_one_nat
% 5.42/5.62 = ( times_times_nat @ M @ N ) )
% 5.42/5.62 = ( ( M = one_one_nat )
% 5.42/5.62 & ( N = one_one_nat ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_1_eq_mult_iff
% 5.42/5.62 thf(fact_50_nat__mult__eq__1__iff,axiom,
% 5.42/5.62 ! [M: nat,N: nat] :
% 5.42/5.62 ( ( ( times_times_nat @ M @ N )
% 5.42/5.62 = one_one_nat )
% 5.42/5.62 = ( ( M = one_one_nat )
% 5.42/5.62 & ( N = one_one_nat ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_mult_eq_1_iff
% 5.42/5.62 thf(fact_51_numeral__eq__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ( numera6690914467698888265omplex @ M )
% 5.42/5.62 = ( numera6690914467698888265omplex @ N ) )
% 5.42/5.62 = ( M = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_iff
% 5.42/5.62 thf(fact_52_numeral__eq__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ( numeral_numeral_real @ M )
% 5.42/5.62 = ( numeral_numeral_real @ N ) )
% 5.42/5.62 = ( M = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_iff
% 5.42/5.62 thf(fact_53_numeral__eq__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ( numeral_numeral_rat @ M )
% 5.42/5.62 = ( numeral_numeral_rat @ N ) )
% 5.42/5.62 = ( M = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_iff
% 5.42/5.62 thf(fact_54_numeral__eq__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ( numeral_numeral_nat @ M )
% 5.42/5.62 = ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( M = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_iff
% 5.42/5.62 thf(fact_55_numeral__eq__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ( numeral_numeral_int @ M )
% 5.42/5.62 = ( numeral_numeral_int @ N ) )
% 5.42/5.62 = ( M = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_eq_iff
% 5.42/5.62 thf(fact_56_pow__sum,axiom,
% 5.42/5.62 ! [A: nat,B: nat] :
% 5.42/5.62 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.42/5.62 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % pow_sum
% 5.42/5.62 thf(fact_57_high__def,axiom,
% 5.42/5.62 ( vEBT_VEBT_high
% 5.42/5.62 = ( ^ [X: nat,N2: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % high_def
% 5.42/5.62 thf(fact_58_high__bound__aux,axiom,
% 5.42/5.62 ! [Ma: nat,N: nat,M: nat] :
% 5.42/5.62 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.42/5.62 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % high_bound_aux
% 5.42/5.62 thf(fact_59_numeral__less__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.42/5.62 = ( ord_less_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_less_iff
% 5.42/5.62 thf(fact_60_numeral__less__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.42/5.62 = ( ord_less_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_less_iff
% 5.42/5.62 thf(fact_61_numeral__less__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( ord_less_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_less_iff
% 5.42/5.62 thf(fact_62_numeral__less__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.42/5.62 = ( ord_less_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_less_iff
% 5.42/5.62 thf(fact_63_high__inv,axiom,
% 5.42/5.62 ! [X2: nat,N: nat,Y2: nat] :
% 5.42/5.62 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.62 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.42/5.62 = Y2 ) ) ).
% 5.42/5.62
% 5.42/5.62 % high_inv
% 5.42/5.62 thf(fact_64_mult__numeral__left__semiring__numeral,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: complex] :
% 5.42/5.62 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.42/5.62 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_left_semiring_numeral
% 5.42/5.62 thf(fact_65_mult__numeral__left__semiring__numeral,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: real] :
% 5.42/5.62 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.42/5.62 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_left_semiring_numeral
% 5.42/5.62 thf(fact_66_mult__numeral__left__semiring__numeral,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: rat] :
% 5.42/5.62 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.42/5.62 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_left_semiring_numeral
% 5.42/5.62 thf(fact_67_mult__numeral__left__semiring__numeral,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: nat] :
% 5.42/5.62 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.42/5.62 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_left_semiring_numeral
% 5.42/5.62 thf(fact_68_mult__numeral__left__semiring__numeral,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: int] :
% 5.42/5.62 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.42/5.62 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_left_semiring_numeral
% 5.42/5.62 thf(fact_69_numeral__times__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.42/5.62 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_times_numeral
% 5.42/5.62 thf(fact_70_numeral__times__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.42/5.62 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_times_numeral
% 5.42/5.62 thf(fact_71_numeral__times__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.42/5.62 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_times_numeral
% 5.42/5.62 thf(fact_72_numeral__times__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_times_numeral
% 5.42/5.62 thf(fact_73_numeral__times__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.42/5.62 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_times_numeral
% 5.42/5.62 thf(fact_74_num__double,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.42/5.62 = ( bit0 @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % num_double
% 5.42/5.62 thf(fact_75_nat__add__left__cancel__less,axiom,
% 5.42/5.62 ! [K: nat,M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.42/5.62 = ( ord_less_nat @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_add_left_cancel_less
% 5.42/5.62 thf(fact_76_nat__add__left__cancel__le,axiom,
% 5.42/5.62 ! [K: nat,M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.42/5.62 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_add_left_cancel_le
% 5.42/5.62 thf(fact_77_bit__concat__def,axiom,
% 5.42/5.62 ( vEBT_VEBT_bit_concat
% 5.42/5.62 = ( ^ [H: nat,L: nat,D: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D ) ) @ L ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % bit_concat_def
% 5.42/5.62 thf(fact_78_add__numeral__left,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: complex] :
% 5.42/5.62 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.42/5.62 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_numeral_left
% 5.42/5.62 thf(fact_79_add__numeral__left,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: real] :
% 5.42/5.62 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.42/5.62 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_numeral_left
% 5.42/5.62 thf(fact_80_add__numeral__left,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: rat] :
% 5.42/5.62 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.42/5.62 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_numeral_left
% 5.42/5.62 thf(fact_81_add__numeral__left,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: nat] :
% 5.42/5.62 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.42/5.62 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_numeral_left
% 5.42/5.62 thf(fact_82_add__numeral__left,axiom,
% 5.42/5.62 ! [V: num,W: num,Z: int] :
% 5.42/5.62 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.42/5.62 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_numeral_left
% 5.42/5.62 thf(fact_83_numeral__plus__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.42/5.62 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_numeral
% 5.42/5.62 thf(fact_84_numeral__plus__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.42/5.62 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_numeral
% 5.42/5.62 thf(fact_85_numeral__plus__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.42/5.62 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_numeral
% 5.42/5.62 thf(fact_86_numeral__plus__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_numeral
% 5.42/5.62 thf(fact_87_numeral__plus__numeral,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.42/5.62 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_plus_numeral
% 5.42/5.62 thf(fact_88_numeral__le__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.42/5.62 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_le_iff
% 5.42/5.62 thf(fact_89_numeral__le__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.42/5.62 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_le_iff
% 5.42/5.62 thf(fact_90_numeral__le__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_le_iff
% 5.42/5.62 thf(fact_91_numeral__le__iff,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.42/5.62 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_le_iff
% 5.42/5.62 thf(fact_92_one__less__numeral__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.42/5.62 = ( ord_less_num @ one @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_less_numeral_iff
% 5.42/5.62 thf(fact_93_one__less__numeral__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.42/5.62 = ( ord_less_num @ one @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_less_numeral_iff
% 5.42/5.62 thf(fact_94_one__less__numeral__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( ord_less_num @ one @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_less_numeral_iff
% 5.42/5.62 thf(fact_95_one__less__numeral__iff,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.42/5.62 = ( ord_less_num @ one @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_less_numeral_iff
% 5.42/5.62 thf(fact_96_le__divide__eq__numeral1_I1_J,axiom,
% 5.42/5.62 ! [A: real,B: real,W: num] :
% 5.42/5.62 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.42/5.62 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_divide_eq_numeral1(1)
% 5.42/5.62 thf(fact_97_le__divide__eq__numeral1_I1_J,axiom,
% 5.42/5.62 ! [A: rat,B: rat,W: num] :
% 5.42/5.62 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.42/5.62 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_divide_eq_numeral1(1)
% 5.42/5.62 thf(fact_98_divide__le__eq__numeral1_I1_J,axiom,
% 5.42/5.62 ! [B: real,W: num,A: real] :
% 5.42/5.62 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.42/5.62 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % divide_le_eq_numeral1(1)
% 5.42/5.62 thf(fact_99_divide__le__eq__numeral1_I1_J,axiom,
% 5.42/5.62 ! [B: rat,W: num,A: rat] :
% 5.42/5.62 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.42/5.62 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % divide_le_eq_numeral1(1)
% 5.42/5.62 thf(fact_100_less__divide__eq__numeral1_I1_J,axiom,
% 5.42/5.62 ! [A: real,B: real,W: num] :
% 5.42/5.62 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.42/5.62 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % less_divide_eq_numeral1(1)
% 5.42/5.62 thf(fact_101_less__divide__eq__numeral1_I1_J,axiom,
% 5.42/5.62 ! [A: rat,B: rat,W: num] :
% 5.42/5.62 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.42/5.62 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % less_divide_eq_numeral1(1)
% 5.42/5.62 thf(fact_102_divide__less__eq__numeral1_I1_J,axiom,
% 5.42/5.62 ! [B: real,W: num,A: real] :
% 5.42/5.62 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.42/5.62 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % divide_less_eq_numeral1(1)
% 5.42/5.62 thf(fact_103_divide__less__eq__numeral1_I1_J,axiom,
% 5.42/5.62 ! [B: rat,W: num,A: rat] :
% 5.42/5.62 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.42/5.62 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % divide_less_eq_numeral1(1)
% 5.42/5.62 thf(fact_104_nat__neq__iff,axiom,
% 5.42/5.62 ! [M: nat,N: nat] :
% 5.42/5.62 ( ( M != N )
% 5.42/5.62 = ( ( ord_less_nat @ M @ N )
% 5.42/5.62 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_neq_iff
% 5.42/5.62 thf(fact_105_less__not__refl,axiom,
% 5.42/5.62 ! [N: nat] :
% 5.42/5.62 ~ ( ord_less_nat @ N @ N ) ).
% 5.42/5.62
% 5.42/5.62 % less_not_refl
% 5.42/5.62 thf(fact_106_less__not__refl2,axiom,
% 5.42/5.62 ! [N: nat,M: nat] :
% 5.42/5.62 ( ( ord_less_nat @ N @ M )
% 5.42/5.62 => ( M != N ) ) ).
% 5.42/5.62
% 5.42/5.62 % less_not_refl2
% 5.42/5.62 thf(fact_107_less__not__refl3,axiom,
% 5.42/5.62 ! [S: nat,T: nat] :
% 5.42/5.62 ( ( ord_less_nat @ S @ T )
% 5.42/5.62 => ( S != T ) ) ).
% 5.42/5.62
% 5.42/5.62 % less_not_refl3
% 5.42/5.62 thf(fact_108_mem__Collect__eq,axiom,
% 5.42/5.62 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.42/5.62 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 5.42/5.62 = ( P @ A ) ) ).
% 5.42/5.62
% 5.42/5.62 % mem_Collect_eq
% 5.42/5.62 thf(fact_109_mem__Collect__eq,axiom,
% 5.42/5.62 ! [A: complex,P: complex > $o] :
% 5.42/5.62 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.42/5.62 = ( P @ A ) ) ).
% 5.42/5.62
% 5.42/5.62 % mem_Collect_eq
% 5.42/5.62 thf(fact_110_mem__Collect__eq,axiom,
% 5.42/5.62 ! [A: real,P: real > $o] :
% 5.42/5.62 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.42/5.62 = ( P @ A ) ) ).
% 5.42/5.62
% 5.42/5.62 % mem_Collect_eq
% 5.42/5.62 thf(fact_111_mem__Collect__eq,axiom,
% 5.42/5.62 ! [A: list_nat,P: list_nat > $o] :
% 5.42/5.62 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.42/5.62 = ( P @ A ) ) ).
% 5.42/5.62
% 5.42/5.62 % mem_Collect_eq
% 5.42/5.62 thf(fact_112_mem__Collect__eq,axiom,
% 5.42/5.62 ! [A: nat,P: nat > $o] :
% 5.42/5.62 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.42/5.62 = ( P @ A ) ) ).
% 5.42/5.62
% 5.42/5.62 % mem_Collect_eq
% 5.42/5.62 thf(fact_113_mem__Collect__eq,axiom,
% 5.42/5.62 ! [A: int,P: int > $o] :
% 5.42/5.62 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.42/5.62 = ( P @ A ) ) ).
% 5.42/5.62
% 5.42/5.62 % mem_Collect_eq
% 5.42/5.62 thf(fact_114_Collect__mem__eq,axiom,
% 5.42/5.62 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.42/5.62 ( ( collec3392354462482085612at_nat
% 5.42/5.62 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A2 ) )
% 5.42/5.62 = A2 ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_mem_eq
% 5.42/5.62 thf(fact_115_Collect__mem__eq,axiom,
% 5.42/5.62 ! [A2: set_complex] :
% 5.42/5.62 ( ( collect_complex
% 5.42/5.62 @ ^ [X: complex] : ( member_complex @ X @ A2 ) )
% 5.42/5.62 = A2 ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_mem_eq
% 5.42/5.62 thf(fact_116_Collect__mem__eq,axiom,
% 5.42/5.62 ! [A2: set_real] :
% 5.42/5.62 ( ( collect_real
% 5.42/5.62 @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 5.42/5.62 = A2 ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_mem_eq
% 5.42/5.62 thf(fact_117_Collect__mem__eq,axiom,
% 5.42/5.62 ! [A2: set_list_nat] :
% 5.42/5.62 ( ( collect_list_nat
% 5.42/5.62 @ ^ [X: list_nat] : ( member_list_nat @ X @ A2 ) )
% 5.42/5.62 = A2 ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_mem_eq
% 5.42/5.62 thf(fact_118_Collect__mem__eq,axiom,
% 5.42/5.62 ! [A2: set_nat] :
% 5.42/5.62 ( ( collect_nat
% 5.42/5.62 @ ^ [X: nat] : ( member_nat @ X @ A2 ) )
% 5.42/5.62 = A2 ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_mem_eq
% 5.42/5.62 thf(fact_119_Collect__mem__eq,axiom,
% 5.42/5.62 ! [A2: set_int] :
% 5.42/5.62 ( ( collect_int
% 5.42/5.62 @ ^ [X: int] : ( member_int @ X @ A2 ) )
% 5.42/5.62 = A2 ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_mem_eq
% 5.42/5.62 thf(fact_120_Collect__cong,axiom,
% 5.42/5.62 ! [P: complex > $o,Q: complex > $o] :
% 5.42/5.62 ( ! [X3: complex] :
% 5.42/5.62 ( ( P @ X3 )
% 5.42/5.62 = ( Q @ X3 ) )
% 5.42/5.62 => ( ( collect_complex @ P )
% 5.42/5.62 = ( collect_complex @ Q ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_cong
% 5.42/5.62 thf(fact_121_Collect__cong,axiom,
% 5.42/5.62 ! [P: real > $o,Q: real > $o] :
% 5.42/5.62 ( ! [X3: real] :
% 5.42/5.62 ( ( P @ X3 )
% 5.42/5.62 = ( Q @ X3 ) )
% 5.42/5.62 => ( ( collect_real @ P )
% 5.42/5.62 = ( collect_real @ Q ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_cong
% 5.42/5.62 thf(fact_122_Collect__cong,axiom,
% 5.42/5.62 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.42/5.62 ( ! [X3: list_nat] :
% 5.42/5.62 ( ( P @ X3 )
% 5.42/5.62 = ( Q @ X3 ) )
% 5.42/5.62 => ( ( collect_list_nat @ P )
% 5.42/5.62 = ( collect_list_nat @ Q ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_cong
% 5.42/5.62 thf(fact_123_Collect__cong,axiom,
% 5.42/5.62 ! [P: nat > $o,Q: nat > $o] :
% 5.42/5.62 ( ! [X3: nat] :
% 5.42/5.62 ( ( P @ X3 )
% 5.42/5.62 = ( Q @ X3 ) )
% 5.42/5.62 => ( ( collect_nat @ P )
% 5.42/5.62 = ( collect_nat @ Q ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_cong
% 5.42/5.62 thf(fact_124_Collect__cong,axiom,
% 5.42/5.62 ! [P: int > $o,Q: int > $o] :
% 5.42/5.62 ( ! [X3: int] :
% 5.42/5.62 ( ( P @ X3 )
% 5.42/5.62 = ( Q @ X3 ) )
% 5.42/5.62 => ( ( collect_int @ P )
% 5.42/5.62 = ( collect_int @ Q ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % Collect_cong
% 5.42/5.62 thf(fact_125_less__irrefl__nat,axiom,
% 5.42/5.62 ! [N: nat] :
% 5.42/5.62 ~ ( ord_less_nat @ N @ N ) ).
% 5.42/5.62
% 5.42/5.62 % less_irrefl_nat
% 5.42/5.62 thf(fact_126_nat__less__induct,axiom,
% 5.42/5.62 ! [P: nat > $o,N: nat] :
% 5.42/5.62 ( ! [N3: nat] :
% 5.42/5.62 ( ! [M2: nat] :
% 5.42/5.62 ( ( ord_less_nat @ M2 @ N3 )
% 5.42/5.62 => ( P @ M2 ) )
% 5.42/5.62 => ( P @ N3 ) )
% 5.42/5.62 => ( P @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_less_induct
% 5.42/5.62 thf(fact_127_infinite__descent,axiom,
% 5.42/5.62 ! [P: nat > $o,N: nat] :
% 5.42/5.62 ( ! [N3: nat] :
% 5.42/5.62 ( ~ ( P @ N3 )
% 5.42/5.62 => ? [M2: nat] :
% 5.42/5.62 ( ( ord_less_nat @ M2 @ N3 )
% 5.42/5.62 & ~ ( P @ M2 ) ) )
% 5.42/5.62 => ( P @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % infinite_descent
% 5.42/5.62 thf(fact_128_linorder__neqE__nat,axiom,
% 5.42/5.62 ! [X2: nat,Y2: nat] :
% 5.42/5.62 ( ( X2 != Y2 )
% 5.42/5.62 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 5.42/5.62 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % linorder_neqE_nat
% 5.42/5.62 thf(fact_129_add__One__commute,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_num @ one @ N )
% 5.42/5.62 = ( plus_plus_num @ N @ one ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_One_commute
% 5.42/5.62 thf(fact_130_le__num__One__iff,axiom,
% 5.42/5.62 ! [X2: num] :
% 5.42/5.62 ( ( ord_less_eq_num @ X2 @ one )
% 5.42/5.62 = ( X2 = one ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_num_One_iff
% 5.42/5.62 thf(fact_131_less__numeral__extra_I4_J,axiom,
% 5.42/5.62 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.42/5.62
% 5.42/5.62 % less_numeral_extra(4)
% 5.42/5.62 thf(fact_132_less__numeral__extra_I4_J,axiom,
% 5.42/5.62 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.42/5.62
% 5.42/5.62 % less_numeral_extra(4)
% 5.42/5.62 thf(fact_133_less__numeral__extra_I4_J,axiom,
% 5.42/5.62 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.42/5.62
% 5.42/5.62 % less_numeral_extra(4)
% 5.42/5.62 thf(fact_134_less__numeral__extra_I4_J,axiom,
% 5.42/5.62 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.42/5.62
% 5.42/5.62 % less_numeral_extra(4)
% 5.42/5.62 thf(fact_135_less__mono__imp__le__mono,axiom,
% 5.42/5.62 ! [F: nat > nat,I: nat,J: nat] :
% 5.42/5.62 ( ! [I2: nat,J2: nat] :
% 5.42/5.62 ( ( ord_less_nat @ I2 @ J2 )
% 5.42/5.62 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 5.42/5.62 => ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.62 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % less_mono_imp_le_mono
% 5.42/5.62 thf(fact_136_le__neq__implies__less,axiom,
% 5.42/5.62 ! [M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.62 => ( ( M != N )
% 5.42/5.62 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_neq_implies_less
% 5.42/5.62 thf(fact_137_less__or__eq__imp__le,axiom,
% 5.42/5.62 ! [M: nat,N: nat] :
% 5.42/5.62 ( ( ( ord_less_nat @ M @ N )
% 5.42/5.62 | ( M = N ) )
% 5.42/5.62 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % less_or_eq_imp_le
% 5.42/5.62 thf(fact_138_le__eq__less__or__eq,axiom,
% 5.42/5.62 ( ord_less_eq_nat
% 5.42/5.62 = ( ^ [M3: nat,N2: nat] :
% 5.42/5.62 ( ( ord_less_nat @ M3 @ N2 )
% 5.42/5.62 | ( M3 = N2 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_eq_less_or_eq
% 5.42/5.62 thf(fact_139_less__imp__le__nat,axiom,
% 5.42/5.62 ! [M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_nat @ M @ N )
% 5.42/5.62 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % less_imp_le_nat
% 5.42/5.62 thf(fact_140_nat__less__le,axiom,
% 5.42/5.62 ( ord_less_nat
% 5.42/5.62 = ( ^ [M3: nat,N2: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.42/5.62 & ( M3 != N2 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_less_le
% 5.42/5.62 thf(fact_141_less__add__eq__less,axiom,
% 5.42/5.62 ! [K: nat,L2: nat,M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_nat @ K @ L2 )
% 5.42/5.62 => ( ( ( plus_plus_nat @ M @ L2 )
% 5.42/5.62 = ( plus_plus_nat @ K @ N ) )
% 5.42/5.62 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % less_add_eq_less
% 5.42/5.62 thf(fact_142_trans__less__add2,axiom,
% 5.42/5.62 ! [I: nat,J: nat,M: nat] :
% 5.42/5.62 ( ( ord_less_nat @ I @ J )
% 5.42/5.62 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % trans_less_add2
% 5.42/5.62 thf(fact_143_trans__less__add1,axiom,
% 5.42/5.62 ! [I: nat,J: nat,M: nat] :
% 5.42/5.62 ( ( ord_less_nat @ I @ J )
% 5.42/5.62 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % trans_less_add1
% 5.42/5.62 thf(fact_144_add__less__mono1,axiom,
% 5.42/5.62 ! [I: nat,J: nat,K: nat] :
% 5.42/5.62 ( ( ord_less_nat @ I @ J )
% 5.42/5.62 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_less_mono1
% 5.42/5.62 thf(fact_145_not__add__less2,axiom,
% 5.42/5.62 ! [J: nat,I: nat] :
% 5.42/5.62 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 5.42/5.62
% 5.42/5.62 % not_add_less2
% 5.42/5.62 thf(fact_146_not__add__less1,axiom,
% 5.42/5.62 ! [I: nat,J: nat] :
% 5.42/5.62 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 5.42/5.62
% 5.42/5.62 % not_add_less1
% 5.42/5.62 thf(fact_147_add__less__mono,axiom,
% 5.42/5.62 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.62 ( ( ord_less_nat @ I @ J )
% 5.42/5.62 => ( ( ord_less_nat @ K @ L2 )
% 5.42/5.62 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_less_mono
% 5.42/5.62 thf(fact_148_add__lessD1,axiom,
% 5.42/5.62 ! [I: nat,J: nat,K: nat] :
% 5.42/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.42/5.62 => ( ord_less_nat @ I @ K ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_lessD1
% 5.42/5.62 thf(fact_149_is__num__normalize_I1_J,axiom,
% 5.42/5.62 ! [A: real,B: real,C: real] :
% 5.42/5.62 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.42/5.62 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % is_num_normalize(1)
% 5.42/5.62 thf(fact_150_is__num__normalize_I1_J,axiom,
% 5.42/5.62 ! [A: rat,B: rat,C: rat] :
% 5.42/5.62 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.42/5.62 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % is_num_normalize(1)
% 5.42/5.62 thf(fact_151_is__num__normalize_I1_J,axiom,
% 5.42/5.62 ! [A: int,B: int,C: int] :
% 5.42/5.62 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.42/5.62 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % is_num_normalize(1)
% 5.42/5.62 thf(fact_152_Nat_Oex__has__greatest__nat,axiom,
% 5.42/5.62 ! [P: nat > $o,K: nat,B: nat] :
% 5.42/5.62 ( ( P @ K )
% 5.42/5.62 => ( ! [Y3: nat] :
% 5.42/5.62 ( ( P @ Y3 )
% 5.42/5.62 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.42/5.62 => ? [X3: nat] :
% 5.42/5.62 ( ( P @ X3 )
% 5.42/5.62 & ! [Y4: nat] :
% 5.42/5.62 ( ( P @ Y4 )
% 5.42/5.62 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % Nat.ex_has_greatest_nat
% 5.42/5.62 thf(fact_153_nat__le__linear,axiom,
% 5.42/5.62 ! [M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.62 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_le_linear
% 5.42/5.62 thf(fact_154_le__antisym,axiom,
% 5.42/5.62 ! [M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.62 => ( ( ord_less_eq_nat @ N @ M )
% 5.42/5.62 => ( M = N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_antisym
% 5.42/5.62 thf(fact_155_eq__imp__le,axiom,
% 5.42/5.62 ! [M: nat,N: nat] :
% 5.42/5.62 ( ( M = N )
% 5.42/5.62 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % eq_imp_le
% 5.42/5.62 thf(fact_156_le__trans,axiom,
% 5.42/5.62 ! [I: nat,J: nat,K: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.62 => ( ( ord_less_eq_nat @ J @ K )
% 5.42/5.62 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_trans
% 5.42/5.62 thf(fact_157_le__refl,axiom,
% 5.42/5.62 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.42/5.62
% 5.42/5.62 % le_refl
% 5.42/5.62 thf(fact_158_divide__numeral__1,axiom,
% 5.42/5.62 ! [A: complex] :
% 5.42/5.62 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % divide_numeral_1
% 5.42/5.62 thf(fact_159_divide__numeral__1,axiom,
% 5.42/5.62 ! [A: real] :
% 5.42/5.62 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % divide_numeral_1
% 5.42/5.62 thf(fact_160_divide__numeral__1,axiom,
% 5.42/5.62 ! [A: rat] :
% 5.42/5.62 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % divide_numeral_1
% 5.42/5.62 thf(fact_161_not__numeral__less__one,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.42/5.62
% 5.42/5.62 % not_numeral_less_one
% 5.42/5.62 thf(fact_162_not__numeral__less__one,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.42/5.62
% 5.42/5.62 % not_numeral_less_one
% 5.42/5.62 thf(fact_163_not__numeral__less__one,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.42/5.62
% 5.42/5.62 % not_numeral_less_one
% 5.42/5.62 thf(fact_164_not__numeral__less__one,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.42/5.62
% 5.42/5.62 % not_numeral_less_one
% 5.42/5.62 thf(fact_165_mono__nat__linear__lb,axiom,
% 5.42/5.62 ! [F: nat > nat,M: nat,K: nat] :
% 5.42/5.62 ( ! [M4: nat,N3: nat] :
% 5.42/5.62 ( ( ord_less_nat @ M4 @ N3 )
% 5.42/5.62 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 5.42/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % mono_nat_linear_lb
% 5.42/5.62 thf(fact_166_le__numeral__extra_I4_J,axiom,
% 5.42/5.62 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.42/5.62
% 5.42/5.62 % le_numeral_extra(4)
% 5.42/5.62 thf(fact_167_le__numeral__extra_I4_J,axiom,
% 5.42/5.62 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.42/5.62
% 5.42/5.62 % le_numeral_extra(4)
% 5.42/5.62 thf(fact_168_le__numeral__extra_I4_J,axiom,
% 5.42/5.62 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.42/5.62
% 5.42/5.62 % le_numeral_extra(4)
% 5.42/5.62 thf(fact_169_le__numeral__extra_I4_J,axiom,
% 5.42/5.62 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.42/5.62
% 5.42/5.62 % le_numeral_extra(4)
% 5.42/5.62 thf(fact_170_nat__le__iff__add,axiom,
% 5.42/5.62 ( ord_less_eq_nat
% 5.42/5.62 = ( ^ [M3: nat,N2: nat] :
% 5.42/5.62 ? [K2: nat] :
% 5.42/5.62 ( N2
% 5.42/5.62 = ( plus_plus_nat @ M3 @ K2 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_le_iff_add
% 5.42/5.62 thf(fact_171_trans__le__add2,axiom,
% 5.42/5.62 ! [I: nat,J: nat,M: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.62 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % trans_le_add2
% 5.42/5.62 thf(fact_172_trans__le__add1,axiom,
% 5.42/5.62 ! [I: nat,J: nat,M: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.62 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % trans_le_add1
% 5.42/5.62 thf(fact_173_add__le__mono1,axiom,
% 5.42/5.62 ! [I: nat,J: nat,K: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_le_mono1
% 5.42/5.62 thf(fact_174_add__le__mono,axiom,
% 5.42/5.62 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.62 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.42/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_le_mono
% 5.42/5.62 thf(fact_175_le__Suc__ex,axiom,
% 5.42/5.62 ! [K: nat,L2: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ K @ L2 )
% 5.42/5.62 => ? [N3: nat] :
% 5.42/5.62 ( L2
% 5.42/5.62 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_Suc_ex
% 5.42/5.62 thf(fact_176_add__leD2,axiom,
% 5.42/5.62 ! [M: nat,K: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.42/5.62 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_leD2
% 5.42/5.62 thf(fact_177_add__leD1,axiom,
% 5.42/5.62 ! [M: nat,K: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.42/5.62 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_leD1
% 5.42/5.62 thf(fact_178_le__add2,axiom,
% 5.42/5.62 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_add2
% 5.42/5.62 thf(fact_179_le__add1,axiom,
% 5.42/5.62 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_add1
% 5.42/5.62 thf(fact_180_add__leE,axiom,
% 5.42/5.62 ! [M: nat,K: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.42/5.62 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.62 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_leE
% 5.42/5.62 thf(fact_181_mult__le__mono2,axiom,
% 5.42/5.62 ! [I: nat,J: nat,K: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.62 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_le_mono2
% 5.42/5.62 thf(fact_182_mult__le__mono1,axiom,
% 5.42/5.62 ! [I: nat,J: nat,K: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.62 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_le_mono1
% 5.42/5.62 thf(fact_183_mult__le__mono,axiom,
% 5.42/5.62 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.62 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.42/5.62 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_le_mono
% 5.42/5.62 thf(fact_184_le__square,axiom,
% 5.42/5.62 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_square
% 5.42/5.62 thf(fact_185_le__cube,axiom,
% 5.42/5.62 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % le_cube
% 5.42/5.62 thf(fact_186_add__mult__distrib2,axiom,
% 5.42/5.62 ! [K: nat,M: nat,N: nat] :
% 5.42/5.62 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.42/5.62 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_mult_distrib2
% 5.42/5.62 thf(fact_187_add__mult__distrib,axiom,
% 5.42/5.62 ! [M: nat,N: nat,K: nat] :
% 5.42/5.62 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.42/5.62 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % add_mult_distrib
% 5.42/5.62 thf(fact_188_nat__mult__1__right,axiom,
% 5.42/5.62 ! [N: nat] :
% 5.42/5.62 ( ( times_times_nat @ N @ one_one_nat )
% 5.42/5.62 = N ) ).
% 5.42/5.62
% 5.42/5.62 % nat_mult_1_right
% 5.42/5.62 thf(fact_189_nat__mult__1,axiom,
% 5.42/5.62 ! [N: nat] :
% 5.42/5.62 ( ( times_times_nat @ one_one_nat @ N )
% 5.42/5.62 = N ) ).
% 5.42/5.62
% 5.42/5.62 % nat_mult_1
% 5.42/5.62 thf(fact_190_one__le__numeral,axiom,
% 5.42/5.62 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_le_numeral
% 5.42/5.62 thf(fact_191_one__le__numeral,axiom,
% 5.42/5.62 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_le_numeral
% 5.42/5.62 thf(fact_192_one__le__numeral,axiom,
% 5.42/5.62 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_le_numeral
% 5.42/5.62 thf(fact_193_one__le__numeral,axiom,
% 5.42/5.62 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_le_numeral
% 5.42/5.62 thf(fact_194_mult__numeral__1__right,axiom,
% 5.42/5.62 ! [A: complex] :
% 5.42/5.62 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1_right
% 5.42/5.62 thf(fact_195_mult__numeral__1__right,axiom,
% 5.42/5.62 ! [A: real] :
% 5.42/5.62 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1_right
% 5.42/5.62 thf(fact_196_mult__numeral__1__right,axiom,
% 5.42/5.62 ! [A: rat] :
% 5.42/5.62 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1_right
% 5.42/5.62 thf(fact_197_mult__numeral__1__right,axiom,
% 5.42/5.62 ! [A: nat] :
% 5.42/5.62 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1_right
% 5.42/5.62 thf(fact_198_mult__numeral__1__right,axiom,
% 5.42/5.62 ! [A: int] :
% 5.42/5.62 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1_right
% 5.42/5.62 thf(fact_199_mult__numeral__1,axiom,
% 5.42/5.62 ! [A: complex] :
% 5.42/5.62 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1
% 5.42/5.62 thf(fact_200_mult__numeral__1,axiom,
% 5.42/5.62 ! [A: real] :
% 5.42/5.62 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1
% 5.42/5.62 thf(fact_201_mult__numeral__1,axiom,
% 5.42/5.62 ! [A: rat] :
% 5.42/5.62 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1
% 5.42/5.62 thf(fact_202_mult__numeral__1,axiom,
% 5.42/5.62 ! [A: nat] :
% 5.42/5.62 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1
% 5.42/5.62 thf(fact_203_mult__numeral__1,axiom,
% 5.42/5.62 ! [A: int] :
% 5.42/5.62 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % mult_numeral_1
% 5.42/5.62 thf(fact_204_numeral__Bit0,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.42/5.62 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit0
% 5.42/5.62 thf(fact_205_numeral__Bit0,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.42/5.62 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit0
% 5.42/5.62 thf(fact_206_numeral__Bit0,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.42/5.62 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit0
% 5.42/5.62 thf(fact_207_numeral__Bit0,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.42/5.62 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit0
% 5.42/5.62 thf(fact_208_numeral__Bit0,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.42/5.62 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit0
% 5.42/5.62 thf(fact_209_one__plus__numeral__commute,axiom,
% 5.42/5.62 ! [X2: num] :
% 5.42/5.62 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X2 ) )
% 5.42/5.62 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral_commute
% 5.42/5.62 thf(fact_210_one__plus__numeral__commute,axiom,
% 5.42/5.62 ! [X2: num] :
% 5.42/5.62 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 5.42/5.62 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral_commute
% 5.42/5.62 thf(fact_211_one__plus__numeral__commute,axiom,
% 5.42/5.62 ! [X2: num] :
% 5.42/5.62 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.42/5.62 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral_commute
% 5.42/5.62 thf(fact_212_one__plus__numeral__commute,axiom,
% 5.42/5.62 ! [X2: num] :
% 5.42/5.62 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.42/5.62 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral_commute
% 5.42/5.62 thf(fact_213_one__plus__numeral__commute,axiom,
% 5.42/5.62 ! [X2: num] :
% 5.42/5.62 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 5.42/5.62 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_plus_numeral_commute
% 5.42/5.62 thf(fact_214_numeral__One,axiom,
% 5.42/5.62 ( ( numera6690914467698888265omplex @ one )
% 5.42/5.62 = one_one_complex ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_One
% 5.42/5.62 thf(fact_215_numeral__One,axiom,
% 5.42/5.62 ( ( numeral_numeral_real @ one )
% 5.42/5.62 = one_one_real ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_One
% 5.42/5.62 thf(fact_216_numeral__One,axiom,
% 5.42/5.62 ( ( numeral_numeral_rat @ one )
% 5.42/5.62 = one_one_rat ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_One
% 5.42/5.62 thf(fact_217_numeral__One,axiom,
% 5.42/5.62 ( ( numeral_numeral_nat @ one )
% 5.42/5.62 = one_one_nat ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_One
% 5.42/5.62 thf(fact_218_numeral__One,axiom,
% 5.42/5.62 ( ( numeral_numeral_int @ one )
% 5.42/5.62 = one_one_int ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_One
% 5.42/5.62 thf(fact_219_num_Oexhaust,axiom,
% 5.42/5.62 ! [Y2: num] :
% 5.42/5.62 ( ( Y2 != one )
% 5.42/5.62 => ( ! [X22: num] :
% 5.42/5.62 ( Y2
% 5.42/5.62 != ( bit0 @ X22 ) )
% 5.42/5.62 => ~ ! [X32: num] :
% 5.42/5.62 ( Y2
% 5.42/5.62 != ( bit1 @ X32 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % num.exhaust
% 5.42/5.62 thf(fact_220_numerals_I1_J,axiom,
% 5.42/5.62 ( ( numeral_numeral_nat @ one )
% 5.42/5.62 = one_one_nat ) ).
% 5.42/5.62
% 5.42/5.62 % numerals(1)
% 5.42/5.62 thf(fact_221_numeral__Bit1,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.42/5.62 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit1
% 5.42/5.62 thf(fact_222_numeral__Bit1,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.42/5.62 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit1
% 5.42/5.62 thf(fact_223_numeral__Bit1,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.42/5.62 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit1
% 5.42/5.62 thf(fact_224_numeral__Bit1,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.42/5.62 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit1
% 5.42/5.62 thf(fact_225_numeral__Bit1,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.42/5.62 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit1
% 5.42/5.62 thf(fact_226_left__add__twice,axiom,
% 5.42/5.62 ! [A: complex,B: complex] :
% 5.42/5.62 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.42/5.62 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_add_twice
% 5.42/5.62 thf(fact_227_left__add__twice,axiom,
% 5.42/5.62 ! [A: real,B: real] :
% 5.42/5.62 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.42/5.62 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_add_twice
% 5.42/5.62 thf(fact_228_left__add__twice,axiom,
% 5.42/5.62 ! [A: rat,B: rat] :
% 5.42/5.62 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.42/5.62 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_add_twice
% 5.42/5.62 thf(fact_229_left__add__twice,axiom,
% 5.42/5.62 ! [A: nat,B: nat] :
% 5.42/5.62 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.42/5.62 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_add_twice
% 5.42/5.62 thf(fact_230_left__add__twice,axiom,
% 5.42/5.62 ! [A: int,B: int] :
% 5.42/5.62 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.42/5.62 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_add_twice
% 5.42/5.62 thf(fact_231_mult__2__right,axiom,
% 5.42/5.62 ! [Z: complex] :
% 5.42/5.62 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.42/5.62 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2_right
% 5.42/5.62 thf(fact_232_mult__2__right,axiom,
% 5.42/5.62 ! [Z: real] :
% 5.42/5.62 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.42/5.62 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2_right
% 5.42/5.62 thf(fact_233_mult__2__right,axiom,
% 5.42/5.62 ! [Z: rat] :
% 5.42/5.62 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.42/5.62 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2_right
% 5.42/5.62 thf(fact_234_mult__2__right,axiom,
% 5.42/5.62 ! [Z: nat] :
% 5.42/5.62 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.62 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2_right
% 5.42/5.62 thf(fact_235_mult__2__right,axiom,
% 5.42/5.62 ! [Z: int] :
% 5.42/5.62 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.62 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2_right
% 5.42/5.62 thf(fact_236_mult__2,axiom,
% 5.42/5.62 ! [Z: complex] :
% 5.42/5.62 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.42/5.62 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2
% 5.42/5.62 thf(fact_237_mult__2,axiom,
% 5.42/5.62 ! [Z: real] :
% 5.42/5.62 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.42/5.62 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2
% 5.42/5.62 thf(fact_238_mult__2,axiom,
% 5.42/5.62 ! [Z: rat] :
% 5.42/5.62 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.42/5.62 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2
% 5.42/5.62 thf(fact_239_mult__2,axiom,
% 5.42/5.62 ! [Z: nat] :
% 5.42/5.62 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.42/5.62 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2
% 5.42/5.62 thf(fact_240_mult__2,axiom,
% 5.42/5.62 ! [Z: int] :
% 5.42/5.62 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.42/5.62 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.42/5.62
% 5.42/5.62 % mult_2
% 5.42/5.62 thf(fact_241_nat__1__add__1,axiom,
% 5.42/5.62 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.42/5.62 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % nat_1_add_1
% 5.42/5.62 thf(fact_242_add__self__div__2,axiom,
% 5.42/5.62 ! [M: nat] :
% 5.42/5.62 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.62 = M ) ).
% 5.42/5.62
% 5.42/5.62 % add_self_div_2
% 5.42/5.62 thf(fact_243_power__increasing__iff,axiom,
% 5.42/5.62 ! [B: real,X2: nat,Y2: nat] :
% 5.42/5.62 ( ( ord_less_real @ one_one_real @ B )
% 5.42/5.62 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y2 ) )
% 5.42/5.62 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_increasing_iff
% 5.42/5.62 thf(fact_244_power__increasing__iff,axiom,
% 5.42/5.62 ! [B: rat,X2: nat,Y2: nat] :
% 5.42/5.62 ( ( ord_less_rat @ one_one_rat @ B )
% 5.42/5.62 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y2 ) )
% 5.42/5.62 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_increasing_iff
% 5.42/5.62 thf(fact_245_power__increasing__iff,axiom,
% 5.42/5.62 ! [B: nat,X2: nat,Y2: nat] :
% 5.42/5.62 ( ( ord_less_nat @ one_one_nat @ B )
% 5.42/5.62 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y2 ) )
% 5.42/5.62 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_increasing_iff
% 5.42/5.62 thf(fact_246_power__increasing__iff,axiom,
% 5.42/5.62 ! [B: int,X2: nat,Y2: nat] :
% 5.42/5.62 ( ( ord_less_int @ one_one_int @ B )
% 5.42/5.62 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y2 ) )
% 5.42/5.62 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_increasing_iff
% 5.42/5.62 thf(fact_247_semiring__norm_I3_J,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.42/5.62 = ( bit1 @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(3)
% 5.42/5.62 thf(fact_248_semiring__norm_I4_J,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.42/5.62 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(4)
% 5.42/5.62 thf(fact_249_semiring__norm_I5_J,axiom,
% 5.42/5.62 ! [M: num] :
% 5.42/5.62 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.42/5.62 = ( bit1 @ M ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(5)
% 5.42/5.62 thf(fact_250_semiring__norm_I8_J,axiom,
% 5.42/5.62 ! [M: num] :
% 5.42/5.62 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.42/5.62 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(8)
% 5.42/5.62 thf(fact_251_semiring__norm_I10_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.42/5.62 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(10)
% 5.42/5.62 thf(fact_252_power__add__numeral2,axiom,
% 5.42/5.62 ! [A: complex,M: num,N: num,B: complex] :
% 5.42/5.62 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.42/5.62 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral2
% 5.42/5.62 thf(fact_253_power__add__numeral2,axiom,
% 5.42/5.62 ! [A: real,M: num,N: num,B: real] :
% 5.42/5.62 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.42/5.62 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral2
% 5.42/5.62 thf(fact_254_power__add__numeral2,axiom,
% 5.42/5.62 ! [A: rat,M: num,N: num,B: rat] :
% 5.42/5.62 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.42/5.62 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral2
% 5.42/5.62 thf(fact_255_power__add__numeral2,axiom,
% 5.42/5.62 ! [A: nat,M: num,N: num,B: nat] :
% 5.42/5.62 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.42/5.62 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral2
% 5.42/5.62 thf(fact_256_power__add__numeral2,axiom,
% 5.42/5.62 ! [A: int,M: num,N: num,B: int] :
% 5.42/5.62 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.42/5.62 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral2
% 5.42/5.62 thf(fact_257_power__add__numeral,axiom,
% 5.42/5.62 ! [A: complex,M: num,N: num] :
% 5.42/5.62 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.42/5.62 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral
% 5.42/5.62 thf(fact_258_power__add__numeral,axiom,
% 5.42/5.62 ! [A: real,M: num,N: num] :
% 5.42/5.62 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.42/5.62 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral
% 5.42/5.62 thf(fact_259_power__add__numeral,axiom,
% 5.42/5.62 ! [A: rat,M: num,N: num] :
% 5.42/5.62 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.42/5.62 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral
% 5.42/5.62 thf(fact_260_power__add__numeral,axiom,
% 5.42/5.62 ! [A: nat,M: num,N: num] :
% 5.42/5.62 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.42/5.62 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral
% 5.42/5.62 thf(fact_261_power__add__numeral,axiom,
% 5.42/5.62 ! [A: int,M: num,N: num] :
% 5.42/5.62 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.42/5.62 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add_numeral
% 5.42/5.62 thf(fact_262_power__strict__increasing__iff,axiom,
% 5.42/5.62 ! [B: real,X2: nat,Y2: nat] :
% 5.42/5.62 ( ( ord_less_real @ one_one_real @ B )
% 5.42/5.62 => ( ( ord_less_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y2 ) )
% 5.42/5.62 = ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_strict_increasing_iff
% 5.42/5.62 thf(fact_263_power__strict__increasing__iff,axiom,
% 5.42/5.62 ! [B: rat,X2: nat,Y2: nat] :
% 5.42/5.62 ( ( ord_less_rat @ one_one_rat @ B )
% 5.42/5.62 => ( ( ord_less_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y2 ) )
% 5.42/5.62 = ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_strict_increasing_iff
% 5.42/5.62 thf(fact_264_power__strict__increasing__iff,axiom,
% 5.42/5.62 ! [B: nat,X2: nat,Y2: nat] :
% 5.42/5.62 ( ( ord_less_nat @ one_one_nat @ B )
% 5.42/5.62 => ( ( ord_less_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y2 ) )
% 5.42/5.62 = ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_strict_increasing_iff
% 5.42/5.62 thf(fact_265_power__strict__increasing__iff,axiom,
% 5.42/5.62 ! [B: int,X2: nat,Y2: nat] :
% 5.42/5.62 ( ( ord_less_int @ one_one_int @ B )
% 5.42/5.62 => ( ( ord_less_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y2 ) )
% 5.42/5.62 = ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_strict_increasing_iff
% 5.42/5.62 thf(fact_266_semiring__norm_I70_J,axiom,
% 5.42/5.62 ! [M: num] :
% 5.42/5.62 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(70)
% 5.42/5.62 thf(fact_267_semiring__norm_I72_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.42/5.62 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(72)
% 5.42/5.62 thf(fact_268_semiring__norm_I87_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ( bit0 @ M )
% 5.42/5.62 = ( bit0 @ N ) )
% 5.42/5.62 = ( M = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(87)
% 5.42/5.62 thf(fact_269_semiring__norm_I90_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ( bit1 @ M )
% 5.42/5.62 = ( bit1 @ N ) )
% 5.42/5.62 = ( M = N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(90)
% 5.42/5.62 thf(fact_270_semiring__norm_I85_J,axiom,
% 5.42/5.62 ! [M: num] :
% 5.42/5.62 ( ( bit0 @ M )
% 5.42/5.62 != one ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(85)
% 5.42/5.62 thf(fact_271_semiring__norm_I83_J,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( one
% 5.42/5.62 != ( bit0 @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(83)
% 5.42/5.62 thf(fact_272_power__one,axiom,
% 5.42/5.62 ! [N: nat] :
% 5.42/5.62 ( ( power_power_rat @ one_one_rat @ N )
% 5.42/5.62 = one_one_rat ) ).
% 5.42/5.62
% 5.42/5.62 % power_one
% 5.42/5.62 thf(fact_273_power__one,axiom,
% 5.42/5.62 ! [N: nat] :
% 5.42/5.62 ( ( power_power_nat @ one_one_nat @ N )
% 5.42/5.62 = one_one_nat ) ).
% 5.42/5.62
% 5.42/5.62 % power_one
% 5.42/5.62 thf(fact_274_power__one,axiom,
% 5.42/5.62 ! [N: nat] :
% 5.42/5.62 ( ( power_power_real @ one_one_real @ N )
% 5.42/5.62 = one_one_real ) ).
% 5.42/5.62
% 5.42/5.62 % power_one
% 5.42/5.62 thf(fact_275_power__one,axiom,
% 5.42/5.62 ! [N: nat] :
% 5.42/5.62 ( ( power_power_complex @ one_one_complex @ N )
% 5.42/5.62 = one_one_complex ) ).
% 5.42/5.62
% 5.42/5.62 % power_one
% 5.42/5.62 thf(fact_276_power__one,axiom,
% 5.42/5.62 ! [N: nat] :
% 5.42/5.62 ( ( power_power_int @ one_one_int @ N )
% 5.42/5.62 = one_one_int ) ).
% 5.42/5.62
% 5.42/5.62 % power_one
% 5.42/5.62 thf(fact_277_semiring__norm_I89_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( bit1 @ M )
% 5.42/5.62 != ( bit0 @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(89)
% 5.42/5.62 thf(fact_278_semiring__norm_I88_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( bit0 @ M )
% 5.42/5.62 != ( bit1 @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(88)
% 5.42/5.62 thf(fact_279_semiring__norm_I86_J,axiom,
% 5.42/5.62 ! [M: num] :
% 5.42/5.62 ( ( bit1 @ M )
% 5.42/5.62 != one ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(86)
% 5.42/5.62 thf(fact_280_semiring__norm_I84_J,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( one
% 5.42/5.62 != ( bit1 @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(84)
% 5.42/5.62 thf(fact_281_power__one__right,axiom,
% 5.42/5.62 ! [A: nat] :
% 5.42/5.62 ( ( power_power_nat @ A @ one_one_nat )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % power_one_right
% 5.42/5.62 thf(fact_282_power__one__right,axiom,
% 5.42/5.62 ! [A: real] :
% 5.42/5.62 ( ( power_power_real @ A @ one_one_nat )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % power_one_right
% 5.42/5.62 thf(fact_283_power__one__right,axiom,
% 5.42/5.62 ! [A: complex] :
% 5.42/5.62 ( ( power_power_complex @ A @ one_one_nat )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % power_one_right
% 5.42/5.62 thf(fact_284_power__one__right,axiom,
% 5.42/5.62 ! [A: int] :
% 5.42/5.62 ( ( power_power_int @ A @ one_one_nat )
% 5.42/5.62 = A ) ).
% 5.42/5.62
% 5.42/5.62 % power_one_right
% 5.42/5.62 thf(fact_285_semiring__norm_I6_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.42/5.62 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(6)
% 5.42/5.62 thf(fact_286_semiring__norm_I13_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.42/5.62 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(13)
% 5.42/5.62 thf(fact_287_semiring__norm_I12_J,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( times_times_num @ one @ N )
% 5.42/5.62 = N ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(12)
% 5.42/5.62 thf(fact_288_semiring__norm_I11_J,axiom,
% 5.42/5.62 ! [M: num] :
% 5.42/5.62 ( ( times_times_num @ M @ one )
% 5.42/5.62 = M ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(11)
% 5.42/5.62 thf(fact_289_semiring__norm_I78_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.42/5.62 = ( ord_less_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(78)
% 5.42/5.62 thf(fact_290_semiring__norm_I71_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.42/5.62 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(71)
% 5.42/5.62 thf(fact_291_semiring__norm_I75_J,axiom,
% 5.42/5.62 ! [M: num] :
% 5.42/5.62 ~ ( ord_less_num @ M @ one ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(75)
% 5.42/5.62 thf(fact_292_semiring__norm_I68_J,axiom,
% 5.42/5.62 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(68)
% 5.42/5.62 thf(fact_293_semiring__norm_I80_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.42/5.62 = ( ord_less_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(80)
% 5.42/5.62 thf(fact_294_semiring__norm_I73_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.42/5.62 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(73)
% 5.42/5.62 thf(fact_295_power__inject__exp,axiom,
% 5.42/5.62 ! [A: real,M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_real @ one_one_real @ A )
% 5.42/5.62 => ( ( ( power_power_real @ A @ M )
% 5.42/5.62 = ( power_power_real @ A @ N ) )
% 5.42/5.62 = ( M = N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_inject_exp
% 5.42/5.62 thf(fact_296_power__inject__exp,axiom,
% 5.42/5.62 ! [A: rat,M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_rat @ one_one_rat @ A )
% 5.42/5.62 => ( ( ( power_power_rat @ A @ M )
% 5.42/5.62 = ( power_power_rat @ A @ N ) )
% 5.42/5.62 = ( M = N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_inject_exp
% 5.42/5.62 thf(fact_297_power__inject__exp,axiom,
% 5.42/5.62 ! [A: nat,M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_nat @ one_one_nat @ A )
% 5.42/5.62 => ( ( ( power_power_nat @ A @ M )
% 5.42/5.62 = ( power_power_nat @ A @ N ) )
% 5.42/5.62 = ( M = N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_inject_exp
% 5.42/5.62 thf(fact_298_power__inject__exp,axiom,
% 5.42/5.62 ! [A: int,M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_int @ one_one_int @ A )
% 5.42/5.62 => ( ( ( power_power_int @ A @ M )
% 5.42/5.62 = ( power_power_int @ A @ N ) )
% 5.42/5.62 = ( M = N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_inject_exp
% 5.42/5.62 thf(fact_299_semiring__norm_I2_J,axiom,
% 5.42/5.62 ( ( plus_plus_num @ one @ one )
% 5.42/5.62 = ( bit0 @ one ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(2)
% 5.42/5.62 thf(fact_300_semiring__norm_I9_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.42/5.62 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(9)
% 5.42/5.62 thf(fact_301_semiring__norm_I7_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.42/5.62 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(7)
% 5.42/5.62 thf(fact_302_power__mult__numeral,axiom,
% 5.42/5.62 ! [A: nat,M: num,N: num] :
% 5.42/5.62 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult_numeral
% 5.42/5.62 thf(fact_303_power__mult__numeral,axiom,
% 5.42/5.62 ! [A: real,M: num,N: num] :
% 5.42/5.62 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult_numeral
% 5.42/5.62 thf(fact_304_power__mult__numeral,axiom,
% 5.42/5.62 ! [A: complex,M: num,N: num] :
% 5.42/5.62 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult_numeral
% 5.42/5.62 thf(fact_305_power__mult__numeral,axiom,
% 5.42/5.62 ! [A: int,M: num,N: num] :
% 5.42/5.62 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.42/5.62 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult_numeral
% 5.42/5.62 thf(fact_306_semiring__norm_I15_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.42/5.62 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(15)
% 5.42/5.62 thf(fact_307_semiring__norm_I14_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.42/5.62 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(14)
% 5.42/5.62 thf(fact_308_semiring__norm_I76_J,axiom,
% 5.42/5.62 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(76)
% 5.42/5.62 thf(fact_309_semiring__norm_I69_J,axiom,
% 5.42/5.62 ! [M: num] :
% 5.42/5.62 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(69)
% 5.42/5.62 thf(fact_310_semiring__norm_I81_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.42/5.62 = ( ord_less_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(81)
% 5.42/5.62 thf(fact_311_semiring__norm_I77_J,axiom,
% 5.42/5.62 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(77)
% 5.42/5.62 thf(fact_312_semiring__norm_I16_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.42/5.62 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(16)
% 5.42/5.62 thf(fact_313_semiring__norm_I79_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.42/5.62 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(79)
% 5.42/5.62 thf(fact_314_semiring__norm_I74_J,axiom,
% 5.42/5.62 ! [M: num,N: num] :
% 5.42/5.62 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.42/5.62 = ( ord_less_num @ M @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % semiring_norm(74)
% 5.42/5.62 thf(fact_315_div__mult2__numeral__eq,axiom,
% 5.42/5.62 ! [A: nat,K: num,L2: num] :
% 5.42/5.62 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 5.42/5.62 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % div_mult2_numeral_eq
% 5.42/5.62 thf(fact_316_div__mult2__numeral__eq,axiom,
% 5.42/5.62 ! [A: int,K: num,L2: num] :
% 5.42/5.62 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 5.42/5.62 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % div_mult2_numeral_eq
% 5.42/5.62 thf(fact_317_power__commutes,axiom,
% 5.42/5.62 ! [A: complex,N: nat] :
% 5.42/5.62 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.42/5.62 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commutes
% 5.42/5.62 thf(fact_318_power__commutes,axiom,
% 5.42/5.62 ! [A: real,N: nat] :
% 5.42/5.62 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.42/5.62 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commutes
% 5.42/5.62 thf(fact_319_power__commutes,axiom,
% 5.42/5.62 ! [A: rat,N: nat] :
% 5.42/5.62 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.42/5.62 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commutes
% 5.42/5.62 thf(fact_320_power__commutes,axiom,
% 5.42/5.62 ! [A: nat,N: nat] :
% 5.42/5.62 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.42/5.62 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commutes
% 5.42/5.62 thf(fact_321_power__commutes,axiom,
% 5.42/5.62 ! [A: int,N: nat] :
% 5.42/5.62 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.42/5.62 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commutes
% 5.42/5.62 thf(fact_322_power__mult__distrib,axiom,
% 5.42/5.62 ! [A: complex,B: complex,N: nat] :
% 5.42/5.62 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 5.42/5.62 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult_distrib
% 5.42/5.62 thf(fact_323_power__mult__distrib,axiom,
% 5.42/5.62 ! [A: real,B: real,N: nat] :
% 5.42/5.62 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 5.42/5.62 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult_distrib
% 5.42/5.62 thf(fact_324_power__mult__distrib,axiom,
% 5.42/5.62 ! [A: rat,B: rat,N: nat] :
% 5.42/5.62 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 5.42/5.62 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult_distrib
% 5.42/5.62 thf(fact_325_power__mult__distrib,axiom,
% 5.42/5.62 ! [A: nat,B: nat,N: nat] :
% 5.42/5.62 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 5.42/5.62 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult_distrib
% 5.42/5.62 thf(fact_326_power__mult__distrib,axiom,
% 5.42/5.62 ! [A: int,B: int,N: nat] :
% 5.42/5.62 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 5.42/5.62 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult_distrib
% 5.42/5.62 thf(fact_327_power__commuting__commutes,axiom,
% 5.42/5.62 ! [X2: complex,Y2: complex,N: nat] :
% 5.42/5.62 ( ( ( times_times_complex @ X2 @ Y2 )
% 5.42/5.62 = ( times_times_complex @ Y2 @ X2 ) )
% 5.42/5.62 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ Y2 )
% 5.42/5.62 = ( times_times_complex @ Y2 @ ( power_power_complex @ X2 @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commuting_commutes
% 5.42/5.62 thf(fact_328_power__commuting__commutes,axiom,
% 5.42/5.62 ! [X2: real,Y2: real,N: nat] :
% 5.42/5.62 ( ( ( times_times_real @ X2 @ Y2 )
% 5.42/5.62 = ( times_times_real @ Y2 @ X2 ) )
% 5.42/5.62 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ Y2 )
% 5.42/5.62 = ( times_times_real @ Y2 @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commuting_commutes
% 5.42/5.62 thf(fact_329_power__commuting__commutes,axiom,
% 5.42/5.62 ! [X2: rat,Y2: rat,N: nat] :
% 5.42/5.62 ( ( ( times_times_rat @ X2 @ Y2 )
% 5.42/5.62 = ( times_times_rat @ Y2 @ X2 ) )
% 5.42/5.62 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ Y2 )
% 5.42/5.62 = ( times_times_rat @ Y2 @ ( power_power_rat @ X2 @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commuting_commutes
% 5.42/5.62 thf(fact_330_power__commuting__commutes,axiom,
% 5.42/5.62 ! [X2: nat,Y2: nat,N: nat] :
% 5.42/5.62 ( ( ( times_times_nat @ X2 @ Y2 )
% 5.42/5.62 = ( times_times_nat @ Y2 @ X2 ) )
% 5.42/5.62 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ Y2 )
% 5.42/5.62 = ( times_times_nat @ Y2 @ ( power_power_nat @ X2 @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commuting_commutes
% 5.42/5.62 thf(fact_331_power__commuting__commutes,axiom,
% 5.42/5.62 ! [X2: int,Y2: int,N: nat] :
% 5.42/5.62 ( ( ( times_times_int @ X2 @ Y2 )
% 5.42/5.62 = ( times_times_int @ Y2 @ X2 ) )
% 5.42/5.62 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ Y2 )
% 5.42/5.62 = ( times_times_int @ Y2 @ ( power_power_int @ X2 @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_commuting_commutes
% 5.42/5.62 thf(fact_332_power__divide,axiom,
% 5.42/5.62 ! [A: complex,B: complex,N: nat] :
% 5.42/5.62 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 5.42/5.62 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_divide
% 5.42/5.62 thf(fact_333_power__divide,axiom,
% 5.42/5.62 ! [A: real,B: real,N: nat] :
% 5.42/5.62 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 5.42/5.62 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_divide
% 5.42/5.62 thf(fact_334_power__divide,axiom,
% 5.42/5.62 ! [A: rat,B: rat,N: nat] :
% 5.42/5.62 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 5.42/5.62 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_divide
% 5.42/5.62 thf(fact_335_power__mult,axiom,
% 5.42/5.62 ! [A: nat,M: nat,N: nat] :
% 5.42/5.62 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 5.42/5.62 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult
% 5.42/5.62 thf(fact_336_power__mult,axiom,
% 5.42/5.62 ! [A: real,M: nat,N: nat] :
% 5.42/5.62 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 5.42/5.62 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult
% 5.42/5.62 thf(fact_337_power__mult,axiom,
% 5.42/5.62 ! [A: complex,M: nat,N: nat] :
% 5.42/5.62 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 5.42/5.62 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult
% 5.42/5.62 thf(fact_338_power__mult,axiom,
% 5.42/5.62 ! [A: int,M: nat,N: nat] :
% 5.42/5.62 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 5.42/5.62 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_mult
% 5.42/5.62 thf(fact_339_div__le__mono,axiom,
% 5.42/5.62 ! [M: nat,N: nat,K: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.62 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % div_le_mono
% 5.42/5.62 thf(fact_340_div__le__dividend,axiom,
% 5.42/5.62 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.42/5.62
% 5.42/5.62 % div_le_dividend
% 5.42/5.62 thf(fact_341_left__add__mult__distrib,axiom,
% 5.42/5.62 ! [I: nat,U: nat,J: nat,K: nat] :
% 5.42/5.62 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.42/5.62 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_add_mult_distrib
% 5.42/5.62 thf(fact_342_div__mult2__eq,axiom,
% 5.42/5.62 ! [M: nat,N: nat,Q2: nat] :
% 5.42/5.62 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.42/5.62 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 5.42/5.62
% 5.42/5.62 % div_mult2_eq
% 5.42/5.62 thf(fact_343_one__le__power,axiom,
% 5.42/5.62 ! [A: real,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.42/5.62 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_le_power
% 5.42/5.62 thf(fact_344_one__le__power,axiom,
% 5.42/5.62 ! [A: rat,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.42/5.62 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_le_power
% 5.42/5.62 thf(fact_345_one__le__power,axiom,
% 5.42/5.62 ! [A: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.42/5.62 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_le_power
% 5.42/5.62 thf(fact_346_one__le__power,axiom,
% 5.42/5.62 ! [A: int,N: nat] :
% 5.42/5.62 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.42/5.62 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % one_le_power
% 5.42/5.62 thf(fact_347_left__right__inverse__power,axiom,
% 5.42/5.62 ! [X2: complex,Y2: complex,N: nat] :
% 5.42/5.62 ( ( ( times_times_complex @ X2 @ Y2 )
% 5.42/5.62 = one_one_complex )
% 5.42/5.62 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 5.42/5.62 = one_one_complex ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_right_inverse_power
% 5.42/5.62 thf(fact_348_left__right__inverse__power,axiom,
% 5.42/5.62 ! [X2: real,Y2: real,N: nat] :
% 5.42/5.62 ( ( ( times_times_real @ X2 @ Y2 )
% 5.42/5.62 = one_one_real )
% 5.42/5.62 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y2 @ N ) )
% 5.42/5.62 = one_one_real ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_right_inverse_power
% 5.42/5.62 thf(fact_349_left__right__inverse__power,axiom,
% 5.42/5.62 ! [X2: rat,Y2: rat,N: nat] :
% 5.42/5.62 ( ( ( times_times_rat @ X2 @ Y2 )
% 5.42/5.62 = one_one_rat )
% 5.42/5.62 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 5.42/5.62 = one_one_rat ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_right_inverse_power
% 5.42/5.62 thf(fact_350_left__right__inverse__power,axiom,
% 5.42/5.62 ! [X2: nat,Y2: nat,N: nat] :
% 5.42/5.62 ( ( ( times_times_nat @ X2 @ Y2 )
% 5.42/5.62 = one_one_nat )
% 5.42/5.62 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y2 @ N ) )
% 5.42/5.62 = one_one_nat ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_right_inverse_power
% 5.42/5.62 thf(fact_351_left__right__inverse__power,axiom,
% 5.42/5.62 ! [X2: int,Y2: int,N: nat] :
% 5.42/5.62 ( ( ( times_times_int @ X2 @ Y2 )
% 5.42/5.62 = one_one_int )
% 5.42/5.62 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y2 @ N ) )
% 5.42/5.62 = one_one_int ) ) ).
% 5.42/5.62
% 5.42/5.62 % left_right_inverse_power
% 5.42/5.62 thf(fact_352_power__one__over,axiom,
% 5.42/5.62 ! [A: complex,N: nat] :
% 5.42/5.62 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.42/5.62 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_one_over
% 5.42/5.62 thf(fact_353_power__one__over,axiom,
% 5.42/5.62 ! [A: real,N: nat] :
% 5.42/5.62 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.42/5.62 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_one_over
% 5.42/5.62 thf(fact_354_power__one__over,axiom,
% 5.42/5.62 ! [A: rat,N: nat] :
% 5.42/5.62 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.42/5.62 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_one_over
% 5.42/5.62 thf(fact_355_power__add,axiom,
% 5.42/5.62 ! [A: complex,M: nat,N: nat] :
% 5.42/5.62 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 5.42/5.62 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add
% 5.42/5.62 thf(fact_356_power__add,axiom,
% 5.42/5.62 ! [A: real,M: nat,N: nat] :
% 5.42/5.62 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 5.42/5.62 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add
% 5.42/5.62 thf(fact_357_power__add,axiom,
% 5.42/5.62 ! [A: rat,M: nat,N: nat] :
% 5.42/5.62 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.42/5.62 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add
% 5.42/5.62 thf(fact_358_power__add,axiom,
% 5.42/5.62 ! [A: nat,M: nat,N: nat] :
% 5.42/5.62 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.42/5.62 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add
% 5.42/5.62 thf(fact_359_power__add,axiom,
% 5.42/5.62 ! [A: int,M: nat,N: nat] :
% 5.42/5.62 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 5.42/5.62 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_add
% 5.42/5.62 thf(fact_360_less__mult__imp__div__less,axiom,
% 5.42/5.62 ! [M: nat,I: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 5.42/5.62 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 5.42/5.62
% 5.42/5.62 % less_mult_imp_div_less
% 5.42/5.62 thf(fact_361_div__times__less__eq__dividend,axiom,
% 5.42/5.62 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.42/5.62
% 5.42/5.62 % div_times_less_eq_dividend
% 5.42/5.62 thf(fact_362_times__div__less__eq__dividend,axiom,
% 5.42/5.62 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.42/5.62
% 5.42/5.62 % times_div_less_eq_dividend
% 5.42/5.62 thf(fact_363_power__gt1__lemma,axiom,
% 5.42/5.62 ! [A: real,N: nat] :
% 5.42/5.62 ( ( ord_less_real @ one_one_real @ A )
% 5.42/5.62 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_gt1_lemma
% 5.42/5.62 thf(fact_364_power__gt1__lemma,axiom,
% 5.42/5.62 ! [A: rat,N: nat] :
% 5.42/5.62 ( ( ord_less_rat @ one_one_rat @ A )
% 5.42/5.62 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_gt1_lemma
% 5.42/5.62 thf(fact_365_power__gt1__lemma,axiom,
% 5.42/5.62 ! [A: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_nat @ one_one_nat @ A )
% 5.42/5.62 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_gt1_lemma
% 5.42/5.62 thf(fact_366_power__gt1__lemma,axiom,
% 5.42/5.62 ! [A: int,N: nat] :
% 5.42/5.62 ( ( ord_less_int @ one_one_int @ A )
% 5.42/5.62 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_gt1_lemma
% 5.42/5.62 thf(fact_367_power__less__power__Suc,axiom,
% 5.42/5.62 ! [A: real,N: nat] :
% 5.42/5.62 ( ( ord_less_real @ one_one_real @ A )
% 5.42/5.62 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_less_power_Suc
% 5.42/5.62 thf(fact_368_power__less__power__Suc,axiom,
% 5.42/5.62 ! [A: rat,N: nat] :
% 5.42/5.62 ( ( ord_less_rat @ one_one_rat @ A )
% 5.42/5.62 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_less_power_Suc
% 5.42/5.62 thf(fact_369_power__less__power__Suc,axiom,
% 5.42/5.62 ! [A: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_nat @ one_one_nat @ A )
% 5.42/5.62 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_less_power_Suc
% 5.42/5.62 thf(fact_370_power__less__power__Suc,axiom,
% 5.42/5.62 ! [A: int,N: nat] :
% 5.42/5.62 ( ( ord_less_int @ one_one_int @ A )
% 5.42/5.62 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_less_power_Suc
% 5.42/5.62 thf(fact_371_numeral__Bit0__div__2,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.62 = ( numeral_numeral_nat @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit0_div_2
% 5.42/5.62 thf(fact_372_numeral__Bit0__div__2,axiom,
% 5.42/5.62 ! [N: num] :
% 5.42/5.62 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.62 = ( numeral_numeral_int @ N ) ) ).
% 5.42/5.62
% 5.42/5.62 % numeral_Bit0_div_2
% 5.42/5.62 thf(fact_373_power__strict__increasing,axiom,
% 5.42/5.62 ! [N: nat,N4: nat,A: real] :
% 5.42/5.62 ( ( ord_less_nat @ N @ N4 )
% 5.42/5.62 => ( ( ord_less_real @ one_one_real @ A )
% 5.42/5.62 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_strict_increasing
% 5.42/5.62 thf(fact_374_power__strict__increasing,axiom,
% 5.42/5.62 ! [N: nat,N4: nat,A: rat] :
% 5.42/5.62 ( ( ord_less_nat @ N @ N4 )
% 5.42/5.62 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.42/5.62 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_strict_increasing
% 5.42/5.62 thf(fact_375_power__strict__increasing,axiom,
% 5.42/5.62 ! [N: nat,N4: nat,A: nat] :
% 5.42/5.62 ( ( ord_less_nat @ N @ N4 )
% 5.42/5.62 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.42/5.62 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_strict_increasing
% 5.42/5.62 thf(fact_376_power__strict__increasing,axiom,
% 5.42/5.62 ! [N: nat,N4: nat,A: int] :
% 5.42/5.62 ( ( ord_less_nat @ N @ N4 )
% 5.42/5.62 => ( ( ord_less_int @ one_one_int @ A )
% 5.42/5.62 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.42/5.62
% 5.42/5.62 % power_strict_increasing
% 5.42/5.62 thf(fact_377_power__less__imp__less__exp,axiom,
% 5.42/5.62 ! [A: real,M: nat,N: nat] :
% 5.42/5.62 ( ( ord_less_real @ one_one_real @ A )
% 5.42/5.63 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.42/5.63 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_less_imp_less_exp
% 5.42/5.63 thf(fact_378_power__less__imp__less__exp,axiom,
% 5.42/5.63 ! [A: rat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_rat @ one_one_rat @ A )
% 5.42/5.63 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.42/5.63 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_less_imp_less_exp
% 5.42/5.63 thf(fact_379_power__less__imp__less__exp,axiom,
% 5.42/5.63 ! [A: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ one_one_nat @ A )
% 5.42/5.63 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.42/5.63 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_less_imp_less_exp
% 5.42/5.63 thf(fact_380_power__less__imp__less__exp,axiom,
% 5.42/5.63 ! [A: int,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_int @ one_one_int @ A )
% 5.42/5.63 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.42/5.63 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_less_imp_less_exp
% 5.42/5.63 thf(fact_381_power__increasing,axiom,
% 5.42/5.63 ! [N: nat,N4: nat,A: real] :
% 5.42/5.63 ( ( ord_less_eq_nat @ N @ N4 )
% 5.42/5.63 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.42/5.63 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_increasing
% 5.42/5.63 thf(fact_382_power__increasing,axiom,
% 5.42/5.63 ! [N: nat,N4: nat,A: rat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ N @ N4 )
% 5.42/5.63 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.42/5.63 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_increasing
% 5.42/5.63 thf(fact_383_power__increasing,axiom,
% 5.42/5.63 ! [N: nat,N4: nat,A: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ N @ N4 )
% 5.42/5.63 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.42/5.63 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_increasing
% 5.42/5.63 thf(fact_384_power__increasing,axiom,
% 5.42/5.63 ! [N: nat,N4: nat,A: int] :
% 5.42/5.63 ( ( ord_less_eq_nat @ N @ N4 )
% 5.42/5.63 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.42/5.63 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_increasing
% 5.42/5.63 thf(fact_385_power__le__imp__le__exp,axiom,
% 5.42/5.63 ! [A: real,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_real @ one_one_real @ A )
% 5.42/5.63 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.42/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_le_imp_le_exp
% 5.42/5.63 thf(fact_386_power__le__imp__le__exp,axiom,
% 5.42/5.63 ! [A: rat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_rat @ one_one_rat @ A )
% 5.42/5.63 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.42/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_le_imp_le_exp
% 5.42/5.63 thf(fact_387_power__le__imp__le__exp,axiom,
% 5.42/5.63 ! [A: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ one_one_nat @ A )
% 5.42/5.63 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.42/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_le_imp_le_exp
% 5.42/5.63 thf(fact_388_power__le__imp__le__exp,axiom,
% 5.42/5.63 ! [A: int,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_int @ one_one_int @ A )
% 5.42/5.63 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.42/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_le_imp_le_exp
% 5.42/5.63 thf(fact_389_power4__eq__xxxx,axiom,
% 5.42/5.63 ! [X2: complex] :
% 5.42/5.63 ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.42/5.63 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % power4_eq_xxxx
% 5.42/5.63 thf(fact_390_power4__eq__xxxx,axiom,
% 5.42/5.63 ! [X2: real] :
% 5.42/5.63 ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.42/5.63 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % power4_eq_xxxx
% 5.42/5.63 thf(fact_391_power4__eq__xxxx,axiom,
% 5.42/5.63 ! [X2: rat] :
% 5.42/5.63 ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.42/5.63 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % power4_eq_xxxx
% 5.42/5.63 thf(fact_392_power4__eq__xxxx,axiom,
% 5.42/5.63 ! [X2: nat] :
% 5.42/5.63 ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.42/5.63 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % power4_eq_xxxx
% 5.42/5.63 thf(fact_393_power4__eq__xxxx,axiom,
% 5.42/5.63 ! [X2: int] :
% 5.42/5.63 ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.42/5.63 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % power4_eq_xxxx
% 5.42/5.63 thf(fact_394_power2__eq__square,axiom,
% 5.42/5.63 ! [A: complex] :
% 5.42/5.63 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( times_times_complex @ A @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_eq_square
% 5.42/5.63 thf(fact_395_power2__eq__square,axiom,
% 5.42/5.63 ! [A: real] :
% 5.42/5.63 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( times_times_real @ A @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_eq_square
% 5.42/5.63 thf(fact_396_power2__eq__square,axiom,
% 5.42/5.63 ! [A: rat] :
% 5.42/5.63 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( times_times_rat @ A @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_eq_square
% 5.42/5.63 thf(fact_397_power2__eq__square,axiom,
% 5.42/5.63 ! [A: nat] :
% 5.42/5.63 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( times_times_nat @ A @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_eq_square
% 5.42/5.63 thf(fact_398_power2__eq__square,axiom,
% 5.42/5.63 ! [A: int] :
% 5.42/5.63 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( times_times_int @ A @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_eq_square
% 5.42/5.63 thf(fact_399_one__power2,axiom,
% 5.42/5.63 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_rat ) ).
% 5.42/5.63
% 5.42/5.63 % one_power2
% 5.42/5.63 thf(fact_400_one__power2,axiom,
% 5.42/5.63 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_nat ) ).
% 5.42/5.63
% 5.42/5.63 % one_power2
% 5.42/5.63 thf(fact_401_one__power2,axiom,
% 5.42/5.63 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_real ) ).
% 5.42/5.63
% 5.42/5.63 % one_power2
% 5.42/5.63 thf(fact_402_one__power2,axiom,
% 5.42/5.63 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_complex ) ).
% 5.42/5.63
% 5.42/5.63 % one_power2
% 5.42/5.63 thf(fact_403_one__power2,axiom,
% 5.42/5.63 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_int ) ).
% 5.42/5.63
% 5.42/5.63 % one_power2
% 5.42/5.63 thf(fact_404_numeral__Bit1__div__2,axiom,
% 5.42/5.63 ! [N: num] :
% 5.42/5.63 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( numeral_numeral_nat @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % numeral_Bit1_div_2
% 5.42/5.63 thf(fact_405_numeral__Bit1__div__2,axiom,
% 5.42/5.63 ! [N: num] :
% 5.42/5.63 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( numeral_numeral_int @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % numeral_Bit1_div_2
% 5.42/5.63 thf(fact_406_power3__eq__cube,axiom,
% 5.42/5.63 ! [A: complex] :
% 5.42/5.63 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.42/5.63 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power3_eq_cube
% 5.42/5.63 thf(fact_407_power3__eq__cube,axiom,
% 5.42/5.63 ! [A: real] :
% 5.42/5.63 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.42/5.63 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power3_eq_cube
% 5.42/5.63 thf(fact_408_power3__eq__cube,axiom,
% 5.42/5.63 ! [A: rat] :
% 5.42/5.63 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.42/5.63 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power3_eq_cube
% 5.42/5.63 thf(fact_409_power3__eq__cube,axiom,
% 5.42/5.63 ! [A: nat] :
% 5.42/5.63 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.42/5.63 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power3_eq_cube
% 5.42/5.63 thf(fact_410_power3__eq__cube,axiom,
% 5.42/5.63 ! [A: int] :
% 5.42/5.63 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.42/5.63 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power3_eq_cube
% 5.42/5.63 thf(fact_411_power__even__eq,axiom,
% 5.42/5.63 ! [A: nat,N: nat] :
% 5.42/5.63 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_even_eq
% 5.42/5.63 thf(fact_412_power__even__eq,axiom,
% 5.42/5.63 ! [A: real,N: nat] :
% 5.42/5.63 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_even_eq
% 5.42/5.63 thf(fact_413_power__even__eq,axiom,
% 5.42/5.63 ! [A: complex,N: nat] :
% 5.42/5.63 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_even_eq
% 5.42/5.63 thf(fact_414_power__even__eq,axiom,
% 5.42/5.63 ! [A: int,N: nat] :
% 5.42/5.63 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_even_eq
% 5.42/5.63 thf(fact_415_less__exp,axiom,
% 5.42/5.63 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_exp
% 5.42/5.63 thf(fact_416_self__le__ge2__pow,axiom,
% 5.42/5.63 ! [K: nat,M: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.42/5.63 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % self_le_ge2_pow
% 5.42/5.63 thf(fact_417_power2__nat__le__eq__le,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.63 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_nat_le_eq_le
% 5.42/5.63 thf(fact_418_power2__nat__le__imp__le,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_nat_le_imp_le
% 5.42/5.63 thf(fact_419_power2__sum,axiom,
% 5.42/5.63 ! [X2: complex,Y2: complex] :
% 5.42/5.63 ( ( power_power_complex @ ( plus_plus_complex @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_sum
% 5.42/5.63 thf(fact_420_power2__sum,axiom,
% 5.42/5.63 ! [X2: real,Y2: real] :
% 5.42/5.63 ( ( power_power_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_sum
% 5.42/5.63 thf(fact_421_power2__sum,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat] :
% 5.42/5.63 ( ( power_power_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_sum
% 5.42/5.63 thf(fact_422_power2__sum,axiom,
% 5.42/5.63 ! [X2: nat,Y2: nat] :
% 5.42/5.63 ( ( power_power_nat @ ( plus_plus_nat @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_sum
% 5.42/5.63 thf(fact_423_power2__sum,axiom,
% 5.42/5.63 ! [X2: int,Y2: int] :
% 5.42/5.63 ( ( power_power_int @ ( plus_plus_int @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_sum
% 5.42/5.63 thf(fact_424_ex__power__ivl1,axiom,
% 5.42/5.63 ! [B: nat,K: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.42/5.63 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.42/5.63 => ? [N3: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.42/5.63 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ex_power_ivl1
% 5.42/5.63 thf(fact_425_ex__power__ivl2,axiom,
% 5.42/5.63 ! [B: nat,K: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.42/5.63 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.42/5.63 => ? [N3: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.42/5.63 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ex_power_ivl2
% 5.42/5.63 thf(fact_426_sum__squares__bound,axiom,
% 5.42/5.63 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % sum_squares_bound
% 5.42/5.63 thf(fact_427_sum__squares__bound,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % sum_squares_bound
% 5.42/5.63 thf(fact_428_div__exp__eq,axiom,
% 5.42/5.63 ! [A: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_exp_eq
% 5.42/5.63 thf(fact_429_div__exp__eq,axiom,
% 5.42/5.63 ! [A: int,M: nat,N: nat] :
% 5.42/5.63 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_exp_eq
% 5.42/5.63 thf(fact_430_field__less__half__sum,axiom,
% 5.42/5.63 ! [X2: real,Y2: real] :
% 5.42/5.63 ( ( ord_less_real @ X2 @ Y2 )
% 5.42/5.63 => ( ord_less_real @ X2 @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % field_less_half_sum
% 5.42/5.63 thf(fact_431_field__less__half__sum,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat] :
% 5.42/5.63 ( ( ord_less_rat @ X2 @ Y2 )
% 5.42/5.63 => ( ord_less_rat @ X2 @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % field_less_half_sum
% 5.42/5.63 thf(fact_432__092_060open_062T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ax_A_092_060le_062_A23_A_L_A_Iif_AminNull_A_ItreeList_A_B_Ahigh_A_Iif_Ax_A_060_Ami_Athen_Ami_Aelse_Ax_J_A_Ideg_Adiv_A2_J_J_Athen_AT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Asummary_A_Ihigh_A_Iif_Ax_A_060_Ami_Athen_Ami_Aelse_Ax_J_A_Ideg_Adiv_A2_J_J_Aelse_A1_J_092_060close_062,axiom,
% 5.42/5.63 ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) ).
% 5.42/5.63
% 5.42/5.63 % \<open>T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t (Node (Some (mi, ma)) deg treeList summary) x \<le> 23 + (if minNull (treeList ! high (if x < mi then mi else x) (deg div 2)) then T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t summary (high (if x < mi then mi else x) (deg div 2)) else 1)\<close>
% 5.42/5.63 thf(fact_433_mi__ma__2__deg,axiom,
% 5.42/5.63 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.42/5.63 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.42/5.63 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mi_ma_2_deg
% 5.42/5.63 thf(fact_434_True,axiom,
% 5.42/5.63 vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % True
% 5.42/5.63 thf(fact_435_enat__ord__number_I1_J,axiom,
% 5.42/5.63 ! [M: num,N: num] :
% 5.42/5.63 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.42/5.63 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % enat_ord_number(1)
% 5.42/5.63 thf(fact_436_enat__ord__number_I2_J,axiom,
% 5.42/5.63 ! [M: num,N: num] :
% 5.42/5.63 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.42/5.63 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % enat_ord_number(2)
% 5.42/5.63 thf(fact_437_zdiv__numeral__Bit1,axiom,
% 5.42/5.63 ! [V: num,W: num] :
% 5.42/5.63 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.42/5.63 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % zdiv_numeral_Bit1
% 5.42/5.63 thf(fact_438_div__by__1,axiom,
% 5.42/5.63 ! [A: complex] :
% 5.42/5.63 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % div_by_1
% 5.42/5.63 thf(fact_439_div__by__1,axiom,
% 5.42/5.63 ! [A: real] :
% 5.42/5.63 ( ( divide_divide_real @ A @ one_one_real )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % div_by_1
% 5.42/5.63 thf(fact_440_div__by__1,axiom,
% 5.42/5.63 ! [A: rat] :
% 5.42/5.63 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % div_by_1
% 5.42/5.63 thf(fact_441_div__by__1,axiom,
% 5.42/5.63 ! [A: nat] :
% 5.42/5.63 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % div_by_1
% 5.42/5.63 thf(fact_442_div__by__1,axiom,
% 5.42/5.63 ! [A: int] :
% 5.42/5.63 ( ( divide_divide_int @ A @ one_one_int )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % div_by_1
% 5.42/5.63 thf(fact_443_bits__div__by__1,axiom,
% 5.42/5.63 ! [A: nat] :
% 5.42/5.63 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % bits_div_by_1
% 5.42/5.63 thf(fact_444_bits__div__by__1,axiom,
% 5.42/5.63 ! [A: int] :
% 5.42/5.63 ( ( divide_divide_int @ A @ one_one_int )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % bits_div_by_1
% 5.42/5.63 thf(fact_445_times__divide__eq__left,axiom,
% 5.42/5.63 ! [B: complex,C: complex,A: complex] :
% 5.42/5.63 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.42/5.63 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % times_divide_eq_left
% 5.42/5.63 thf(fact_446_times__divide__eq__left,axiom,
% 5.42/5.63 ! [B: real,C: real,A: real] :
% 5.42/5.63 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.42/5.63 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % times_divide_eq_left
% 5.42/5.63 thf(fact_447_times__divide__eq__left,axiom,
% 5.42/5.63 ! [B: rat,C: rat,A: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.42/5.63 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % times_divide_eq_left
% 5.42/5.63 thf(fact_448_deg__deg__n,axiom,
% 5.42/5.63 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.42/5.63 => ( Deg = N ) ) ).
% 5.42/5.63
% 5.42/5.63 % deg_deg_n
% 5.42/5.63 thf(fact_449__C5_Ohyps_C_I1_J,axiom,
% 5.42/5.63 vEBT_invar_vebt @ summary @ m ).
% 5.42/5.63
% 5.42/5.63 % "5.hyps"(1)
% 5.42/5.63 thf(fact_450_times__divide__eq__right,axiom,
% 5.42/5.63 ! [A: complex,B: complex,C: complex] :
% 5.42/5.63 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.42/5.63 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % times_divide_eq_right
% 5.42/5.63 thf(fact_451_times__divide__eq__right,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.42/5.63 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % times_divide_eq_right
% 5.42/5.63 thf(fact_452_times__divide__eq__right,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.42/5.63 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % times_divide_eq_right
% 5.42/5.63 thf(fact_453_divide__divide__eq__right,axiom,
% 5.42/5.63 ! [A: complex,B: complex,C: complex] :
% 5.42/5.63 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.42/5.63 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_eq_right
% 5.42/5.63 thf(fact_454_divide__divide__eq__right,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.42/5.63 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_eq_right
% 5.42/5.63 thf(fact_455_divide__divide__eq__right,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.42/5.63 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_eq_right
% 5.42/5.63 thf(fact_456_divide__divide__eq__left,axiom,
% 5.42/5.63 ! [A: complex,B: complex,C: complex] :
% 5.42/5.63 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.42/5.63 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_eq_left
% 5.42/5.63 thf(fact_457_divide__divide__eq__left,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.42/5.63 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_eq_left
% 5.42/5.63 thf(fact_458_divide__divide__eq__left,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.42/5.63 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_eq_left
% 5.42/5.63 thf(fact_459_two__powr__height__bound__deg,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % two_powr_height_bound_deg
% 5.42/5.63 thf(fact_460_zdiv__numeral__Bit0,axiom,
% 5.42/5.63 ! [V: num,W: num] :
% 5.42/5.63 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.42/5.63 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % zdiv_numeral_Bit0
% 5.42/5.63 thf(fact_461_enat__less__induct,axiom,
% 5.42/5.63 ! [P: extended_enat > $o,N: extended_enat] :
% 5.42/5.63 ( ! [N3: extended_enat] :
% 5.42/5.63 ( ! [M2: extended_enat] :
% 5.42/5.63 ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 5.42/5.63 => ( P @ M2 ) )
% 5.42/5.63 => ( P @ N3 ) )
% 5.42/5.63 => ( P @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % enat_less_induct
% 5.42/5.63 thf(fact_462_insertsimp,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat,L2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ( vEBT_VEBT_minNull @ T )
% 5.42/5.63 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % insertsimp
% 5.42/5.63 thf(fact_463_linordered__field__no__lb,axiom,
% 5.42/5.63 ! [X4: real] :
% 5.42/5.63 ? [Y3: real] : ( ord_less_real @ Y3 @ X4 ) ).
% 5.42/5.63
% 5.42/5.63 % linordered_field_no_lb
% 5.42/5.63 thf(fact_464_linordered__field__no__lb,axiom,
% 5.42/5.63 ! [X4: rat] :
% 5.42/5.63 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X4 ) ).
% 5.42/5.63
% 5.42/5.63 % linordered_field_no_lb
% 5.42/5.63 thf(fact_465_linordered__field__no__ub,axiom,
% 5.42/5.63 ! [X4: real] :
% 5.42/5.63 ? [X_1: real] : ( ord_less_real @ X4 @ X_1 ) ).
% 5.42/5.63
% 5.42/5.63 % linordered_field_no_ub
% 5.42/5.63 thf(fact_466_linordered__field__no__ub,axiom,
% 5.42/5.63 ! [X4: rat] :
% 5.42/5.63 ? [X_1: rat] : ( ord_less_rat @ X4 @ X_1 ) ).
% 5.42/5.63
% 5.42/5.63 % linordered_field_no_ub
% 5.42/5.63 thf(fact_467_linorder__neqE__linordered__idom,axiom,
% 5.42/5.63 ! [X2: real,Y2: real] :
% 5.42/5.63 ( ( X2 != Y2 )
% 5.42/5.63 => ( ~ ( ord_less_real @ X2 @ Y2 )
% 5.42/5.63 => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % linorder_neqE_linordered_idom
% 5.42/5.63 thf(fact_468_linorder__neqE__linordered__idom,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat] :
% 5.42/5.63 ( ( X2 != Y2 )
% 5.42/5.63 => ( ~ ( ord_less_rat @ X2 @ Y2 )
% 5.42/5.63 => ( ord_less_rat @ Y2 @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % linorder_neqE_linordered_idom
% 5.42/5.63 thf(fact_469_linorder__neqE__linordered__idom,axiom,
% 5.42/5.63 ! [X2: int,Y2: int] :
% 5.42/5.63 ( ( X2 != Y2 )
% 5.42/5.63 => ( ~ ( ord_less_int @ X2 @ Y2 )
% 5.42/5.63 => ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % linorder_neqE_linordered_idom
% 5.42/5.63 thf(fact_470_height__node,axiom,
% 5.42/5.63 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % height_node
% 5.42/5.63 thf(fact_471_combine__common__factor,axiom,
% 5.42/5.63 ! [A: real,E: real,B: real,C: real] :
% 5.42/5.63 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % combine_common_factor
% 5.42/5.63 thf(fact_472_combine__common__factor,axiom,
% 5.42/5.63 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % combine_common_factor
% 5.42/5.63 thf(fact_473_combine__common__factor,axiom,
% 5.42/5.63 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % combine_common_factor
% 5.42/5.63 thf(fact_474_combine__common__factor,axiom,
% 5.42/5.63 ! [A: int,E: int,B: int,C: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % combine_common_factor
% 5.42/5.63 thf(fact_475_distrib__right,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % distrib_right
% 5.42/5.63 thf(fact_476_distrib__right,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % distrib_right
% 5.42/5.63 thf(fact_477_distrib__right,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % distrib_right
% 5.42/5.63 thf(fact_478_distrib__right,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % distrib_right
% 5.42/5.63 thf(fact_479_distrib__left,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % distrib_left
% 5.42/5.63 thf(fact_480_distrib__left,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % distrib_left
% 5.42/5.63 thf(fact_481_distrib__left,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % distrib_left
% 5.42/5.63 thf(fact_482_distrib__left,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % distrib_left
% 5.42/5.63 thf(fact_483_comm__semiring__class_Odistrib,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % comm_semiring_class.distrib
% 5.42/5.63 thf(fact_484_comm__semiring__class_Odistrib,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % comm_semiring_class.distrib
% 5.42/5.63 thf(fact_485_comm__semiring__class_Odistrib,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % comm_semiring_class.distrib
% 5.42/5.63 thf(fact_486_comm__semiring__class_Odistrib,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % comm_semiring_class.distrib
% 5.42/5.63 thf(fact_487_ring__class_Oring__distribs_I1_J,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ring_class.ring_distribs(1)
% 5.42/5.63 thf(fact_488_ring__class_Oring__distribs_I1_J,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ring_class.ring_distribs(1)
% 5.42/5.63 thf(fact_489_ring__class_Oring__distribs_I1_J,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ring_class.ring_distribs(1)
% 5.42/5.63 thf(fact_490_ring__class_Oring__distribs_I2_J,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ring_class.ring_distribs(2)
% 5.42/5.63 thf(fact_491_ring__class_Oring__distribs_I2_J,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ring_class.ring_distribs(2)
% 5.42/5.63 thf(fact_492_ring__class_Oring__distribs_I2_J,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ring_class.ring_distribs(2)
% 5.42/5.63 thf(fact_493_two__realpow__ge__one,axiom,
% 5.42/5.63 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % two_realpow_ge_one
% 5.42/5.63 thf(fact_494_divide__divide__eq__left_H,axiom,
% 5.42/5.63 ! [A: complex,B: complex,C: complex] :
% 5.42/5.63 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.42/5.63 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_eq_left'
% 5.42/5.63 thf(fact_495_divide__divide__eq__left_H,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.42/5.63 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_eq_left'
% 5.42/5.63 thf(fact_496_divide__divide__eq__left_H,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.42/5.63 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_eq_left'
% 5.42/5.63 thf(fact_497_divide__divide__times__eq,axiom,
% 5.42/5.63 ! [X2: complex,Y2: complex,Z: complex,W: complex] :
% 5.42/5.63 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.42/5.63 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ W ) @ ( times_times_complex @ Y2 @ Z ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_times_eq
% 5.42/5.63 thf(fact_498_divide__divide__times__eq,axiom,
% 5.42/5.63 ! [X2: real,Y2: real,Z: real,W: real] :
% 5.42/5.63 ( ( divide_divide_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 5.42/5.63 = ( divide_divide_real @ ( times_times_real @ X2 @ W ) @ ( times_times_real @ Y2 @ Z ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_times_eq
% 5.42/5.63 thf(fact_499_divide__divide__times__eq,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat,Z: rat,W: rat] :
% 5.42/5.63 ( ( divide_divide_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.42/5.63 = ( divide_divide_rat @ ( times_times_rat @ X2 @ W ) @ ( times_times_rat @ Y2 @ Z ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divide_divide_times_eq
% 5.42/5.63 thf(fact_500_times__divide__times__eq,axiom,
% 5.42/5.63 ! [X2: complex,Y2: complex,Z: complex,W: complex] :
% 5.42/5.63 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.42/5.63 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ Y2 @ W ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % times_divide_times_eq
% 5.42/5.63 thf(fact_501_times__divide__times__eq,axiom,
% 5.42/5.63 ! [X2: real,Y2: real,Z: real,W: real] :
% 5.42/5.63 ( ( times_times_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 5.42/5.63 = ( divide_divide_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y2 @ W ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % times_divide_times_eq
% 5.42/5.63 thf(fact_502_times__divide__times__eq,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat,Z: rat,W: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.42/5.63 = ( divide_divide_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y2 @ W ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % times_divide_times_eq
% 5.42/5.63 thf(fact_503_add__divide__distrib,axiom,
% 5.42/5.63 ! [A: complex,B: complex,C: complex] :
% 5.42/5.63 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_divide_distrib
% 5.42/5.63 thf(fact_504_add__divide__distrib,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_divide_distrib
% 5.42/5.63 thf(fact_505_add__divide__distrib,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_divide_distrib
% 5.42/5.63 thf(fact_506_less__1__mult,axiom,
% 5.42/5.63 ! [M: real,N: real] :
% 5.42/5.63 ( ( ord_less_real @ one_one_real @ M )
% 5.42/5.63 => ( ( ord_less_real @ one_one_real @ N )
% 5.42/5.63 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_1_mult
% 5.42/5.63 thf(fact_507_less__1__mult,axiom,
% 5.42/5.63 ! [M: rat,N: rat] :
% 5.42/5.63 ( ( ord_less_rat @ one_one_rat @ M )
% 5.42/5.63 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.42/5.63 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_1_mult
% 5.42/5.63 thf(fact_508_less__1__mult,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ one_one_nat @ M )
% 5.42/5.63 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.42/5.63 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_1_mult
% 5.42/5.63 thf(fact_509_less__1__mult,axiom,
% 5.42/5.63 ! [M: int,N: int] :
% 5.42/5.63 ( ( ord_less_int @ one_one_int @ M )
% 5.42/5.63 => ( ( ord_less_int @ one_one_int @ N )
% 5.42/5.63 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_1_mult
% 5.42/5.63 thf(fact_510_add__mono1,axiom,
% 5.42/5.63 ! [A: real,B: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono1
% 5.42/5.63 thf(fact_511_add__mono1,axiom,
% 5.42/5.63 ! [A: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono1
% 5.42/5.63 thf(fact_512_add__mono1,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_nat @ A @ B )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono1
% 5.42/5.63 thf(fact_513_add__mono1,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( ord_less_int @ A @ B )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono1
% 5.42/5.63 thf(fact_514_less__add__one,axiom,
% 5.42/5.63 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_one
% 5.42/5.63 thf(fact_515_less__add__one,axiom,
% 5.42/5.63 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_one
% 5.42/5.63 thf(fact_516_less__add__one,axiom,
% 5.42/5.63 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_one
% 5.42/5.63 thf(fact_517_less__add__one,axiom,
% 5.42/5.63 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_one
% 5.42/5.63 thf(fact_518_L2__set__mult__ineq__lemma,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % L2_set_mult_ineq_lemma
% 5.42/5.63 thf(fact_519_four__x__squared,axiom,
% 5.42/5.63 ! [X2: real] :
% 5.42/5.63 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.63 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % four_x_squared
% 5.42/5.63 thf(fact_520_discrete,axiom,
% 5.42/5.63 ( ord_less_nat
% 5.42/5.63 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % discrete
% 5.42/5.63 thf(fact_521_discrete,axiom,
% 5.42/5.63 ( ord_less_int
% 5.42/5.63 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % discrete
% 5.42/5.63 thf(fact_522_less__half__sum,axiom,
% 5.42/5.63 ! [A: real,B: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_half_sum
% 5.42/5.63 thf(fact_523_less__half__sum,axiom,
% 5.42/5.63 ! [A: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_half_sum
% 5.42/5.63 thf(fact_524_gt__half__sum,axiom,
% 5.42/5.63 ! [A: real,B: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % gt_half_sum
% 5.42/5.63 thf(fact_525_gt__half__sum,axiom,
% 5.42/5.63 ! [A: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % gt_half_sum
% 5.42/5.63 thf(fact_526_field__sum__of__halves,axiom,
% 5.42/5.63 ! [X2: real] :
% 5.42/5.63 ( ( plus_plus_real @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.42/5.63 = X2 ) ).
% 5.42/5.63
% 5.42/5.63 % field_sum_of_halves
% 5.42/5.63 thf(fact_527_field__sum__of__halves,axiom,
% 5.42/5.63 ! [X2: rat] :
% 5.42/5.63 ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.42/5.63 = X2 ) ).
% 5.42/5.63
% 5.42/5.63 % field_sum_of_halves
% 5.42/5.63 thf(fact_528__C2_C,axiom,
% 5.42/5.63 ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) ).
% 5.42/5.63
% 5.42/5.63 % "2"
% 5.42/5.63 thf(fact_529__092_060open_062T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_A_ItreeList_A_B_Ahigh_A_Iif_Ax_A_060_Ami_Athen_Ami_Aelse_Ax_J_A_Ideg_Adiv_A2_J_J_A_Ilow_A_Iif_Ax_A_060_Ami_Athen_Ami_Aelse_Ax_J_A_Ideg_Adiv_A2_J_J_A_092_060le_062_A3_092_060close_062,axiom,
% 5.42/5.63 ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ).
% 5.42/5.63
% 5.42/5.63 % \<open>T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t (treeList ! high (if x < mi then mi else x) (deg div 2)) (low (if x < mi then mi else x) (deg div 2)) \<le> 3\<close>
% 5.42/5.63 thf(fact_530_post__member__pre__member,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat,X2: nat,Y2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X2 ) @ Y2 )
% 5.42/5.63 => ( ( vEBT_vebt_member @ T @ Y2 )
% 5.42/5.63 | ( X2 = Y2 ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % post_member_pre_member
% 5.42/5.63 thf(fact_531__C5_OIH_C_I1_J,axiom,
% 5.42/5.63 ! [X4: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.42/5.63 => ( ( vEBT_invar_vebt @ X4 @ na )
% 5.42/5.63 & ! [Xa: nat] : ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ X4 @ Xa ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % "5.IH"(1)
% 5.42/5.63 thf(fact_532__C1_C,axiom,
% 5.42/5.63 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.42/5.63 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % "1"
% 5.42/5.63 thf(fact_533_member__bound,axiom,
% 5.42/5.63 ! [Tree: vEBT_VEBT,X2: nat,N: nat] :
% 5.42/5.63 ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.42/5.63 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.42/5.63 => ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % member_bound
% 5.42/5.63 thf(fact_534_mult__1,axiom,
% 5.42/5.63 ! [A: complex] :
% 5.42/5.63 ( ( times_times_complex @ one_one_complex @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult_1
% 5.42/5.63 thf(fact_535_mult__1,axiom,
% 5.42/5.63 ! [A: real] :
% 5.42/5.63 ( ( times_times_real @ one_one_real @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult_1
% 5.42/5.63 thf(fact_536_mult__1,axiom,
% 5.42/5.63 ! [A: rat] :
% 5.42/5.63 ( ( times_times_rat @ one_one_rat @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult_1
% 5.42/5.63 thf(fact_537_mult__1,axiom,
% 5.42/5.63 ! [A: nat] :
% 5.42/5.63 ( ( times_times_nat @ one_one_nat @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult_1
% 5.42/5.63 thf(fact_538_mult__1,axiom,
% 5.42/5.63 ! [A: int] :
% 5.42/5.63 ( ( times_times_int @ one_one_int @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult_1
% 5.42/5.63 thf(fact_539_mult_Oright__neutral,axiom,
% 5.42/5.63 ! [A: complex] :
% 5.42/5.63 ( ( times_times_complex @ A @ one_one_complex )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.right_neutral
% 5.42/5.63 thf(fact_540_mult_Oright__neutral,axiom,
% 5.42/5.63 ! [A: real] :
% 5.42/5.63 ( ( times_times_real @ A @ one_one_real )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.right_neutral
% 5.42/5.63 thf(fact_541_mult_Oright__neutral,axiom,
% 5.42/5.63 ! [A: rat] :
% 5.42/5.63 ( ( times_times_rat @ A @ one_one_rat )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.right_neutral
% 5.42/5.63 thf(fact_542_mult_Oright__neutral,axiom,
% 5.42/5.63 ! [A: nat] :
% 5.42/5.63 ( ( times_times_nat @ A @ one_one_nat )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.right_neutral
% 5.42/5.63 thf(fact_543_mult_Oright__neutral,axiom,
% 5.42/5.63 ! [A: int] :
% 5.42/5.63 ( ( times_times_int @ A @ one_one_int )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.right_neutral
% 5.42/5.63 thf(fact_544_add__less__cancel__right,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real] :
% 5.42/5.63 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.42/5.63 = ( ord_less_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_cancel_right
% 5.42/5.63 thf(fact_545_add__less__cancel__right,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.42/5.63 = ( ord_less_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_cancel_right
% 5.42/5.63 thf(fact_546_add__less__cancel__right,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.42/5.63 = ( ord_less_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_cancel_right
% 5.42/5.63 thf(fact_547_add__less__cancel__right,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.42/5.63 = ( ord_less_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_cancel_right
% 5.42/5.63 thf(fact_548_add__less__cancel__left,axiom,
% 5.42/5.63 ! [C: real,A: real,B: real] :
% 5.42/5.63 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.42/5.63 = ( ord_less_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_cancel_left
% 5.42/5.63 thf(fact_549_add__less__cancel__left,axiom,
% 5.42/5.63 ! [C: rat,A: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.42/5.63 = ( ord_less_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_cancel_left
% 5.42/5.63 thf(fact_550_add__less__cancel__left,axiom,
% 5.42/5.63 ! [C: nat,A: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.42/5.63 = ( ord_less_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_cancel_left
% 5.42/5.63 thf(fact_551_add__less__cancel__left,axiom,
% 5.42/5.63 ! [C: int,A: int,B: int] :
% 5.42/5.63 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.42/5.63 = ( ord_less_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_cancel_left
% 5.42/5.63 thf(fact_552_add__le__cancel__right,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.42/5.63 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_cancel_right
% 5.42/5.63 thf(fact_553_add__le__cancel__right,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.42/5.63 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_cancel_right
% 5.42/5.63 thf(fact_554_add__le__cancel__right,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.42/5.63 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_cancel_right
% 5.42/5.63 thf(fact_555_add__le__cancel__right,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.42/5.63 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_cancel_right
% 5.42/5.63 thf(fact_556_min__Null__member,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,X2: nat] :
% 5.42/5.63 ( ( vEBT_VEBT_minNull @ T )
% 5.42/5.63 => ~ ( vEBT_vebt_member @ T @ X2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % min_Null_member
% 5.42/5.63 thf(fact_557__C5_Ohyps_C_I4_J,axiom,
% 5.42/5.63 ( deg
% 5.42/5.63 = ( plus_plus_nat @ na @ m ) ) ).
% 5.42/5.63
% 5.42/5.63 % "5.hyps"(4)
% 5.42/5.63 thf(fact_558_bit__split__inv,axiom,
% 5.42/5.63 ! [X2: nat,D2: nat] :
% 5.42/5.63 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X2 @ D2 ) @ ( vEBT_VEBT_low @ X2 @ D2 ) @ D2 )
% 5.42/5.63 = X2 ) ).
% 5.42/5.63
% 5.42/5.63 % bit_split_inv
% 5.42/5.63 thf(fact_559_add__left__cancel,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ( plus_plus_real @ A @ B )
% 5.42/5.63 = ( plus_plus_real @ A @ C ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_cancel
% 5.42/5.63 thf(fact_560_add__left__cancel,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ( plus_plus_rat @ A @ B )
% 5.42/5.63 = ( plus_plus_rat @ A @ C ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_cancel
% 5.42/5.63 thf(fact_561_add__left__cancel,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ( plus_plus_nat @ A @ B )
% 5.42/5.63 = ( plus_plus_nat @ A @ C ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_cancel
% 5.42/5.63 thf(fact_562_add__left__cancel,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ( plus_plus_int @ A @ B )
% 5.42/5.63 = ( plus_plus_int @ A @ C ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_cancel
% 5.42/5.63 thf(fact_563_add__right__cancel,axiom,
% 5.42/5.63 ! [B: real,A: real,C: real] :
% 5.42/5.63 ( ( ( plus_plus_real @ B @ A )
% 5.42/5.63 = ( plus_plus_real @ C @ A ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_cancel
% 5.42/5.63 thf(fact_564_add__right__cancel,axiom,
% 5.42/5.63 ! [B: rat,A: rat,C: rat] :
% 5.42/5.63 ( ( ( plus_plus_rat @ B @ A )
% 5.42/5.63 = ( plus_plus_rat @ C @ A ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_cancel
% 5.42/5.63 thf(fact_565_add__right__cancel,axiom,
% 5.42/5.63 ! [B: nat,A: nat,C: nat] :
% 5.42/5.63 ( ( ( plus_plus_nat @ B @ A )
% 5.42/5.63 = ( plus_plus_nat @ C @ A ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_cancel
% 5.42/5.63 thf(fact_566_add__right__cancel,axiom,
% 5.42/5.63 ! [B: int,A: int,C: int] :
% 5.42/5.63 ( ( ( plus_plus_int @ B @ A )
% 5.42/5.63 = ( plus_plus_int @ C @ A ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_cancel
% 5.42/5.63 thf(fact_567_real__divide__square__eq,axiom,
% 5.42/5.63 ! [R: real,A: real] :
% 5.42/5.63 ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 5.42/5.63 = ( divide_divide_real @ A @ R ) ) ).
% 5.42/5.63
% 5.42/5.63 % real_divide_square_eq
% 5.42/5.63 thf(fact_568_height__compose__child,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % height_compose_child
% 5.42/5.63 thf(fact_569_add__le__cancel__left,axiom,
% 5.42/5.63 ! [C: real,A: real,B: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.42/5.63 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_cancel_left
% 5.42/5.63 thf(fact_570_add__le__cancel__left,axiom,
% 5.42/5.63 ! [C: rat,A: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.42/5.63 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_cancel_left
% 5.42/5.63 thf(fact_571_add__le__cancel__left,axiom,
% 5.42/5.63 ! [C: nat,A: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.42/5.63 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_cancel_left
% 5.42/5.63 thf(fact_572_add__le__cancel__left,axiom,
% 5.42/5.63 ! [C: int,A: int,B: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.42/5.63 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_cancel_left
% 5.42/5.63 thf(fact_573_low__inv,axiom,
% 5.42/5.63 ! [X2: nat,N: nat,Y2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.42/5.63 = X2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % low_inv
% 5.42/5.63 thf(fact_574_member__correct,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.42/5.63 = ( member_nat @ X2 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % member_correct
% 5.42/5.63 thf(fact_575__C5_Ohyps_C_I3_J,axiom,
% 5.42/5.63 ( m
% 5.42/5.63 = ( suc @ na ) ) ).
% 5.42/5.63
% 5.42/5.63 % "5.hyps"(3)
% 5.42/5.63 thf(fact_576__C5_Ohyps_C_I2_J,axiom,
% 5.42/5.63 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.42/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.42/5.63
% 5.42/5.63 % "5.hyps"(2)
% 5.42/5.63 thf(fact_577__C5_Ohyps_C_I6_J,axiom,
% 5.42/5.63 ( ( mi = ma )
% 5.42/5.63 => ! [X4: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.42/5.63 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % "5.hyps"(6)
% 5.42/5.63 thf(fact_578__C5_Ohyps_C_I5_J,axiom,
% 5.42/5.63 ! [I3: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.42/5.63 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I3 ) @ X5 ) )
% 5.42/5.63 = ( vEBT_V8194947554948674370ptions @ summary @ I3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % "5.hyps"(5)
% 5.42/5.63 thf(fact_579__C5_Ohyps_C_I9_J,axiom,
% 5.42/5.63 ( ( mi != ma )
% 5.42/5.63 => ! [I3: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.42/5.63 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.42/5.63 = I3 )
% 5.42/5.63 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I3 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.42/5.63 & ! [X4: nat] :
% 5.42/5.63 ( ( ( ( vEBT_VEBT_high @ X4 @ na )
% 5.42/5.63 = I3 )
% 5.42/5.63 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ na ) ) )
% 5.42/5.63 => ( ( ord_less_nat @ mi @ X4 )
% 5.42/5.63 & ( ord_less_eq_nat @ X4 @ ma ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % "5.hyps"(9)
% 5.42/5.63 thf(fact_580_real__arch__pow,axiom,
% 5.42/5.63 ! [X2: real,Y2: real] :
% 5.42/5.63 ( ( ord_less_real @ one_one_real @ X2 )
% 5.42/5.63 => ? [N3: nat] : ( ord_less_real @ Y2 @ ( power_power_real @ X2 @ N3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % real_arch_pow
% 5.42/5.63 thf(fact_581_less__eq__real__def,axiom,
% 5.42/5.63 ( ord_less_eq_real
% 5.42/5.63 = ( ^ [X: real,Y: real] :
% 5.42/5.63 ( ( ord_less_real @ X @ Y )
% 5.42/5.63 | ( X = Y ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_eq_real_def
% 5.42/5.63 thf(fact_582_complete__real,axiom,
% 5.42/5.63 ! [S2: set_real] :
% 5.42/5.63 ( ? [X4: real] : ( member_real @ X4 @ S2 )
% 5.42/5.63 => ( ? [Z2: real] :
% 5.42/5.63 ! [X3: real] :
% 5.42/5.63 ( ( member_real @ X3 @ S2 )
% 5.42/5.63 => ( ord_less_eq_real @ X3 @ Z2 ) )
% 5.42/5.63 => ? [Y3: real] :
% 5.42/5.63 ( ! [X4: real] :
% 5.42/5.63 ( ( member_real @ X4 @ S2 )
% 5.42/5.63 => ( ord_less_eq_real @ X4 @ Y3 ) )
% 5.42/5.63 & ! [Z2: real] :
% 5.42/5.63 ( ! [X3: real] :
% 5.42/5.63 ( ( member_real @ X3 @ S2 )
% 5.42/5.63 => ( ord_less_eq_real @ X3 @ Z2 ) )
% 5.42/5.63 => ( ord_less_eq_real @ Y3 @ Z2 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % complete_real
% 5.42/5.63 thf(fact_583_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.42/5.63 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ab_semigroup_mult_class.mult_ac(1)
% 5.42/5.63 thf(fact_584_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.42/5.63 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ab_semigroup_mult_class.mult_ac(1)
% 5.42/5.63 thf(fact_585_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.42/5.63 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ab_semigroup_mult_class.mult_ac(1)
% 5.42/5.63 thf(fact_586_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.42/5.63 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ab_semigroup_mult_class.mult_ac(1)
% 5.42/5.63 thf(fact_587_mult_Oassoc,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.42/5.63 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.assoc
% 5.42/5.63 thf(fact_588_mult_Oassoc,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.42/5.63 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.assoc
% 5.42/5.63 thf(fact_589_mult_Oassoc,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.42/5.63 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.assoc
% 5.42/5.63 thf(fact_590_mult_Oassoc,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.42/5.63 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.assoc
% 5.42/5.63 thf(fact_591_mult_Ocommute,axiom,
% 5.42/5.63 ( times_times_real
% 5.42/5.63 = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.commute
% 5.42/5.63 thf(fact_592_mult_Ocommute,axiom,
% 5.42/5.63 ( times_times_rat
% 5.42/5.63 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ B2 @ A3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.commute
% 5.42/5.63 thf(fact_593_mult_Ocommute,axiom,
% 5.42/5.63 ( times_times_nat
% 5.42/5.63 = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.commute
% 5.42/5.63 thf(fact_594_mult_Ocommute,axiom,
% 5.42/5.63 ( times_times_int
% 5.42/5.63 = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.commute
% 5.42/5.63 thf(fact_595_mult_Oleft__commute,axiom,
% 5.42/5.63 ! [B: real,A: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.42/5.63 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.left_commute
% 5.42/5.63 thf(fact_596_mult_Oleft__commute,axiom,
% 5.42/5.63 ! [B: rat,A: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.42/5.63 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.left_commute
% 5.42/5.63 thf(fact_597_mult_Oleft__commute,axiom,
% 5.42/5.63 ! [B: nat,A: nat,C: nat] :
% 5.42/5.63 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.42/5.63 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.left_commute
% 5.42/5.63 thf(fact_598_mult_Oleft__commute,axiom,
% 5.42/5.63 ! [B: int,A: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.42/5.63 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult.left_commute
% 5.42/5.63 thf(fact_599_one__reorient,axiom,
% 5.42/5.63 ! [X2: complex] :
% 5.42/5.63 ( ( one_one_complex = X2 )
% 5.42/5.63 = ( X2 = one_one_complex ) ) ).
% 5.42/5.63
% 5.42/5.63 % one_reorient
% 5.42/5.63 thf(fact_600_one__reorient,axiom,
% 5.42/5.63 ! [X2: real] :
% 5.42/5.63 ( ( one_one_real = X2 )
% 5.42/5.63 = ( X2 = one_one_real ) ) ).
% 5.42/5.63
% 5.42/5.63 % one_reorient
% 5.42/5.63 thf(fact_601_one__reorient,axiom,
% 5.42/5.63 ! [X2: rat] :
% 5.42/5.63 ( ( one_one_rat = X2 )
% 5.42/5.63 = ( X2 = one_one_rat ) ) ).
% 5.42/5.63
% 5.42/5.63 % one_reorient
% 5.42/5.63 thf(fact_602_one__reorient,axiom,
% 5.42/5.63 ! [X2: nat] :
% 5.42/5.63 ( ( one_one_nat = X2 )
% 5.42/5.63 = ( X2 = one_one_nat ) ) ).
% 5.42/5.63
% 5.42/5.63 % one_reorient
% 5.42/5.63 thf(fact_603_one__reorient,axiom,
% 5.42/5.63 ! [X2: int] :
% 5.42/5.63 ( ( one_one_int = X2 )
% 5.42/5.63 = ( X2 = one_one_int ) ) ).
% 5.42/5.63
% 5.42/5.63 % one_reorient
% 5.42/5.63 thf(fact_604_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ab_semigroup_add_class.add_ac(1)
% 5.42/5.63 thf(fact_605_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ab_semigroup_add_class.add_ac(1)
% 5.42/5.63 thf(fact_606_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ab_semigroup_add_class.add_ac(1)
% 5.42/5.63 thf(fact_607_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ab_semigroup_add_class.add_ac(1)
% 5.42/5.63 thf(fact_608_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.42/5.63 ! [I: real,J: real,K: real,L2: real] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ( plus_plus_real @ I @ K )
% 5.42/5.63 = ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(4)
% 5.42/5.63 thf(fact_609_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.42/5.63 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ( plus_plus_rat @ I @ K )
% 5.42/5.63 = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(4)
% 5.42/5.63 thf(fact_610_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ( plus_plus_nat @ I @ K )
% 5.42/5.63 = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(4)
% 5.42/5.63 thf(fact_611_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.42/5.63 ! [I: int,J: int,K: int,L2: int] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ( plus_plus_int @ I @ K )
% 5.42/5.63 = ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(4)
% 5.42/5.63 thf(fact_612_group__cancel_Oadd1,axiom,
% 5.42/5.63 ! [A2: real,K: real,A: real,B: real] :
% 5.42/5.63 ( ( A2
% 5.42/5.63 = ( plus_plus_real @ K @ A ) )
% 5.42/5.63 => ( ( plus_plus_real @ A2 @ B )
% 5.42/5.63 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.add1
% 5.42/5.63 thf(fact_613_group__cancel_Oadd1,axiom,
% 5.42/5.63 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.42/5.63 ( ( A2
% 5.42/5.63 = ( plus_plus_rat @ K @ A ) )
% 5.42/5.63 => ( ( plus_plus_rat @ A2 @ B )
% 5.42/5.63 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.add1
% 5.42/5.63 thf(fact_614_group__cancel_Oadd1,axiom,
% 5.42/5.63 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.42/5.63 ( ( A2
% 5.42/5.63 = ( plus_plus_nat @ K @ A ) )
% 5.42/5.63 => ( ( plus_plus_nat @ A2 @ B )
% 5.42/5.63 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.add1
% 5.42/5.63 thf(fact_615_group__cancel_Oadd1,axiom,
% 5.42/5.63 ! [A2: int,K: int,A: int,B: int] :
% 5.42/5.63 ( ( A2
% 5.42/5.63 = ( plus_plus_int @ K @ A ) )
% 5.42/5.63 => ( ( plus_plus_int @ A2 @ B )
% 5.42/5.63 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.add1
% 5.42/5.63 thf(fact_616_group__cancel_Oadd2,axiom,
% 5.42/5.63 ! [B3: real,K: real,B: real,A: real] :
% 5.42/5.63 ( ( B3
% 5.42/5.63 = ( plus_plus_real @ K @ B ) )
% 5.42/5.63 => ( ( plus_plus_real @ A @ B3 )
% 5.42/5.63 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.add2
% 5.42/5.63 thf(fact_617_group__cancel_Oadd2,axiom,
% 5.42/5.63 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.42/5.63 ( ( B3
% 5.42/5.63 = ( plus_plus_rat @ K @ B ) )
% 5.42/5.63 => ( ( plus_plus_rat @ A @ B3 )
% 5.42/5.63 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.add2
% 5.42/5.63 thf(fact_618_group__cancel_Oadd2,axiom,
% 5.42/5.63 ! [B3: nat,K: nat,B: nat,A: nat] :
% 5.42/5.63 ( ( B3
% 5.42/5.63 = ( plus_plus_nat @ K @ B ) )
% 5.42/5.63 => ( ( plus_plus_nat @ A @ B3 )
% 5.42/5.63 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.add2
% 5.42/5.63 thf(fact_619_group__cancel_Oadd2,axiom,
% 5.42/5.63 ! [B3: int,K: int,B: int,A: int] :
% 5.42/5.63 ( ( B3
% 5.42/5.63 = ( plus_plus_int @ K @ B ) )
% 5.42/5.63 => ( ( plus_plus_int @ A @ B3 )
% 5.42/5.63 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.add2
% 5.42/5.63 thf(fact_620_add_Oassoc,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.assoc
% 5.42/5.63 thf(fact_621_add_Oassoc,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.assoc
% 5.42/5.63 thf(fact_622_add_Oassoc,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.assoc
% 5.42/5.63 thf(fact_623_add_Oassoc,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.42/5.63 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.assoc
% 5.42/5.63 thf(fact_624_add_Oleft__cancel,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ( plus_plus_real @ A @ B )
% 5.42/5.63 = ( plus_plus_real @ A @ C ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.left_cancel
% 5.42/5.63 thf(fact_625_add_Oleft__cancel,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ( plus_plus_rat @ A @ B )
% 5.42/5.63 = ( plus_plus_rat @ A @ C ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.left_cancel
% 5.42/5.63 thf(fact_626_add_Oleft__cancel,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ( plus_plus_int @ A @ B )
% 5.42/5.63 = ( plus_plus_int @ A @ C ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.left_cancel
% 5.42/5.63 thf(fact_627_add_Oright__cancel,axiom,
% 5.42/5.63 ! [B: real,A: real,C: real] :
% 5.42/5.63 ( ( ( plus_plus_real @ B @ A )
% 5.42/5.63 = ( plus_plus_real @ C @ A ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.right_cancel
% 5.42/5.63 thf(fact_628_add_Oright__cancel,axiom,
% 5.42/5.63 ! [B: rat,A: rat,C: rat] :
% 5.42/5.63 ( ( ( plus_plus_rat @ B @ A )
% 5.42/5.63 = ( plus_plus_rat @ C @ A ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.right_cancel
% 5.42/5.63 thf(fact_629_add_Oright__cancel,axiom,
% 5.42/5.63 ! [B: int,A: int,C: int] :
% 5.42/5.63 ( ( ( plus_plus_int @ B @ A )
% 5.42/5.63 = ( plus_plus_int @ C @ A ) )
% 5.42/5.63 = ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.right_cancel
% 5.42/5.63 thf(fact_630_add_Ocommute,axiom,
% 5.42/5.63 ( plus_plus_real
% 5.42/5.63 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.commute
% 5.42/5.63 thf(fact_631_add_Ocommute,axiom,
% 5.42/5.63 ( plus_plus_rat
% 5.42/5.63 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.commute
% 5.42/5.63 thf(fact_632_add_Ocommute,axiom,
% 5.42/5.63 ( plus_plus_nat
% 5.42/5.63 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.commute
% 5.42/5.63 thf(fact_633_add_Ocommute,axiom,
% 5.42/5.63 ( plus_plus_int
% 5.42/5.63 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.commute
% 5.42/5.63 thf(fact_634_add_Oleft__commute,axiom,
% 5.42/5.63 ! [B: real,A: real,C: real] :
% 5.42/5.63 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.42/5.63 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.left_commute
% 5.42/5.63 thf(fact_635_add_Oleft__commute,axiom,
% 5.42/5.63 ! [B: rat,A: rat,C: rat] :
% 5.42/5.63 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.42/5.63 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.left_commute
% 5.42/5.63 thf(fact_636_add_Oleft__commute,axiom,
% 5.42/5.63 ! [B: nat,A: nat,C: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.42/5.63 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.left_commute
% 5.42/5.63 thf(fact_637_add_Oleft__commute,axiom,
% 5.42/5.63 ! [B: int,A: int,C: int] :
% 5.42/5.63 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.42/5.63 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add.left_commute
% 5.42/5.63 thf(fact_638_add__left__imp__eq,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ( plus_plus_real @ A @ B )
% 5.42/5.63 = ( plus_plus_real @ A @ C ) )
% 5.42/5.63 => ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_imp_eq
% 5.42/5.63 thf(fact_639_add__left__imp__eq,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ( plus_plus_rat @ A @ B )
% 5.42/5.63 = ( plus_plus_rat @ A @ C ) )
% 5.42/5.63 => ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_imp_eq
% 5.42/5.63 thf(fact_640_add__left__imp__eq,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ( plus_plus_nat @ A @ B )
% 5.42/5.63 = ( plus_plus_nat @ A @ C ) )
% 5.42/5.63 => ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_imp_eq
% 5.42/5.63 thf(fact_641_add__left__imp__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ( plus_plus_int @ A @ B )
% 5.42/5.63 = ( plus_plus_int @ A @ C ) )
% 5.42/5.63 => ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_imp_eq
% 5.42/5.63 thf(fact_642_add__right__imp__eq,axiom,
% 5.42/5.63 ! [B: real,A: real,C: real] :
% 5.42/5.63 ( ( ( plus_plus_real @ B @ A )
% 5.42/5.63 = ( plus_plus_real @ C @ A ) )
% 5.42/5.63 => ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_imp_eq
% 5.42/5.63 thf(fact_643_add__right__imp__eq,axiom,
% 5.42/5.63 ! [B: rat,A: rat,C: rat] :
% 5.42/5.63 ( ( ( plus_plus_rat @ B @ A )
% 5.42/5.63 = ( plus_plus_rat @ C @ A ) )
% 5.42/5.63 => ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_imp_eq
% 5.42/5.63 thf(fact_644_add__right__imp__eq,axiom,
% 5.42/5.63 ! [B: nat,A: nat,C: nat] :
% 5.42/5.63 ( ( ( plus_plus_nat @ B @ A )
% 5.42/5.63 = ( plus_plus_nat @ C @ A ) )
% 5.42/5.63 => ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_imp_eq
% 5.42/5.63 thf(fact_645_add__right__imp__eq,axiom,
% 5.42/5.63 ! [B: int,A: int,C: int] :
% 5.42/5.63 ( ( ( plus_plus_int @ B @ A )
% 5.42/5.63 = ( plus_plus_int @ C @ A ) )
% 5.42/5.63 => ( B = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_imp_eq
% 5.42/5.63 thf(fact_646_minNull__bound,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 5.42/5.63
% 5.42/5.63 % minNull_bound
% 5.42/5.63 thf(fact_647_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I5_J,axiom,
% 5.42/5.63 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.42/5.63 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) )
% 5.42/5.63 = one_one_nat ) ).
% 5.42/5.63
% 5.42/5.63 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(5)
% 5.42/5.63 thf(fact_648_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.42/5.63 ! [I: real,J: real,K: real,L2: real] :
% 5.42/5.63 ( ( ( ord_less_eq_real @ I @ J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(3)
% 5.42/5.63 thf(fact_649_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.42/5.63 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.42/5.63 ( ( ( ord_less_eq_rat @ I @ J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(3)
% 5.42/5.63 thf(fact_650_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.63 ( ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(3)
% 5.42/5.63 thf(fact_651_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.42/5.63 ! [I: int,J: int,K: int,L2: int] :
% 5.42/5.63 ( ( ( ord_less_eq_int @ I @ J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(3)
% 5.42/5.63 thf(fact_652_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.42/5.63 ! [I: real,J: real,K: real,L2: real] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( ord_less_eq_real @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(2)
% 5.42/5.63 thf(fact_653_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.42/5.63 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(2)
% 5.42/5.63 thf(fact_654_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(2)
% 5.42/5.63 thf(fact_655_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.42/5.63 ! [I: int,J: int,K: int,L2: int] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( ord_less_eq_int @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(2)
% 5.42/5.63 thf(fact_656_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.42/5.63 ! [I: real,J: real,K: real,L2: real] :
% 5.42/5.63 ( ( ( ord_less_eq_real @ I @ J )
% 5.42/5.63 & ( ord_less_eq_real @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(1)
% 5.42/5.63 thf(fact_657_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.42/5.63 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.42/5.63 ( ( ( ord_less_eq_rat @ I @ J )
% 5.42/5.63 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(1)
% 5.42/5.63 thf(fact_658_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.63 ( ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(1)
% 5.42/5.63 thf(fact_659_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.42/5.63 ! [I: int,J: int,K: int,L2: int] :
% 5.42/5.63 ( ( ( ord_less_eq_int @ I @ J )
% 5.42/5.63 & ( ord_less_eq_int @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_semiring(1)
% 5.42/5.63 thf(fact_660_add__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real,D2: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_real @ C @ D2 )
% 5.42/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono
% 5.42/5.63 thf(fact_661_add__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.42/5.63 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono
% 5.42/5.63 thf(fact_662_add__mono,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.42/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono
% 5.42/5.63 thf(fact_663_add__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int,D2: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_int @ C @ D2 )
% 5.42/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono
% 5.42/5.63 thf(fact_664_add__left__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.42/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_mono
% 5.42/5.63 thf(fact_665_add__left__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.63 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_mono
% 5.42/5.63 thf(fact_666_add__left__mono,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_mono
% 5.42/5.63 thf(fact_667_add__left__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_left_mono
% 5.42/5.63 thf(fact_668_less__eqE,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ~ ! [C2: nat] :
% 5.42/5.63 ( B
% 5.42/5.63 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_eqE
% 5.42/5.63 thf(fact_669_add__right__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.42/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_mono
% 5.42/5.63 thf(fact_670_add__right__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.63 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_mono
% 5.42/5.63 thf(fact_671_add__right__mono,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_mono
% 5.42/5.63 thf(fact_672_add__right__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_right_mono
% 5.42/5.63 thf(fact_673_le__iff__add,axiom,
% 5.42/5.63 ( ord_less_eq_nat
% 5.42/5.63 = ( ^ [A3: nat,B2: nat] :
% 5.42/5.63 ? [C3: nat] :
% 5.42/5.63 ( B2
% 5.42/5.63 = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_iff_add
% 5.42/5.63 thf(fact_674_add__le__imp__le__left,axiom,
% 5.42/5.63 ! [C: real,A: real,B: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.42/5.63 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_left
% 5.42/5.63 thf(fact_675_add__le__imp__le__left,axiom,
% 5.42/5.63 ! [C: rat,A: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.42/5.63 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_left
% 5.42/5.63 thf(fact_676_add__le__imp__le__left,axiom,
% 5.42/5.63 ! [C: nat,A: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.42/5.63 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_left
% 5.42/5.63 thf(fact_677_add__le__imp__le__left,axiom,
% 5.42/5.63 ! [C: int,A: int,B: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.42/5.63 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_left
% 5.42/5.63 thf(fact_678_add__le__imp__le__right,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.42/5.63 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_right
% 5.42/5.63 thf(fact_679_add__le__imp__le__right,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.42/5.63 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_right
% 5.42/5.63 thf(fact_680_add__le__imp__le__right,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.42/5.63 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_right
% 5.42/5.63 thf(fact_681_add__le__imp__le__right,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.42/5.63 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_right
% 5.42/5.63 thf(fact_682_add__mono__thms__linordered__field_I5_J,axiom,
% 5.42/5.63 ! [I: real,J: real,K: real,L2: real] :
% 5.42/5.63 ( ( ( ord_less_real @ I @ J )
% 5.42/5.63 & ( ord_less_real @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(5)
% 5.42/5.63 thf(fact_683_add__mono__thms__linordered__field_I5_J,axiom,
% 5.42/5.63 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.42/5.63 ( ( ( ord_less_rat @ I @ J )
% 5.42/5.63 & ( ord_less_rat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(5)
% 5.42/5.63 thf(fact_684_add__mono__thms__linordered__field_I5_J,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.63 ( ( ( ord_less_nat @ I @ J )
% 5.42/5.63 & ( ord_less_nat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(5)
% 5.42/5.63 thf(fact_685_add__mono__thms__linordered__field_I5_J,axiom,
% 5.42/5.63 ! [I: int,J: int,K: int,L2: int] :
% 5.42/5.63 ( ( ( ord_less_int @ I @ J )
% 5.42/5.63 & ( ord_less_int @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(5)
% 5.42/5.63 thf(fact_686_add__mono__thms__linordered__field_I2_J,axiom,
% 5.42/5.63 ! [I: real,J: real,K: real,L2: real] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( ord_less_real @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(2)
% 5.42/5.63 thf(fact_687_add__mono__thms__linordered__field_I2_J,axiom,
% 5.42/5.63 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( ord_less_rat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(2)
% 5.42/5.63 thf(fact_688_add__mono__thms__linordered__field_I2_J,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( ord_less_nat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(2)
% 5.42/5.63 thf(fact_689_add__mono__thms__linordered__field_I2_J,axiom,
% 5.42/5.63 ! [I: int,J: int,K: int,L2: int] :
% 5.42/5.63 ( ( ( I = J )
% 5.42/5.63 & ( ord_less_int @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(2)
% 5.42/5.63 thf(fact_690_add__mono__thms__linordered__field_I1_J,axiom,
% 5.42/5.63 ! [I: real,J: real,K: real,L2: real] :
% 5.42/5.63 ( ( ( ord_less_real @ I @ J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(1)
% 5.42/5.63 thf(fact_691_add__mono__thms__linordered__field_I1_J,axiom,
% 5.42/5.63 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.42/5.63 ( ( ( ord_less_rat @ I @ J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(1)
% 5.42/5.63 thf(fact_692_add__mono__thms__linordered__field_I1_J,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.63 ( ( ( ord_less_nat @ I @ J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(1)
% 5.42/5.63 thf(fact_693_add__mono__thms__linordered__field_I1_J,axiom,
% 5.42/5.63 ! [I: int,J: int,K: int,L2: int] :
% 5.42/5.63 ( ( ( ord_less_int @ I @ J )
% 5.42/5.63 & ( K = L2 ) )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(1)
% 5.42/5.63 thf(fact_694_add__strict__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real,D2: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ( ord_less_real @ C @ D2 )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_mono
% 5.42/5.63 thf(fact_695_add__strict__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ( ord_less_rat @ C @ D2 )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_mono
% 5.42/5.63 thf(fact_696_add__strict__mono,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ A @ B )
% 5.42/5.63 => ( ( ord_less_nat @ C @ D2 )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_mono
% 5.42/5.63 thf(fact_697_add__strict__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int,D2: int] :
% 5.42/5.63 ( ( ord_less_int @ A @ B )
% 5.42/5.63 => ( ( ord_less_int @ C @ D2 )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_mono
% 5.42/5.63 thf(fact_698_add__strict__left__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_left_mono
% 5.42/5.63 thf(fact_699_add__strict__left__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_left_mono
% 5.42/5.63 thf(fact_700_add__strict__left__mono,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_nat @ A @ B )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_left_mono
% 5.42/5.63 thf(fact_701_add__strict__left__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ord_less_int @ A @ B )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_left_mono
% 5.42/5.63 thf(fact_702_add__strict__right__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_right_mono
% 5.42/5.63 thf(fact_703_add__strict__right__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_right_mono
% 5.42/5.63 thf(fact_704_add__strict__right__mono,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_nat @ A @ B )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_right_mono
% 5.42/5.63 thf(fact_705_add__strict__right__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ord_less_int @ A @ B )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_strict_right_mono
% 5.42/5.63 thf(fact_706_add__less__imp__less__left,axiom,
% 5.42/5.63 ! [C: real,A: real,B: real] :
% 5.42/5.63 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.42/5.63 => ( ord_less_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_imp_less_left
% 5.42/5.63 thf(fact_707_add__less__imp__less__left,axiom,
% 5.42/5.63 ! [C: rat,A: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.42/5.63 => ( ord_less_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_imp_less_left
% 5.42/5.63 thf(fact_708_add__less__imp__less__left,axiom,
% 5.42/5.63 ! [C: nat,A: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.42/5.63 => ( ord_less_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_imp_less_left
% 5.42/5.63 thf(fact_709_add__less__imp__less__left,axiom,
% 5.42/5.63 ! [C: int,A: int,B: int] :
% 5.42/5.63 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.42/5.63 => ( ord_less_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_imp_less_left
% 5.42/5.63 thf(fact_710_add__less__imp__less__right,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real] :
% 5.42/5.63 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.42/5.63 => ( ord_less_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_imp_less_right
% 5.42/5.63 thf(fact_711_add__less__imp__less__right,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.42/5.63 => ( ord_less_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_imp_less_right
% 5.42/5.63 thf(fact_712_add__less__imp__less__right,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.42/5.63 => ( ord_less_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_imp_less_right
% 5.42/5.63 thf(fact_713_add__less__imp__less__right,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.42/5.63 => ( ord_less_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_imp_less_right
% 5.42/5.63 thf(fact_714_comm__monoid__mult__class_Omult__1,axiom,
% 5.42/5.63 ! [A: complex] :
% 5.42/5.63 ( ( times_times_complex @ one_one_complex @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % comm_monoid_mult_class.mult_1
% 5.42/5.63 thf(fact_715_comm__monoid__mult__class_Omult__1,axiom,
% 5.42/5.63 ! [A: real] :
% 5.42/5.63 ( ( times_times_real @ one_one_real @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % comm_monoid_mult_class.mult_1
% 5.42/5.63 thf(fact_716_comm__monoid__mult__class_Omult__1,axiom,
% 5.42/5.63 ! [A: rat] :
% 5.42/5.63 ( ( times_times_rat @ one_one_rat @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % comm_monoid_mult_class.mult_1
% 5.42/5.63 thf(fact_717_comm__monoid__mult__class_Omult__1,axiom,
% 5.42/5.63 ! [A: nat] :
% 5.42/5.63 ( ( times_times_nat @ one_one_nat @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % comm_monoid_mult_class.mult_1
% 5.42/5.63 thf(fact_718_comm__monoid__mult__class_Omult__1,axiom,
% 5.42/5.63 ! [A: int] :
% 5.42/5.63 ( ( times_times_int @ one_one_int @ A )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % comm_monoid_mult_class.mult_1
% 5.42/5.63 thf(fact_719_mult_Ocomm__neutral,axiom,
% 5.42/5.63 ! [A: complex] :
% 5.42/5.63 ( ( times_times_complex @ A @ one_one_complex )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.comm_neutral
% 5.42/5.63 thf(fact_720_mult_Ocomm__neutral,axiom,
% 5.42/5.63 ! [A: real] :
% 5.42/5.63 ( ( times_times_real @ A @ one_one_real )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.comm_neutral
% 5.42/5.63 thf(fact_721_mult_Ocomm__neutral,axiom,
% 5.42/5.63 ! [A: rat] :
% 5.42/5.63 ( ( times_times_rat @ A @ one_one_rat )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.comm_neutral
% 5.42/5.63 thf(fact_722_mult_Ocomm__neutral,axiom,
% 5.42/5.63 ! [A: nat] :
% 5.42/5.63 ( ( times_times_nat @ A @ one_one_nat )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.comm_neutral
% 5.42/5.63 thf(fact_723_mult_Ocomm__neutral,axiom,
% 5.42/5.63 ! [A: int] :
% 5.42/5.63 ( ( times_times_int @ A @ one_one_int )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult.comm_neutral
% 5.42/5.63 thf(fact_724_add__mono__thms__linordered__field_I4_J,axiom,
% 5.42/5.63 ! [I: real,J: real,K: real,L2: real] :
% 5.42/5.63 ( ( ( ord_less_eq_real @ I @ J )
% 5.42/5.63 & ( ord_less_real @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(4)
% 5.42/5.63 thf(fact_725_add__mono__thms__linordered__field_I4_J,axiom,
% 5.42/5.63 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.42/5.63 ( ( ( ord_less_eq_rat @ I @ J )
% 5.42/5.63 & ( ord_less_rat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(4)
% 5.42/5.63 thf(fact_726_add__mono__thms__linordered__field_I4_J,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.63 ( ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 & ( ord_less_nat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(4)
% 5.42/5.63 thf(fact_727_add__mono__thms__linordered__field_I4_J,axiom,
% 5.42/5.63 ! [I: int,J: int,K: int,L2: int] :
% 5.42/5.63 ( ( ( ord_less_eq_int @ I @ J )
% 5.42/5.63 & ( ord_less_int @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(4)
% 5.42/5.63 thf(fact_728_add__mono__thms__linordered__field_I3_J,axiom,
% 5.42/5.63 ! [I: real,J: real,K: real,L2: real] :
% 5.42/5.63 ( ( ( ord_less_real @ I @ J )
% 5.42/5.63 & ( ord_less_eq_real @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(3)
% 5.42/5.63 thf(fact_729_add__mono__thms__linordered__field_I3_J,axiom,
% 5.42/5.63 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.42/5.63 ( ( ( ord_less_rat @ I @ J )
% 5.42/5.63 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(3)
% 5.42/5.63 thf(fact_730_add__mono__thms__linordered__field_I3_J,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.42/5.63 ( ( ( ord_less_nat @ I @ J )
% 5.42/5.63 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(3)
% 5.42/5.63 thf(fact_731_add__mono__thms__linordered__field_I3_J,axiom,
% 5.42/5.63 ! [I: int,J: int,K: int,L2: int] :
% 5.42/5.63 ( ( ( ord_less_int @ I @ J )
% 5.42/5.63 & ( ord_less_eq_int @ K @ L2 ) )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_mono_thms_linordered_field(3)
% 5.42/5.63 thf(fact_732_add__le__less__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real,D2: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.42/5.63 => ( ( ord_less_real @ C @ D2 )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_less_mono
% 5.42/5.63 thf(fact_733_add__le__less__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.63 => ( ( ord_less_rat @ C @ D2 )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_less_mono
% 5.42/5.63 thf(fact_734_add__le__less__mono,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( ord_less_nat @ C @ D2 )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_less_mono
% 5.42/5.63 thf(fact_735_add__le__less__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int,D2: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.63 => ( ( ord_less_int @ C @ D2 )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_less_mono
% 5.42/5.63 thf(fact_736_add__less__le__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real,D2: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_real @ C @ D2 )
% 5.42/5.63 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_le_mono
% 5.42/5.63 thf(fact_737_add__less__le__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.42/5.63 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_le_mono
% 5.42/5.63 thf(fact_738_add__less__le__mono,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.42/5.63 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_le_mono
% 5.42/5.63 thf(fact_739_add__less__le__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int,D2: int] :
% 5.42/5.63 ( ( ord_less_int @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_int @ C @ D2 )
% 5.42/5.63 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_less_le_mono
% 5.42/5.63 thf(fact_740__C0_C,axiom,
% 5.42/5.63 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.42/5.63 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.42/5.63 @ ( if_nat
% 5.42/5.63 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 5.42/5.63 & ~ ( ( xa = mi )
% 5.42/5.63 | ( xa = ma ) ) )
% 5.42/5.63 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.42/5.63 @ one_one_nat ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % "0"
% 5.42/5.63 thf(fact_741_member__inv,axiom,
% 5.42/5.63 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.42/5.63 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.63 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.63 & ( ( X2 = Mi )
% 5.42/5.63 | ( X2 = Ma )
% 5.42/5.63 | ( ( ord_less_nat @ X2 @ Ma )
% 5.42/5.63 & ( ord_less_nat @ Mi @ X2 )
% 5.42/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.63 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % member_inv
% 5.42/5.63 thf(fact_742_both__member__options__from__complete__tree__to__child,axiom,
% 5.42/5.63 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.42/5.63 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.63 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.63 | ( X2 = Mi )
% 5.42/5.63 | ( X2 = Ma ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % both_member_options_from_complete_tree_to_child
% 5.42/5.63 thf(fact_743_both__member__options__ding,axiom,
% 5.42/5.63 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.42/5.63 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.42/5.63 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.63 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % both_member_options_ding
% 5.42/5.63 thf(fact_744_set__n__deg__not__0,axiom,
% 5.42/5.63 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 5.42/5.63 ( ! [X3: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.63 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.42/5.63 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.42/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % set_n_deg_not_0
% 5.42/5.63 thf(fact_745_power__minus__is__div,axiom,
% 5.42/5.63 ! [B: nat,A: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ B @ A )
% 5.42/5.63 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.42/5.63 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_minus_is_div
% 5.42/5.63 thf(fact_746_valid__insert__both__member__options__add,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X2 ) @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % valid_insert_both_member_options_add
% 5.42/5.63 thf(fact_747_valid__insert__both__member__options__pres,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat,X2: nat,Y2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.42/5.63 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y2 ) @ X2 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % valid_insert_both_member_options_pres
% 5.42/5.63 thf(fact_748_member__bound__height,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % member_bound_height
% 5.42/5.63 thf(fact_749_low__def,axiom,
% 5.42/5.63 ( vEBT_VEBT_low
% 5.42/5.63 = ( ^ [X: nat,N2: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % low_def
% 5.42/5.63 thf(fact_750_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.42/5.63 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.42/5.63 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.42/5.63
% 5.42/5.63 % VEBT_internal.minNull.simps(5)
% 5.42/5.63 thf(fact_751_even__odd__cases,axiom,
% 5.42/5.63 ! [X2: nat] :
% 5.42/5.63 ( ! [N3: nat] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.42/5.63 => ~ ! [N3: nat] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % even_odd_cases
% 5.42/5.63 thf(fact_752_not__min__Null__member,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT] :
% 5.42/5.63 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.42/5.63 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.42/5.63
% 5.42/5.63 % not_min_Null_member
% 5.42/5.63 thf(fact_753_deg__SUcn__Node,axiom,
% 5.42/5.63 ! [Tree: vEBT_VEBT,N: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.42/5.63 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.42/5.63 ( Tree
% 5.42/5.63 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S3 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % deg_SUcn_Node
% 5.42/5.63 thf(fact_754_both__member__options__equiv__member,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.42/5.63 = ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % both_member_options_equiv_member
% 5.42/5.63 thf(fact_755_valid__member__both__member__options,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.42/5.63 => ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % valid_member_both_member_options
% 5.42/5.63 thf(fact_756_inthall,axiom,
% 5.42/5.63 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N: nat] :
% 5.42/5.63 ( ! [X3: product_prod_nat_nat] :
% 5.42/5.63 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.42/5.63 => ( P @ X3 ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % inthall
% 5.42/5.63 thf(fact_757_inthall,axiom,
% 5.42/5.63 ! [Xs2: list_complex,P: complex > $o,N: nat] :
% 5.42/5.63 ( ! [X3: complex] :
% 5.42/5.63 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X3 ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % inthall
% 5.42/5.63 thf(fact_758_inthall,axiom,
% 5.42/5.63 ! [Xs2: list_real,P: real > $o,N: nat] :
% 5.42/5.63 ( ! [X3: real] :
% 5.42/5.63 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X3 ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % inthall
% 5.42/5.63 thf(fact_759_inthall,axiom,
% 5.42/5.63 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.42/5.63 ( ! [X3: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X3 ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % inthall
% 5.42/5.63 thf(fact_760_inthall,axiom,
% 5.42/5.63 ! [Xs2: list_o,P: $o > $o,N: nat] :
% 5.42/5.63 ( ! [X3: $o] :
% 5.42/5.63 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X3 ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % inthall
% 5.42/5.63 thf(fact_761_inthall,axiom,
% 5.42/5.63 ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 5.42/5.63 ( ! [X3: nat] :
% 5.42/5.63 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X3 ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % inthall
% 5.42/5.63 thf(fact_762_inthall,axiom,
% 5.42/5.63 ! [Xs2: list_int,P: int > $o,N: nat] :
% 5.42/5.63 ( ! [X3: int] :
% 5.42/5.63 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X3 ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % inthall
% 5.42/5.63 thf(fact_763_old_Onat_Oinject,axiom,
% 5.42/5.63 ! [Nat: nat,Nat2: nat] :
% 5.42/5.63 ( ( ( suc @ Nat )
% 5.42/5.63 = ( suc @ Nat2 ) )
% 5.42/5.63 = ( Nat = Nat2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % old.nat.inject
% 5.42/5.63 thf(fact_764_nat_Oinject,axiom,
% 5.42/5.63 ! [X23: nat,Y22: nat] :
% 5.42/5.63 ( ( ( suc @ X23 )
% 5.42/5.63 = ( suc @ Y22 ) )
% 5.42/5.63 = ( X23 = Y22 ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat.inject
% 5.42/5.63 thf(fact_765_mod__mod__trivial,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.42/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mod_trivial
% 5.42/5.63 thf(fact_766_mod__mod__trivial,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mod_trivial
% 5.42/5.63 thf(fact_767_mod__mod__trivial,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mod_trivial
% 5.42/5.63 thf(fact_768_mi__eq__ma__no__ch,axiom,
% 5.42/5.63 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.42/5.63 => ( ( Mi = Ma )
% 5.42/5.63 => ( ! [X4: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.63 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) )
% 5.42/5.63 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mi_eq_ma_no_ch
% 5.42/5.63 thf(fact_769_add__diff__cancel__right_H,axiom,
% 5.42/5.63 ! [A: real,B: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_right'
% 5.42/5.63 thf(fact_770_add__diff__cancel__right_H,axiom,
% 5.42/5.63 ! [A: rat,B: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_right'
% 5.42/5.63 thf(fact_771_add__diff__cancel__right_H,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_right'
% 5.42/5.63 thf(fact_772_add__diff__cancel__right_H,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_right'
% 5.42/5.63 thf(fact_773_add__diff__cancel__right,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.42/5.63 = ( minus_minus_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_right
% 5.42/5.63 thf(fact_774_add__diff__cancel__right,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.42/5.63 = ( minus_minus_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_right
% 5.42/5.63 thf(fact_775_add__diff__cancel__right,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.42/5.63 = ( minus_minus_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_right
% 5.42/5.63 thf(fact_776_add__diff__cancel__right,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.42/5.63 = ( minus_minus_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_right
% 5.42/5.63 thf(fact_777_add__diff__cancel__left_H,axiom,
% 5.42/5.63 ! [A: real,B: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.42/5.63 = B ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_left'
% 5.42/5.63 thf(fact_778_add__diff__cancel__left_H,axiom,
% 5.42/5.63 ! [A: rat,B: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.42/5.63 = B ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_left'
% 5.42/5.63 thf(fact_779_add__diff__cancel__left_H,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.42/5.63 = B ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_left'
% 5.42/5.63 thf(fact_780_add__diff__cancel__left_H,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.42/5.63 = B ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_left'
% 5.42/5.63 thf(fact_781_add__diff__cancel__left,axiom,
% 5.42/5.63 ! [C: real,A: real,B: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.42/5.63 = ( minus_minus_real @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_left
% 5.42/5.63 thf(fact_782_add__diff__cancel__left,axiom,
% 5.42/5.63 ! [C: rat,A: rat,B: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.42/5.63 = ( minus_minus_rat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_left
% 5.42/5.63 thf(fact_783_add__diff__cancel__left,axiom,
% 5.42/5.63 ! [C: nat,A: nat,B: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.42/5.63 = ( minus_minus_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_left
% 5.42/5.63 thf(fact_784_add__diff__cancel__left,axiom,
% 5.42/5.63 ! [C: int,A: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.42/5.63 = ( minus_minus_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel_left
% 5.42/5.63 thf(fact_785_diff__add__cancel,axiom,
% 5.42/5.63 ! [A: real,B: real] :
% 5.42/5.63 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_cancel
% 5.42/5.63 thf(fact_786_diff__add__cancel,axiom,
% 5.42/5.63 ! [A: rat,B: rat] :
% 5.42/5.63 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_cancel
% 5.42/5.63 thf(fact_787_diff__add__cancel,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_cancel
% 5.42/5.63 thf(fact_788_add__diff__cancel,axiom,
% 5.42/5.63 ! [A: real,B: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel
% 5.42/5.63 thf(fact_789_add__diff__cancel,axiom,
% 5.42/5.63 ! [A: rat,B: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel
% 5.42/5.63 thf(fact_790_add__diff__cancel,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_cancel
% 5.42/5.63 thf(fact_791_lessI,axiom,
% 5.42/5.63 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % lessI
% 5.42/5.63 thf(fact_792_Suc__mono,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ N )
% 5.42/5.63 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mono
% 5.42/5.63 thf(fact_793_Suc__less__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.42/5.63 = ( ord_less_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_less_eq
% 5.42/5.63 thf(fact_794_Suc__le__mono,axiom,
% 5.42/5.63 ! [N: nat,M: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.42/5.63 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_le_mono
% 5.42/5.63 thf(fact_795_add__Suc__right,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.42/5.63 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_Suc_right
% 5.42/5.63 thf(fact_796_mod__add__self2,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.42/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_self2
% 5.42/5.63 thf(fact_797_mod__add__self2,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_self2
% 5.42/5.63 thf(fact_798_mod__add__self2,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_self2
% 5.42/5.63 thf(fact_799_mod__add__self1,axiom,
% 5.42/5.63 ! [B: nat,A: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.42/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_self1
% 5.42/5.63 thf(fact_800_mod__add__self1,axiom,
% 5.42/5.63 ! [B: int,A: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_self1
% 5.42/5.63 thf(fact_801_mod__add__self1,axiom,
% 5.42/5.63 ! [B: code_integer,A: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_self1
% 5.42/5.63 thf(fact_802_minus__mod__self2,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mod_self2
% 5.42/5.63 thf(fact_803_minus__mod__self2,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mod_self2
% 5.42/5.63 thf(fact_804_Suc__diff__diff,axiom,
% 5.42/5.63 ! [M: nat,N: nat,K: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.42/5.63 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_diff_diff
% 5.42/5.63 thf(fact_805_diff__Suc__Suc,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.42/5.63 = ( minus_minus_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_Suc_Suc
% 5.42/5.63 thf(fact_806_diff__diff__cancel,axiom,
% 5.42/5.63 ! [I: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ N )
% 5.42/5.63 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 5.42/5.63 = I ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_diff_cancel
% 5.42/5.63 thf(fact_807_diff__diff__left,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.42/5.63 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_diff_left
% 5.42/5.63 thf(fact_808_mod__less,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ N )
% 5.42/5.63 => ( ( modulo_modulo_nat @ M @ N )
% 5.42/5.63 = M ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_less
% 5.42/5.63 thf(fact_809_le__add__diff__inverse2,axiom,
% 5.42/5.63 ! [B: real,A: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ B @ A )
% 5.42/5.63 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_add_diff_inverse2
% 5.42/5.63 thf(fact_810_le__add__diff__inverse2,axiom,
% 5.42/5.63 ! [B: rat,A: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ B @ A )
% 5.42/5.63 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_add_diff_inverse2
% 5.42/5.63 thf(fact_811_le__add__diff__inverse2,axiom,
% 5.42/5.63 ! [B: nat,A: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ B @ A )
% 5.42/5.63 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_add_diff_inverse2
% 5.42/5.63 thf(fact_812_le__add__diff__inverse2,axiom,
% 5.42/5.63 ! [B: int,A: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ B @ A )
% 5.42/5.63 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_add_diff_inverse2
% 5.42/5.63 thf(fact_813_le__add__diff__inverse,axiom,
% 5.42/5.63 ! [B: real,A: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ B @ A )
% 5.42/5.63 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_add_diff_inverse
% 5.42/5.63 thf(fact_814_le__add__diff__inverse,axiom,
% 5.42/5.63 ! [B: rat,A: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ B @ A )
% 5.42/5.63 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_add_diff_inverse
% 5.42/5.63 thf(fact_815_le__add__diff__inverse,axiom,
% 5.42/5.63 ! [B: nat,A: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ B @ A )
% 5.42/5.63 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_add_diff_inverse
% 5.42/5.63 thf(fact_816_le__add__diff__inverse,axiom,
% 5.42/5.63 ! [B: int,A: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ B @ A )
% 5.42/5.63 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_add_diff_inverse
% 5.42/5.63 thf(fact_817_right__diff__distrib__numeral,axiom,
% 5.42/5.63 ! [V: num,B: complex,C: complex] :
% 5.42/5.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.42/5.63 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib_numeral
% 5.42/5.63 thf(fact_818_right__diff__distrib__numeral,axiom,
% 5.42/5.63 ! [V: num,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.42/5.63 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib_numeral
% 5.42/5.63 thf(fact_819_right__diff__distrib__numeral,axiom,
% 5.42/5.63 ! [V: num,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.42/5.63 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib_numeral
% 5.42/5.63 thf(fact_820_right__diff__distrib__numeral,axiom,
% 5.42/5.63 ! [V: num,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.42/5.63 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib_numeral
% 5.42/5.63 thf(fact_821_left__diff__distrib__numeral,axiom,
% 5.42/5.63 ! [A: complex,B: complex,V: num] :
% 5.42/5.63 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.42/5.63 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib_numeral
% 5.42/5.63 thf(fact_822_left__diff__distrib__numeral,axiom,
% 5.42/5.63 ! [A: real,B: real,V: num] :
% 5.42/5.63 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.42/5.63 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib_numeral
% 5.42/5.63 thf(fact_823_left__diff__distrib__numeral,axiom,
% 5.42/5.63 ! [A: rat,B: rat,V: num] :
% 5.42/5.63 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.42/5.63 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib_numeral
% 5.42/5.63 thf(fact_824_left__diff__distrib__numeral,axiom,
% 5.42/5.63 ! [A: int,B: int,V: num] :
% 5.42/5.63 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.42/5.63 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib_numeral
% 5.42/5.63 thf(fact_825_mod__mult__self4,axiom,
% 5.42/5.63 ! [B: nat,C: nat,A: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.42/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self4
% 5.42/5.63 thf(fact_826_mod__mult__self4,axiom,
% 5.42/5.63 ! [B: int,C: int,A: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self4
% 5.42/5.63 thf(fact_827_mod__mult__self4,axiom,
% 5.42/5.63 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self4
% 5.42/5.63 thf(fact_828_mod__mult__self3,axiom,
% 5.42/5.63 ! [C: nat,B: nat,A: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.42/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self3
% 5.42/5.63 thf(fact_829_mod__mult__self3,axiom,
% 5.42/5.63 ! [C: int,B: int,A: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self3
% 5.42/5.63 thf(fact_830_mod__mult__self3,axiom,
% 5.42/5.63 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self3
% 5.42/5.63 thf(fact_831_mod__mult__self2,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.42/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self2
% 5.42/5.63 thf(fact_832_mod__mult__self2,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self2
% 5.42/5.63 thf(fact_833_mod__mult__self2,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self2
% 5.42/5.63 thf(fact_834_mod__mult__self1,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.42/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self1
% 5.42/5.63 thf(fact_835_mod__mult__self1,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self1
% 5.42/5.63 thf(fact_836_mod__mult__self1,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_self1
% 5.42/5.63 thf(fact_837_mult__Suc__right,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.42/5.63 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_Suc_right
% 5.42/5.63 thf(fact_838_diff__Suc__1,axiom,
% 5.42/5.63 ! [N: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.42/5.63 = N ) ).
% 5.42/5.63
% 5.42/5.63 % diff_Suc_1
% 5.42/5.63 thf(fact_839_Nat_Odiff__diff__right,axiom,
% 5.42/5.63 ! [K: nat,J: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.42/5.63 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.42/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.diff_diff_right
% 5.42/5.63 thf(fact_840_Nat_Oadd__diff__assoc2,axiom,
% 5.42/5.63 ! [K: nat,J: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.42/5.63 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.42/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.add_diff_assoc2
% 5.42/5.63 thf(fact_841_Nat_Oadd__diff__assoc,axiom,
% 5.42/5.63 ! [K: nat,J: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.42/5.63 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.42/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.add_diff_assoc
% 5.42/5.63 thf(fact_842_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.42/5.63 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.42/5.63 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.42/5.63 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.63 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % both_member_options_from_chilf_to_complete_tree
% 5.42/5.63 thf(fact_843_diff__Suc__diff__eq2,axiom,
% 5.42/5.63 ! [K: nat,J: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.42/5.63 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 5.42/5.63 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_Suc_diff_eq2
% 5.42/5.63 thf(fact_844_diff__Suc__diff__eq1,axiom,
% 5.42/5.63 ! [K: nat,J: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.42/5.63 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.42/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_Suc_diff_eq1
% 5.42/5.63 thf(fact_845_Suc__numeral,axiom,
% 5.42/5.63 ! [N: num] :
% 5.42/5.63 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.42/5.63 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_numeral
% 5.42/5.63 thf(fact_846_Suc__mod__mult__self4,axiom,
% 5.42/5.63 ! [N: nat,K: nat,M: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mod_mult_self4
% 5.42/5.63 thf(fact_847_Suc__mod__mult__self3,axiom,
% 5.42/5.63 ! [K: nat,N: nat,M: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mod_mult_self3
% 5.42/5.63 thf(fact_848_Suc__mod__mult__self2,axiom,
% 5.42/5.63 ! [M: nat,N: nat,K: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mod_mult_self2
% 5.42/5.63 thf(fact_849_Suc__mod__mult__self1,axiom,
% 5.42/5.63 ! [M: nat,K: nat,N: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mod_mult_self1
% 5.42/5.63 thf(fact_850_bits__one__mod__two__eq__one,axiom,
% 5.42/5.63 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_nat ) ).
% 5.42/5.63
% 5.42/5.63 % bits_one_mod_two_eq_one
% 5.42/5.63 thf(fact_851_bits__one__mod__two__eq__one,axiom,
% 5.42/5.63 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_int ) ).
% 5.42/5.63
% 5.42/5.63 % bits_one_mod_two_eq_one
% 5.42/5.63 thf(fact_852_bits__one__mod__two__eq__one,axiom,
% 5.42/5.63 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_Code_integer ) ).
% 5.42/5.63
% 5.42/5.63 % bits_one_mod_two_eq_one
% 5.42/5.63 thf(fact_853_one__mod__two__eq__one,axiom,
% 5.42/5.63 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_nat ) ).
% 5.42/5.63
% 5.42/5.63 % one_mod_two_eq_one
% 5.42/5.63 thf(fact_854_one__mod__two__eq__one,axiom,
% 5.42/5.63 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_int ) ).
% 5.42/5.63
% 5.42/5.63 % one_mod_two_eq_one
% 5.42/5.63 thf(fact_855_one__mod__two__eq__one,axiom,
% 5.42/5.63 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.42/5.63 = one_one_Code_integer ) ).
% 5.42/5.63
% 5.42/5.63 % one_mod_two_eq_one
% 5.42/5.63 thf(fact_856_add__2__eq__Suc_H,axiom,
% 5.42/5.63 ! [N: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( suc @ ( suc @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_2_eq_Suc'
% 5.42/5.63 thf(fact_857_add__2__eq__Suc,axiom,
% 5.42/5.63 ! [N: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.42/5.63 = ( suc @ ( suc @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_2_eq_Suc
% 5.42/5.63 thf(fact_858_Suc__1,axiom,
% 5.42/5.63 ( ( suc @ one_one_nat )
% 5.42/5.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_1
% 5.42/5.63 thf(fact_859_div2__Suc__Suc,axiom,
% 5.42/5.63 ! [M: nat] :
% 5.42/5.63 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div2_Suc_Suc
% 5.42/5.63 thf(fact_860_mod2__Suc__Suc,axiom,
% 5.42/5.63 ! [M: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod2_Suc_Suc
% 5.42/5.63 thf(fact_861_Suc__times__numeral__mod__eq,axiom,
% 5.42/5.63 ! [K: num,N: nat] :
% 5.42/5.63 ( ( ( numeral_numeral_nat @ K )
% 5.42/5.63 != one_one_nat )
% 5.42/5.63 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.42/5.63 = one_one_nat ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_times_numeral_mod_eq
% 5.42/5.63 thf(fact_862_Suc__div__eq__add3__div__numeral,axiom,
% 5.42/5.63 ! [M: nat,V: num] :
% 5.42/5.63 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.42/5.63 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_div_eq_add3_div_numeral
% 5.42/5.63 thf(fact_863_div__Suc__eq__div__add3,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.42/5.63 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_Suc_eq_div_add3
% 5.42/5.63 thf(fact_864_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.42/5.63 ! [M: nat,V: num] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.42/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mod_eq_add3_mod_numeral
% 5.42/5.63 thf(fact_865_mod__Suc__eq__mod__add3,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.42/5.63 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_Suc_eq_mod_add3
% 5.42/5.63 thf(fact_866_diff__right__commute,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.42/5.63 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_right_commute
% 5.42/5.63 thf(fact_867_diff__right__commute,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.42/5.63 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_right_commute
% 5.42/5.63 thf(fact_868_diff__right__commute,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.42/5.63 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_right_commute
% 5.42/5.63 thf(fact_869_diff__eq__diff__eq,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.42/5.63 ( ( ( minus_minus_rat @ A @ B )
% 5.42/5.63 = ( minus_minus_rat @ C @ D2 ) )
% 5.42/5.63 => ( ( A = B )
% 5.42/5.63 = ( C = D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_diff_eq
% 5.42/5.63 thf(fact_870_diff__eq__diff__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int,D2: int] :
% 5.42/5.63 ( ( ( minus_minus_int @ A @ B )
% 5.42/5.63 = ( minus_minus_int @ C @ D2 ) )
% 5.42/5.63 => ( ( A = B )
% 5.42/5.63 = ( C = D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_diff_eq
% 5.42/5.63 thf(fact_871_mod__Suc__Suc__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_Suc_Suc_eq
% 5.42/5.63 thf(fact_872_mod__Suc__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_Suc_eq
% 5.42/5.63 thf(fact_873_mod__diff__right__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_diff_right_eq
% 5.42/5.63 thf(fact_874_mod__diff__right__eq,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_diff_right_eq
% 5.42/5.63 thf(fact_875_mod__diff__left__eq,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_diff_left_eq
% 5.42/5.63 thf(fact_876_mod__diff__left__eq,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_diff_left_eq
% 5.42/5.63 thf(fact_877_mod__diff__cong,axiom,
% 5.42/5.63 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.42/5.63 ( ( ( modulo_modulo_int @ A @ C )
% 5.42/5.63 = ( modulo_modulo_int @ A4 @ C ) )
% 5.42/5.63 => ( ( ( modulo_modulo_int @ B @ C )
% 5.42/5.63 = ( modulo_modulo_int @ B4 @ C ) )
% 5.42/5.63 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_diff_cong
% 5.42/5.63 thf(fact_878_mod__diff__cong,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.42/5.63 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.42/5.63 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.42/5.63 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_diff_cong
% 5.42/5.63 thf(fact_879_mod__diff__eq,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_diff_eq
% 5.42/5.63 thf(fact_880_mod__diff__eq,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_diff_eq
% 5.42/5.63 thf(fact_881_zero__induct__lemma,axiom,
% 5.42/5.63 ! [P: nat > $o,K: nat,I: nat] :
% 5.42/5.63 ( ( P @ K )
% 5.42/5.63 => ( ! [N3: nat] :
% 5.42/5.63 ( ( P @ ( suc @ N3 ) )
% 5.42/5.63 => ( P @ N3 ) )
% 5.42/5.63 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % zero_induct_lemma
% 5.42/5.63 thf(fact_882_diff__commute,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.42/5.63 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_commute
% 5.42/5.63 thf(fact_883_n__not__Suc__n,axiom,
% 5.42/5.63 ! [N: nat] :
% 5.42/5.63 ( N
% 5.42/5.63 != ( suc @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % n_not_Suc_n
% 5.42/5.63 thf(fact_884_Suc__inject,axiom,
% 5.42/5.63 ! [X2: nat,Y2: nat] :
% 5.42/5.63 ( ( ( suc @ X2 )
% 5.42/5.63 = ( suc @ Y2 ) )
% 5.42/5.63 => ( X2 = Y2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_inject
% 5.42/5.63 thf(fact_885_mod__geq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ~ ( ord_less_nat @ M @ N )
% 5.42/5.63 => ( ( modulo_modulo_nat @ M @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_geq
% 5.42/5.63 thf(fact_886_mod__if,axiom,
% 5.42/5.63 ( modulo_modulo_nat
% 5.42/5.63 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N2 ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_if
% 5.42/5.63 thf(fact_887_mod__induct,axiom,
% 5.42/5.63 ! [P: nat > $o,N: nat,P2: nat,M: nat] :
% 5.42/5.63 ( ( P @ N )
% 5.42/5.63 => ( ( ord_less_nat @ N @ P2 )
% 5.42/5.63 => ( ( ord_less_nat @ M @ P2 )
% 5.42/5.63 => ( ! [N3: nat] :
% 5.42/5.63 ( ( ord_less_nat @ N3 @ P2 )
% 5.42/5.63 => ( ( P @ N3 )
% 5.42/5.63 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P2 ) ) ) )
% 5.42/5.63 => ( P @ M ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_induct
% 5.42/5.63 thf(fact_888_le__mod__geq,axiom,
% 5.42/5.63 ! [N: nat,M: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ N @ M )
% 5.42/5.63 => ( ( modulo_modulo_nat @ M @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_mod_geq
% 5.42/5.63 thf(fact_889_mod__Suc__le__divisor,axiom,
% 5.42/5.63 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.42/5.63
% 5.42/5.63 % mod_Suc_le_divisor
% 5.42/5.63 thf(fact_890_Suc__diff__Suc,axiom,
% 5.42/5.63 ! [N: nat,M: nat] :
% 5.42/5.63 ( ( ord_less_nat @ N @ M )
% 5.42/5.63 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.42/5.63 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_diff_Suc
% 5.42/5.63 thf(fact_891_diff__less__Suc,axiom,
% 5.42/5.63 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_less_Suc
% 5.42/5.63 thf(fact_892_Suc__diff__le,axiom,
% 5.42/5.63 ! [N: nat,M: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ N @ M )
% 5.42/5.63 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.42/5.63 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_diff_le
% 5.42/5.63 thf(fact_893_diff__Suc__eq__diff__pred,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.42/5.63 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_Suc_eq_diff_pred
% 5.42/5.63 thf(fact_894_minus__div__mult__eq__mod,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.42/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_div_mult_eq_mod
% 5.42/5.63 thf(fact_895_minus__div__mult__eq__mod,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_div_mult_eq_mod
% 5.42/5.63 thf(fact_896_minus__div__mult__eq__mod,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_div_mult_eq_mod
% 5.42/5.63 thf(fact_897_minus__mod__eq__div__mult,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.42/5.63 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mod_eq_div_mult
% 5.42/5.63 thf(fact_898_minus__mod__eq__div__mult,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.42/5.63 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mod_eq_div_mult
% 5.42/5.63 thf(fact_899_minus__mod__eq__div__mult,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.42/5.63 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mod_eq_div_mult
% 5.42/5.63 thf(fact_900_minus__mod__eq__mult__div,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.42/5.63 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mod_eq_mult_div
% 5.42/5.63 thf(fact_901_minus__mod__eq__mult__div,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.42/5.63 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mod_eq_mult_div
% 5.42/5.63 thf(fact_902_minus__mod__eq__mult__div,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.42/5.63 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mod_eq_mult_div
% 5.42/5.63 thf(fact_903_minus__mult__div__eq__mod,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.42/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mult_div_eq_mod
% 5.42/5.63 thf(fact_904_minus__mult__div__eq__mod,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.42/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mult_div_eq_mod
% 5.42/5.63 thf(fact_905_minus__mult__div__eq__mod,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % minus_mult_div_eq_mod
% 5.42/5.63 thf(fact_906_size__neq__size__imp__neq,axiom,
% 5.42/5.63 ! [X2: list_VEBT_VEBT,Y2: list_VEBT_VEBT] :
% 5.42/5.63 ( ( ( size_s6755466524823107622T_VEBT @ X2 )
% 5.42/5.63 != ( size_s6755466524823107622T_VEBT @ Y2 ) )
% 5.42/5.63 => ( X2 != Y2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % size_neq_size_imp_neq
% 5.42/5.63 thf(fact_907_size__neq__size__imp__neq,axiom,
% 5.42/5.63 ! [X2: list_o,Y2: list_o] :
% 5.42/5.63 ( ( ( size_size_list_o @ X2 )
% 5.42/5.63 != ( size_size_list_o @ Y2 ) )
% 5.42/5.63 => ( X2 != Y2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % size_neq_size_imp_neq
% 5.42/5.63 thf(fact_908_size__neq__size__imp__neq,axiom,
% 5.42/5.63 ! [X2: list_nat,Y2: list_nat] :
% 5.42/5.63 ( ( ( size_size_list_nat @ X2 )
% 5.42/5.63 != ( size_size_list_nat @ Y2 ) )
% 5.42/5.63 => ( X2 != Y2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % size_neq_size_imp_neq
% 5.42/5.63 thf(fact_909_size__neq__size__imp__neq,axiom,
% 5.42/5.63 ! [X2: list_int,Y2: list_int] :
% 5.42/5.63 ( ( ( size_size_list_int @ X2 )
% 5.42/5.63 != ( size_size_list_int @ Y2 ) )
% 5.42/5.63 => ( X2 != Y2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % size_neq_size_imp_neq
% 5.42/5.63 thf(fact_910_size__neq__size__imp__neq,axiom,
% 5.42/5.63 ! [X2: num,Y2: num] :
% 5.42/5.63 ( ( ( size_size_num @ X2 )
% 5.42/5.63 != ( size_size_num @ Y2 ) )
% 5.42/5.63 => ( X2 != Y2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % size_neq_size_imp_neq
% 5.42/5.63 thf(fact_911_modulo__nat__def,axiom,
% 5.42/5.63 ( modulo_modulo_nat
% 5.42/5.63 = ( ^ [M3: nat,N2: nat] : ( minus_minus_nat @ M3 @ ( times_times_nat @ ( divide_divide_nat @ M3 @ N2 ) @ N2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % modulo_nat_def
% 5.42/5.63 thf(fact_912_mod__mult__right__eq,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_right_eq
% 5.42/5.63 thf(fact_913_mod__mult__right__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_right_eq
% 5.42/5.63 thf(fact_914_mod__mult__right__eq,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_right_eq
% 5.42/5.63 thf(fact_915_mod__mult__left__eq,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_left_eq
% 5.42/5.63 thf(fact_916_mod__mult__left__eq,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_left_eq
% 5.42/5.63 thf(fact_917_mod__mult__left__eq,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_left_eq
% 5.42/5.63 thf(fact_918_mult__mod__right,axiom,
% 5.42/5.63 ! [C: nat,A: nat,B: nat] :
% 5.42/5.63 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.42/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_mod_right
% 5.42/5.63 thf(fact_919_mult__mod__right,axiom,
% 5.42/5.63 ! [C: int,A: int,B: int] :
% 5.42/5.63 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.42/5.63 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_mod_right
% 5.42/5.63 thf(fact_920_mult__mod__right,axiom,
% 5.42/5.63 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_mod_right
% 5.42/5.63 thf(fact_921_mod__mult__mult2,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.42/5.63 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_mult2
% 5.42/5.63 thf(fact_922_mod__mult__mult2,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.42/5.63 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_mult2
% 5.42/5.63 thf(fact_923_mod__mult__mult2,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.42/5.63 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_mult2
% 5.42/5.63 thf(fact_924_mod__mult__cong,axiom,
% 5.42/5.63 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.42/5.63 ( ( ( modulo_modulo_nat @ A @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.42/5.63 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.42/5.63 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_cong
% 5.42/5.63 thf(fact_925_mod__mult__cong,axiom,
% 5.42/5.63 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.42/5.63 ( ( ( modulo_modulo_int @ A @ C )
% 5.42/5.63 = ( modulo_modulo_int @ A4 @ C ) )
% 5.42/5.63 => ( ( ( modulo_modulo_int @ B @ C )
% 5.42/5.63 = ( modulo_modulo_int @ B4 @ C ) )
% 5.42/5.63 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_cong
% 5.42/5.63 thf(fact_926_mod__mult__cong,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.42/5.63 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.42/5.63 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.42/5.63 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_cong
% 5.42/5.63 thf(fact_927_mod__mult__eq,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_eq
% 5.42/5.63 thf(fact_928_mod__mult__eq,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_eq
% 5.42/5.63 thf(fact_929_mod__mult__eq,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_eq
% 5.42/5.63 thf(fact_930_mod__add__right__eq,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_right_eq
% 5.42/5.63 thf(fact_931_mod__add__right__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_right_eq
% 5.42/5.63 thf(fact_932_mod__add__right__eq,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_right_eq
% 5.42/5.63 thf(fact_933_mod__add__left__eq,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_left_eq
% 5.42/5.63 thf(fact_934_mod__add__left__eq,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_left_eq
% 5.42/5.63 thf(fact_935_mod__add__left__eq,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_left_eq
% 5.42/5.63 thf(fact_936_mod__add__cong,axiom,
% 5.42/5.63 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.42/5.63 ( ( ( modulo_modulo_nat @ A @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.42/5.63 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.42/5.63 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_cong
% 5.42/5.63 thf(fact_937_mod__add__cong,axiom,
% 5.42/5.63 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.42/5.63 ( ( ( modulo_modulo_int @ A @ C )
% 5.42/5.63 = ( modulo_modulo_int @ A4 @ C ) )
% 5.42/5.63 => ( ( ( modulo_modulo_int @ B @ C )
% 5.42/5.63 = ( modulo_modulo_int @ B4 @ C ) )
% 5.42/5.63 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_cong
% 5.42/5.63 thf(fact_938_mod__add__cong,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.42/5.63 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.42/5.63 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.42/5.63 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_cong
% 5.42/5.63 thf(fact_939_mod__add__eq,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_eq
% 5.42/5.63 thf(fact_940_mod__add__eq,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_eq
% 5.42/5.63 thf(fact_941_mod__add__eq,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_add_eq
% 5.42/5.63 thf(fact_942_power__mod,axiom,
% 5.42/5.63 ! [A: nat,B: nat,N: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 5.42/5.63 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_mod
% 5.42/5.63 thf(fact_943_power__mod,axiom,
% 5.42/5.63 ! [A: int,B: int,N: nat] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 5.42/5.63 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_mod
% 5.42/5.63 thf(fact_944_power__mod,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer,N: nat] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_mod
% 5.42/5.63 thf(fact_945_diff__eq__diff__less__eq,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.42/5.63 ( ( ( minus_minus_rat @ A @ B )
% 5.42/5.63 = ( minus_minus_rat @ C @ D2 ) )
% 5.42/5.63 => ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.63 = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_diff_less_eq
% 5.42/5.63 thf(fact_946_diff__eq__diff__less__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int,D2: int] :
% 5.42/5.63 ( ( ( minus_minus_int @ A @ B )
% 5.42/5.63 = ( minus_minus_int @ C @ D2 ) )
% 5.42/5.63 => ( ( ord_less_eq_int @ A @ B )
% 5.42/5.63 = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_diff_less_eq
% 5.42/5.63 thf(fact_947_diff__right__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.63 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_right_mono
% 5.42/5.63 thf(fact_948_diff__right__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.63 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_right_mono
% 5.42/5.63 thf(fact_949_diff__left__mono,axiom,
% 5.42/5.63 ! [B: rat,A: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ B @ A )
% 5.42/5.63 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_left_mono
% 5.42/5.63 thf(fact_950_diff__left__mono,axiom,
% 5.42/5.63 ! [B: int,A: int,C: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ B @ A )
% 5.42/5.63 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_left_mono
% 5.42/5.63 thf(fact_951_diff__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,D2: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_rat @ D2 @ C )
% 5.42/5.63 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_mono
% 5.42/5.63 thf(fact_952_diff__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,D2: int,C: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_int @ D2 @ C )
% 5.42/5.63 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_mono
% 5.42/5.63 thf(fact_953_diff__strict__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,D2: real,C: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ( ord_less_real @ D2 @ C )
% 5.42/5.63 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_strict_mono
% 5.42/5.63 thf(fact_954_diff__strict__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,D2: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ( ord_less_rat @ D2 @ C )
% 5.42/5.63 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_strict_mono
% 5.42/5.63 thf(fact_955_diff__strict__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,D2: int,C: int] :
% 5.42/5.63 ( ( ord_less_int @ A @ B )
% 5.42/5.63 => ( ( ord_less_int @ D2 @ C )
% 5.42/5.63 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_strict_mono
% 5.42/5.63 thf(fact_956_diff__eq__diff__less,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real,D2: real] :
% 5.42/5.63 ( ( ( minus_minus_real @ A @ B )
% 5.42/5.63 = ( minus_minus_real @ C @ D2 ) )
% 5.42/5.63 => ( ( ord_less_real @ A @ B )
% 5.42/5.63 = ( ord_less_real @ C @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_diff_less
% 5.42/5.63 thf(fact_957_diff__eq__diff__less,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.42/5.63 ( ( ( minus_minus_rat @ A @ B )
% 5.42/5.63 = ( minus_minus_rat @ C @ D2 ) )
% 5.42/5.63 => ( ( ord_less_rat @ A @ B )
% 5.42/5.63 = ( ord_less_rat @ C @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_diff_less
% 5.42/5.63 thf(fact_958_diff__eq__diff__less,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int,D2: int] :
% 5.42/5.63 ( ( ( minus_minus_int @ A @ B )
% 5.42/5.63 = ( minus_minus_int @ C @ D2 ) )
% 5.42/5.63 => ( ( ord_less_int @ A @ B )
% 5.42/5.63 = ( ord_less_int @ C @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_diff_less
% 5.42/5.63 thf(fact_959_diff__strict__left__mono,axiom,
% 5.42/5.63 ! [B: real,A: real,C: real] :
% 5.42/5.63 ( ( ord_less_real @ B @ A )
% 5.42/5.63 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_strict_left_mono
% 5.42/5.63 thf(fact_960_diff__strict__left__mono,axiom,
% 5.42/5.63 ! [B: rat,A: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_rat @ B @ A )
% 5.42/5.63 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_strict_left_mono
% 5.42/5.63 thf(fact_961_diff__strict__left__mono,axiom,
% 5.42/5.63 ! [B: int,A: int,C: int] :
% 5.42/5.63 ( ( ord_less_int @ B @ A )
% 5.42/5.63 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_strict_left_mono
% 5.42/5.63 thf(fact_962_diff__strict__right__mono,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_strict_right_mono
% 5.42/5.63 thf(fact_963_diff__strict__right__mono,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_strict_right_mono
% 5.42/5.63 thf(fact_964_diff__strict__right__mono,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ord_less_int @ A @ B )
% 5.42/5.63 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_strict_right_mono
% 5.42/5.63 thf(fact_965_right__diff__distrib_H,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.42/5.63 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib'
% 5.42/5.63 thf(fact_966_right__diff__distrib_H,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.42/5.63 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib'
% 5.42/5.63 thf(fact_967_right__diff__distrib_H,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.42/5.63 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib'
% 5.42/5.63 thf(fact_968_right__diff__distrib_H,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.42/5.63 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib'
% 5.42/5.63 thf(fact_969_left__diff__distrib_H,axiom,
% 5.42/5.63 ! [B: real,C: real,A: real] :
% 5.42/5.63 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.42/5.63 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib'
% 5.42/5.63 thf(fact_970_left__diff__distrib_H,axiom,
% 5.42/5.63 ! [B: rat,C: rat,A: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.42/5.63 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib'
% 5.42/5.63 thf(fact_971_left__diff__distrib_H,axiom,
% 5.42/5.63 ! [B: nat,C: nat,A: nat] :
% 5.42/5.63 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.42/5.63 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib'
% 5.42/5.63 thf(fact_972_left__diff__distrib_H,axiom,
% 5.42/5.63 ! [B: int,C: int,A: int] :
% 5.42/5.63 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.42/5.63 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib'
% 5.42/5.63 thf(fact_973_right__diff__distrib,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.42/5.63 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib
% 5.42/5.63 thf(fact_974_right__diff__distrib,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.42/5.63 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib
% 5.42/5.63 thf(fact_975_right__diff__distrib,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.42/5.63 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % right_diff_distrib
% 5.42/5.63 thf(fact_976_left__diff__distrib,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib
% 5.42/5.63 thf(fact_977_left__diff__distrib,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib
% 5.42/5.63 thf(fact_978_left__diff__distrib,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % left_diff_distrib
% 5.42/5.63 thf(fact_979_add__diff__add,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real,D2: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) )
% 5.42/5.63 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_add
% 5.42/5.63 thf(fact_980_add__diff__add,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat,D2: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) )
% 5.42/5.63 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_add
% 5.42/5.63 thf(fact_981_add__diff__add,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int,D2: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) )
% 5.42/5.63 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_add
% 5.42/5.63 thf(fact_982_diff__diff__eq,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_diff_eq
% 5.42/5.63 thf(fact_983_diff__diff__eq,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_diff_eq
% 5.42/5.63 thf(fact_984_diff__diff__eq,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_diff_eq
% 5.42/5.63 thf(fact_985_diff__diff__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_diff_eq
% 5.42/5.63 thf(fact_986_add__implies__diff,axiom,
% 5.42/5.63 ! [C: real,B: real,A: real] :
% 5.42/5.63 ( ( ( plus_plus_real @ C @ B )
% 5.42/5.63 = A )
% 5.42/5.63 => ( C
% 5.42/5.63 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_implies_diff
% 5.42/5.63 thf(fact_987_add__implies__diff,axiom,
% 5.42/5.63 ! [C: rat,B: rat,A: rat] :
% 5.42/5.63 ( ( ( plus_plus_rat @ C @ B )
% 5.42/5.63 = A )
% 5.42/5.63 => ( C
% 5.42/5.63 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_implies_diff
% 5.42/5.63 thf(fact_988_add__implies__diff,axiom,
% 5.42/5.63 ! [C: nat,B: nat,A: nat] :
% 5.42/5.63 ( ( ( plus_plus_nat @ C @ B )
% 5.42/5.63 = A )
% 5.42/5.63 => ( C
% 5.42/5.63 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_implies_diff
% 5.42/5.63 thf(fact_989_add__implies__diff,axiom,
% 5.42/5.63 ! [C: int,B: int,A: int] :
% 5.42/5.63 ( ( ( plus_plus_int @ C @ B )
% 5.42/5.63 = A )
% 5.42/5.63 => ( C
% 5.42/5.63 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_implies_diff
% 5.42/5.63 thf(fact_990_diff__add__eq__diff__diff__swap,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.42/5.63 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_eq_diff_diff_swap
% 5.42/5.63 thf(fact_991_diff__add__eq__diff__diff__swap,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.42/5.63 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_eq_diff_diff_swap
% 5.42/5.63 thf(fact_992_diff__add__eq__diff__diff__swap,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.42/5.63 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_eq_diff_diff_swap
% 5.42/5.63 thf(fact_993_diff__add__eq,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_eq
% 5.42/5.63 thf(fact_994_diff__add__eq,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_eq
% 5.42/5.63 thf(fact_995_diff__add__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_eq
% 5.42/5.63 thf(fact_996_diff__diff__eq2,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.42/5.63 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_diff_eq2
% 5.42/5.63 thf(fact_997_diff__diff__eq2,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.42/5.63 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_diff_eq2
% 5.42/5.63 thf(fact_998_diff__diff__eq2,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.42/5.63 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_diff_eq2
% 5.42/5.63 thf(fact_999_add__diff__eq,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.42/5.63 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_eq
% 5.42/5.63 thf(fact_1000_add__diff__eq,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.42/5.63 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_eq
% 5.42/5.63 thf(fact_1001_add__diff__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.42/5.63 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_eq
% 5.42/5.63 thf(fact_1002_eq__diff__eq,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real] :
% 5.42/5.63 ( ( A
% 5.42/5.63 = ( minus_minus_real @ C @ B ) )
% 5.42/5.63 = ( ( plus_plus_real @ A @ B )
% 5.42/5.63 = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_diff_eq
% 5.42/5.63 thf(fact_1003_eq__diff__eq,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat] :
% 5.42/5.63 ( ( A
% 5.42/5.63 = ( minus_minus_rat @ C @ B ) )
% 5.42/5.63 = ( ( plus_plus_rat @ A @ B )
% 5.42/5.63 = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_diff_eq
% 5.42/5.63 thf(fact_1004_eq__diff__eq,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( A
% 5.42/5.63 = ( minus_minus_int @ C @ B ) )
% 5.42/5.63 = ( ( plus_plus_int @ A @ B )
% 5.42/5.63 = C ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_diff_eq
% 5.42/5.63 thf(fact_1005_diff__eq__eq,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ( minus_minus_real @ A @ B )
% 5.42/5.63 = C )
% 5.42/5.63 = ( A
% 5.42/5.63 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_eq
% 5.42/5.63 thf(fact_1006_diff__eq__eq,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ( minus_minus_rat @ A @ B )
% 5.42/5.63 = C )
% 5.42/5.63 = ( A
% 5.42/5.63 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_eq
% 5.42/5.63 thf(fact_1007_diff__eq__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ( minus_minus_int @ A @ B )
% 5.42/5.63 = C )
% 5.42/5.63 = ( A
% 5.42/5.63 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_eq_eq
% 5.42/5.63 thf(fact_1008_group__cancel_Osub1,axiom,
% 5.42/5.63 ! [A2: real,K: real,A: real,B: real] :
% 5.42/5.63 ( ( A2
% 5.42/5.63 = ( plus_plus_real @ K @ A ) )
% 5.42/5.63 => ( ( minus_minus_real @ A2 @ B )
% 5.42/5.63 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.sub1
% 5.42/5.63 thf(fact_1009_group__cancel_Osub1,axiom,
% 5.42/5.63 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.42/5.63 ( ( A2
% 5.42/5.63 = ( plus_plus_rat @ K @ A ) )
% 5.42/5.63 => ( ( minus_minus_rat @ A2 @ B )
% 5.42/5.63 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.sub1
% 5.42/5.63 thf(fact_1010_group__cancel_Osub1,axiom,
% 5.42/5.63 ! [A2: int,K: int,A: int,B: int] :
% 5.42/5.63 ( ( A2
% 5.42/5.63 = ( plus_plus_int @ K @ A ) )
% 5.42/5.63 => ( ( minus_minus_int @ A2 @ B )
% 5.42/5.63 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % group_cancel.sub1
% 5.42/5.63 thf(fact_1011_mod__less__eq__dividend,axiom,
% 5.42/5.63 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.42/5.63
% 5.42/5.63 % mod_less_eq_dividend
% 5.42/5.63 thf(fact_1012_diff__divide__distrib,axiom,
% 5.42/5.63 ! [A: complex,B: complex,C: complex] :
% 5.42/5.63 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_divide_distrib
% 5.42/5.63 thf(fact_1013_diff__divide__distrib,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_divide_distrib
% 5.42/5.63 thf(fact_1014_diff__divide__distrib,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_divide_distrib
% 5.42/5.63 thf(fact_1015_diff__less__mono2,axiom,
% 5.42/5.63 ! [M: nat,N: nat,L2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ N )
% 5.42/5.63 => ( ( ord_less_nat @ M @ L2 )
% 5.42/5.63 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_less_mono2
% 5.42/5.63 thf(fact_1016_less__imp__diff__less,axiom,
% 5.42/5.63 ! [J: nat,K: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ J @ K )
% 5.42/5.63 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_imp_diff_less
% 5.42/5.63 thf(fact_1017_diff__le__mono2,axiom,
% 5.42/5.63 ! [M: nat,N: nat,L2: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_le_mono2
% 5.42/5.63 thf(fact_1018_le__diff__iff_H,axiom,
% 5.42/5.63 ! [A: nat,C: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ C )
% 5.42/5.63 => ( ( ord_less_eq_nat @ B @ C )
% 5.42/5.63 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.42/5.63 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_diff_iff'
% 5.42/5.63 thf(fact_1019_diff__le__self,axiom,
% 5.42/5.63 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.42/5.63
% 5.42/5.63 % diff_le_self
% 5.42/5.63 thf(fact_1020_diff__le__mono,axiom,
% 5.42/5.63 ! [M: nat,N: nat,L2: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_le_mono
% 5.42/5.63 thf(fact_1021_Nat_Odiff__diff__eq,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ M )
% 5.42/5.63 => ( ( ord_less_eq_nat @ K @ N )
% 5.42/5.63 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.42/5.63 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.diff_diff_eq
% 5.42/5.63 thf(fact_1022_le__diff__iff,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ M )
% 5.42/5.63 => ( ( ord_less_eq_nat @ K @ N )
% 5.42/5.63 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.42/5.63 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_diff_iff
% 5.42/5.63 thf(fact_1023_eq__diff__iff,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ M )
% 5.42/5.63 => ( ( ord_less_eq_nat @ K @ N )
% 5.42/5.63 => ( ( ( minus_minus_nat @ M @ K )
% 5.42/5.63 = ( minus_minus_nat @ N @ K ) )
% 5.42/5.63 = ( M = N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_diff_iff
% 5.42/5.63 thf(fact_1024_Nat_OlessE,axiom,
% 5.42/5.63 ! [I: nat,K: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I @ K )
% 5.42/5.63 => ( ( K
% 5.42/5.63 != ( suc @ I ) )
% 5.42/5.63 => ~ ! [J2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I @ J2 )
% 5.42/5.63 => ( K
% 5.42/5.63 != ( suc @ J2 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.lessE
% 5.42/5.63 thf(fact_1025_Suc__lessD,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.42/5.63 => ( ord_less_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_lessD
% 5.42/5.63 thf(fact_1026_Suc__lessE,axiom,
% 5.42/5.63 ! [I: nat,K: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.42/5.63 => ~ ! [J2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I @ J2 )
% 5.42/5.63 => ( K
% 5.42/5.63 != ( suc @ J2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_lessE
% 5.42/5.63 thf(fact_1027_Suc__lessI,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ N )
% 5.42/5.63 => ( ( ( suc @ M )
% 5.42/5.63 != N )
% 5.42/5.63 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_lessI
% 5.42/5.63 thf(fact_1028_less__SucE,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.42/5.63 => ( ~ ( ord_less_nat @ M @ N )
% 5.42/5.63 => ( M = N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_SucE
% 5.42/5.63 thf(fact_1029_less__SucI,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ N )
% 5.42/5.63 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_SucI
% 5.42/5.63 thf(fact_1030_Ex__less__Suc,axiom,
% 5.42/5.63 ! [N: nat,P: nat > $o] :
% 5.42/5.63 ( ( ? [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.42/5.63 & ( P @ I4 ) ) )
% 5.42/5.63 = ( ( P @ N )
% 5.42/5.63 | ? [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ N )
% 5.42/5.63 & ( P @ I4 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Ex_less_Suc
% 5.42/5.63 thf(fact_1031_less__Suc__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.42/5.63 = ( ( ord_less_nat @ M @ N )
% 5.42/5.63 | ( M = N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_Suc_eq
% 5.42/5.63 thf(fact_1032_not__less__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.42/5.63 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % not_less_eq
% 5.42/5.63 thf(fact_1033_All__less__Suc,axiom,
% 5.42/5.63 ! [N: nat,P: nat > $o] :
% 5.42/5.63 ( ( ! [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.42/5.63 => ( P @ I4 ) ) )
% 5.42/5.63 = ( ( P @ N )
% 5.42/5.63 & ! [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ N )
% 5.42/5.63 => ( P @ I4 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % All_less_Suc
% 5.42/5.63 thf(fact_1034_Suc__less__eq2,axiom,
% 5.42/5.63 ! [N: nat,M: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.42/5.63 = ( ? [M5: nat] :
% 5.42/5.63 ( ( M
% 5.42/5.63 = ( suc @ M5 ) )
% 5.42/5.63 & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_less_eq2
% 5.42/5.63 thf(fact_1035_less__antisym,axiom,
% 5.42/5.63 ! [N: nat,M: nat] :
% 5.42/5.63 ( ~ ( ord_less_nat @ N @ M )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.42/5.63 => ( M = N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_antisym
% 5.42/5.63 thf(fact_1036_Suc__less__SucD,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.42/5.63 => ( ord_less_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_less_SucD
% 5.42/5.63 thf(fact_1037_less__trans__Suc,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I @ J )
% 5.42/5.63 => ( ( ord_less_nat @ J @ K )
% 5.42/5.63 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_trans_Suc
% 5.42/5.63 thf(fact_1038_less__Suc__induct,axiom,
% 5.42/5.63 ! [I: nat,J: nat,P: nat > nat > $o] :
% 5.42/5.63 ( ( ord_less_nat @ I @ J )
% 5.42/5.63 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 5.42/5.63 => ( ! [I2: nat,J2: nat,K3: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ J2 )
% 5.42/5.63 => ( ( ord_less_nat @ J2 @ K3 )
% 5.42/5.63 => ( ( P @ I2 @ J2 )
% 5.42/5.63 => ( ( P @ J2 @ K3 )
% 5.42/5.63 => ( P @ I2 @ K3 ) ) ) ) )
% 5.42/5.63 => ( P @ I @ J ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_Suc_induct
% 5.42/5.63 thf(fact_1039_strict__inc__induct,axiom,
% 5.42/5.63 ! [I: nat,J: nat,P: nat > $o] :
% 5.42/5.63 ( ( ord_less_nat @ I @ J )
% 5.42/5.63 => ( ! [I2: nat] :
% 5.42/5.63 ( ( J
% 5.42/5.63 = ( suc @ I2 ) )
% 5.42/5.63 => ( P @ I2 ) )
% 5.42/5.63 => ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ J )
% 5.42/5.63 => ( ( P @ ( suc @ I2 ) )
% 5.42/5.63 => ( P @ I2 ) ) )
% 5.42/5.63 => ( P @ I ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % strict_inc_induct
% 5.42/5.63 thf(fact_1040_not__less__less__Suc__eq,axiom,
% 5.42/5.63 ! [N: nat,M: nat] :
% 5.42/5.63 ( ~ ( ord_less_nat @ N @ M )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.42/5.63 = ( N = M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % not_less_less_Suc_eq
% 5.42/5.63 thf(fact_1041_diff__add__inverse2,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.42/5.63 = M ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_inverse2
% 5.42/5.63 thf(fact_1042_diff__add__inverse,axiom,
% 5.42/5.63 ! [N: nat,M: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.42/5.63 = M ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add_inverse
% 5.42/5.63 thf(fact_1043_diff__cancel2,axiom,
% 5.42/5.63 ! [M: nat,K: nat,N: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.42/5.63 = ( minus_minus_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_cancel2
% 5.42/5.63 thf(fact_1044_Nat_Odiff__cancel,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.42/5.63 = ( minus_minus_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.diff_cancel
% 5.42/5.63 thf(fact_1045_transitive__stepwise__le,axiom,
% 5.42/5.63 ! [M: nat,N: nat,R2: nat > nat > $o] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ! [X3: nat] : ( R2 @ X3 @ X3 )
% 5.42/5.63 => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 5.42/5.63 ( ( R2 @ X3 @ Y3 )
% 5.42/5.63 => ( ( R2 @ Y3 @ Z3 )
% 5.42/5.63 => ( R2 @ X3 @ Z3 ) ) )
% 5.42/5.63 => ( ! [N3: nat] : ( R2 @ N3 @ ( suc @ N3 ) )
% 5.42/5.63 => ( R2 @ M @ N ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % transitive_stepwise_le
% 5.42/5.63 thf(fact_1046_nat__induct__at__least,axiom,
% 5.42/5.63 ! [M: nat,N: nat,P: nat > $o] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ( P @ M )
% 5.42/5.63 => ( ! [N3: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N3 )
% 5.42/5.63 => ( ( P @ N3 )
% 5.42/5.63 => ( P @ ( suc @ N3 ) ) ) )
% 5.42/5.63 => ( P @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_induct_at_least
% 5.42/5.63 thf(fact_1047_full__nat__induct,axiom,
% 5.42/5.63 ! [P: nat > $o,N: nat] :
% 5.42/5.63 ( ! [N3: nat] :
% 5.42/5.63 ( ! [M2: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 5.42/5.63 => ( P @ M2 ) )
% 5.42/5.63 => ( P @ N3 ) )
% 5.42/5.63 => ( P @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % full_nat_induct
% 5.42/5.63 thf(fact_1048_not__less__eq__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.42/5.63 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.42/5.63
% 5.42/5.63 % not_less_eq_eq
% 5.42/5.63 thf(fact_1049_Suc__n__not__le__n,axiom,
% 5.42/5.63 ! [N: nat] :
% 5.42/5.63 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_n_not_le_n
% 5.42/5.63 thf(fact_1050_le__Suc__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.42/5.63 = ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 | ( M
% 5.42/5.63 = ( suc @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_Suc_eq
% 5.42/5.63 thf(fact_1051_Suc__le__D,axiom,
% 5.42/5.63 ! [N: nat,M6: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 5.42/5.63 => ? [M4: nat] :
% 5.42/5.63 ( M6
% 5.42/5.63 = ( suc @ M4 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_le_D
% 5.42/5.63 thf(fact_1052_le__SucI,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_SucI
% 5.42/5.63 thf(fact_1053_le__SucE,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.42/5.63 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( M
% 5.42/5.63 = ( suc @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_SucE
% 5.42/5.63 thf(fact_1054_Suc__leD,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_leD
% 5.42/5.63 thf(fact_1055_add__Suc__shift,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.42/5.63 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_Suc_shift
% 5.42/5.63 thf(fact_1056_add__Suc,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.42/5.63 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_Suc
% 5.42/5.63 thf(fact_1057_nat__arith_Osuc1,axiom,
% 5.42/5.63 ! [A2: nat,K: nat,A: nat] :
% 5.42/5.63 ( ( A2
% 5.42/5.63 = ( plus_plus_nat @ K @ A ) )
% 5.42/5.63 => ( ( suc @ A2 )
% 5.42/5.63 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_arith.suc1
% 5.42/5.63 thf(fact_1058_diff__mult__distrib2,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.42/5.63 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_mult_distrib2
% 5.42/5.63 thf(fact_1059_diff__mult__distrib,axiom,
% 5.42/5.63 ! [M: nat,N: nat,K: nat] :
% 5.42/5.63 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.42/5.63 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_mult_distrib
% 5.42/5.63 thf(fact_1060_Suc__mult__cancel1,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.42/5.63 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.42/5.63 = ( M = N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mult_cancel1
% 5.42/5.63 thf(fact_1061_Suc__mod__eq__add3__mod,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mod_eq_add3_mod
% 5.42/5.63 thf(fact_1062_cong__exp__iff__simps_I9_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.42/5.63 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.42/5.63 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(9)
% 5.42/5.63 thf(fact_1063_cong__exp__iff__simps_I9_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.42/5.63 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.42/5.63 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(9)
% 5.42/5.63 thf(fact_1064_cong__exp__iff__simps_I9_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.42/5.63 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(9)
% 5.42/5.63 thf(fact_1065_cong__exp__iff__simps_I4_J,axiom,
% 5.42/5.63 ! [M: num,N: num] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.42/5.63 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(4)
% 5.42/5.63 thf(fact_1066_cong__exp__iff__simps_I4_J,axiom,
% 5.42/5.63 ! [M: num,N: num] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.42/5.63 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(4)
% 5.42/5.63 thf(fact_1067_cong__exp__iff__simps_I4_J,axiom,
% 5.42/5.63 ! [M: num,N: num] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(4)
% 5.42/5.63 thf(fact_1068_mod__eqE,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( ( modulo_modulo_int @ A @ C )
% 5.42/5.63 = ( modulo_modulo_int @ B @ C ) )
% 5.42/5.63 => ~ ! [D3: int] :
% 5.42/5.63 ( B
% 5.42/5.63 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_eqE
% 5.42/5.63 thf(fact_1069_mod__eqE,axiom,
% 5.42/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.42/5.63 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.42/5.63 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.42/5.63 => ~ ! [D3: code_integer] :
% 5.42/5.63 ( B
% 5.42/5.63 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_eqE
% 5.42/5.63 thf(fact_1070_div__add1__eq,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.42/5.63 = ( 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 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_add1_eq
% 5.42/5.63 thf(fact_1071_div__add1__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.42/5.63 = ( 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 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_add1_eq
% 5.42/5.63 thf(fact_1072_div__add1__eq,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.42/5.63 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.42/5.63 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_add1_eq
% 5.42/5.63 thf(fact_1073_add__le__add__imp__diff__le,axiom,
% 5.42/5.63 ! [I: real,K: real,N: real,J: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.42/5.63 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.42/5.63 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.42/5.63 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.42/5.63 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_add_imp_diff_le
% 5.42/5.63 thf(fact_1074_add__le__add__imp__diff__le,axiom,
% 5.42/5.63 ! [I: rat,K: rat,N: rat,J: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.42/5.63 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.42/5.63 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.42/5.63 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.42/5.63 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_add_imp_diff_le
% 5.42/5.63 thf(fact_1075_add__le__add__imp__diff__le,axiom,
% 5.42/5.63 ! [I: nat,K: nat,N: nat,J: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.42/5.63 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_add_imp_diff_le
% 5.42/5.63 thf(fact_1076_add__le__add__imp__diff__le,axiom,
% 5.42/5.63 ! [I: int,K: int,N: int,J: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.42/5.63 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.42/5.63 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.42/5.63 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.42/5.63 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_add_imp_diff_le
% 5.42/5.63 thf(fact_1077_add__le__imp__le__diff,axiom,
% 5.42/5.63 ! [I: real,K: real,N: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.42/5.63 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_diff
% 5.42/5.63 thf(fact_1078_add__le__imp__le__diff,axiom,
% 5.42/5.63 ! [I: rat,K: rat,N: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.42/5.63 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_diff
% 5.42/5.63 thf(fact_1079_add__le__imp__le__diff,axiom,
% 5.42/5.63 ! [I: nat,K: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_diff
% 5.42/5.63 thf(fact_1080_add__le__imp__le__diff,axiom,
% 5.42/5.63 ! [I: int,K: int,N: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.42/5.63 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_le_imp_le_diff
% 5.42/5.63 thf(fact_1081_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( ( minus_minus_nat @ B @ A )
% 5.42/5.63 = C )
% 5.42/5.63 = ( B
% 5.42/5.63 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.42/5.63 thf(fact_1082_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.42/5.63 = B ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.42/5.63 thf(fact_1083_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.42/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.42/5.63 thf(fact_1084_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.42/5.63 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.42/5.63 thf(fact_1085_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.42/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.42/5.63 thf(fact_1086_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.42/5.63 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.42/5.63 thf(fact_1087_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.42/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.42/5.63 thf(fact_1088_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.42/5.63 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.42/5.63 thf(fact_1089_le__add__diff,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_add_diff
% 5.42/5.63 thf(fact_1090_diff__add,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.42/5.63 = B ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_add
% 5.42/5.63 thf(fact_1091_le__diff__eq,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.42/5.63 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_diff_eq
% 5.42/5.63 thf(fact_1092_le__diff__eq,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.42/5.63 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_diff_eq
% 5.42/5.63 thf(fact_1093_le__diff__eq,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.42/5.63 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_diff_eq
% 5.42/5.63 thf(fact_1094_diff__le__eq,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.42/5.63 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_le_eq
% 5.42/5.63 thf(fact_1095_diff__le__eq,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_le_eq
% 5.42/5.63 thf(fact_1096_diff__le__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.42/5.63 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_le_eq
% 5.42/5.63 thf(fact_1097_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.42/5.63 ! [A: real,B: real] :
% 5.42/5.63 ( ~ ( ord_less_real @ A @ B )
% 5.42/5.63 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % linordered_semidom_class.add_diff_inverse
% 5.42/5.63 thf(fact_1098_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.42/5.63 ! [A: rat,B: rat] :
% 5.42/5.63 ( ~ ( ord_less_rat @ A @ B )
% 5.42/5.63 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % linordered_semidom_class.add_diff_inverse
% 5.42/5.63 thf(fact_1099_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ~ ( ord_less_nat @ A @ B )
% 5.42/5.63 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % linordered_semidom_class.add_diff_inverse
% 5.42/5.63 thf(fact_1100_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ~ ( ord_less_int @ A @ B )
% 5.42/5.63 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.42/5.63 = A ) ) ).
% 5.42/5.63
% 5.42/5.63 % linordered_semidom_class.add_diff_inverse
% 5.42/5.63 thf(fact_1101_less__diff__eq,axiom,
% 5.42/5.63 ! [A: real,C: real,B: real] :
% 5.42/5.63 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.42/5.63 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_diff_eq
% 5.42/5.63 thf(fact_1102_less__diff__eq,axiom,
% 5.42/5.63 ! [A: rat,C: rat,B: rat] :
% 5.42/5.63 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.42/5.63 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_diff_eq
% 5.42/5.63 thf(fact_1103_less__diff__eq,axiom,
% 5.42/5.63 ! [A: int,C: int,B: int] :
% 5.42/5.63 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.42/5.63 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_diff_eq
% 5.42/5.63 thf(fact_1104_diff__less__eq,axiom,
% 5.42/5.63 ! [A: real,B: real,C: real] :
% 5.42/5.63 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.42/5.63 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_less_eq
% 5.42/5.63 thf(fact_1105_diff__less__eq,axiom,
% 5.42/5.63 ! [A: rat,B: rat,C: rat] :
% 5.42/5.63 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.42/5.63 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_less_eq
% 5.42/5.63 thf(fact_1106_diff__less__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.42/5.63 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_less_eq
% 5.42/5.63 thf(fact_1107_mult__diff__mult,axiom,
% 5.42/5.63 ! [X2: real,Y2: real,A: real,B: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( times_times_real @ X2 @ Y2 ) @ ( times_times_real @ A @ B ) )
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ X2 @ ( minus_minus_real @ Y2 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X2 @ A ) @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_diff_mult
% 5.42/5.63 thf(fact_1108_mult__diff__mult,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat,A: rat,B: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ Y2 ) @ ( times_times_rat @ A @ B ) )
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ X2 @ ( minus_minus_rat @ Y2 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X2 @ A ) @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_diff_mult
% 5.42/5.63 thf(fact_1109_mult__diff__mult,axiom,
% 5.42/5.63 ! [X2: int,Y2: int,A: int,B: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( times_times_int @ X2 @ Y2 ) @ ( times_times_int @ A @ B ) )
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ X2 @ ( minus_minus_int @ Y2 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X2 @ A ) @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_diff_mult
% 5.42/5.63 thf(fact_1110_square__diff__square__factored,axiom,
% 5.42/5.63 ! [X2: real,Y2: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) )
% 5.42/5.63 = ( times_times_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( minus_minus_real @ X2 @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % square_diff_square_factored
% 5.42/5.63 thf(fact_1111_square__diff__square__factored,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 5.42/5.63 = ( times_times_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( minus_minus_rat @ X2 @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % square_diff_square_factored
% 5.42/5.63 thf(fact_1112_square__diff__square__factored,axiom,
% 5.42/5.63 ! [X2: int,Y2: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) )
% 5.42/5.63 = ( times_times_int @ ( plus_plus_int @ X2 @ Y2 ) @ ( minus_minus_int @ X2 @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % square_diff_square_factored
% 5.42/5.63 thf(fact_1113_eq__add__iff2,axiom,
% 5.42/5.63 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.42/5.63 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( C
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_add_iff2
% 5.42/5.63 thf(fact_1114_eq__add__iff2,axiom,
% 5.42/5.63 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.42/5.63 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( C
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_add_iff2
% 5.42/5.63 thf(fact_1115_eq__add__iff2,axiom,
% 5.42/5.63 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.42/5.63 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( C
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_add_iff2
% 5.42/5.63 thf(fact_1116_eq__add__iff1,axiom,
% 5.42/5.63 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.42/5.63 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.42/5.63 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.42/5.63 = D2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_add_iff1
% 5.42/5.63 thf(fact_1117_eq__add__iff1,axiom,
% 5.42/5.63 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.42/5.63 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.42/5.63 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.42/5.63 = D2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_add_iff1
% 5.42/5.63 thf(fact_1118_eq__add__iff1,axiom,
% 5.42/5.63 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.42/5.63 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.42/5.63 = D2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % eq_add_iff1
% 5.42/5.63 thf(fact_1119_nat__mod__eq__iff,axiom,
% 5.42/5.63 ! [X2: nat,N: nat,Y2: nat] :
% 5.42/5.63 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ Y2 @ N ) )
% 5.42/5.63 = ( ? [Q1: nat,Q22: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ X2 @ ( times_times_nat @ N @ Q1 ) )
% 5.42/5.63 = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_mod_eq_iff
% 5.42/5.63 thf(fact_1120_lift__Suc__mono__less,axiom,
% 5.42/5.63 ! [F: nat > real,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less
% 5.42/5.63 thf(fact_1121_lift__Suc__mono__less,axiom,
% 5.42/5.63 ! [F: nat > rat,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less
% 5.42/5.63 thf(fact_1122_lift__Suc__mono__less,axiom,
% 5.42/5.63 ! [F: nat > num,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less
% 5.42/5.63 thf(fact_1123_lift__Suc__mono__less,axiom,
% 5.42/5.63 ! [F: nat > nat,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less
% 5.42/5.63 thf(fact_1124_lift__Suc__mono__less,axiom,
% 5.42/5.63 ! [F: nat > int,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less
% 5.42/5.63 thf(fact_1125_lift__Suc__mono__less__iff,axiom,
% 5.42/5.63 ! [F: nat > real,N: nat,M: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.42/5.63 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less_iff
% 5.42/5.63 thf(fact_1126_lift__Suc__mono__less__iff,axiom,
% 5.42/5.63 ! [F: nat > rat,N: nat,M: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.42/5.63 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less_iff
% 5.42/5.63 thf(fact_1127_lift__Suc__mono__less__iff,axiom,
% 5.42/5.63 ! [F: nat > num,N: nat,M: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.42/5.63 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less_iff
% 5.42/5.63 thf(fact_1128_lift__Suc__mono__less__iff,axiom,
% 5.42/5.63 ! [F: nat > nat,N: nat,M: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.42/5.63 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less_iff
% 5.42/5.63 thf(fact_1129_lift__Suc__mono__less__iff,axiom,
% 5.42/5.63 ! [F: nat > int,N: nat,M: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.42/5.63 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_less_iff
% 5.42/5.63 thf(fact_1130_power__Suc,axiom,
% 5.42/5.63 ! [A: complex,N: nat] :
% 5.42/5.63 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc
% 5.42/5.63 thf(fact_1131_power__Suc,axiom,
% 5.42/5.63 ! [A: real,N: nat] :
% 5.42/5.63 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc
% 5.42/5.63 thf(fact_1132_power__Suc,axiom,
% 5.42/5.63 ! [A: rat,N: nat] :
% 5.42/5.63 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc
% 5.42/5.63 thf(fact_1133_power__Suc,axiom,
% 5.42/5.63 ! [A: nat,N: nat] :
% 5.42/5.63 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc
% 5.42/5.63 thf(fact_1134_power__Suc,axiom,
% 5.42/5.63 ! [A: int,N: nat] :
% 5.42/5.63 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc
% 5.42/5.63 thf(fact_1135_power__Suc2,axiom,
% 5.42/5.63 ! [A: complex,N: nat] :
% 5.42/5.63 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc2
% 5.42/5.63 thf(fact_1136_power__Suc2,axiom,
% 5.42/5.63 ! [A: real,N: nat] :
% 5.42/5.63 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc2
% 5.42/5.63 thf(fact_1137_power__Suc2,axiom,
% 5.42/5.63 ! [A: rat,N: nat] :
% 5.42/5.63 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc2
% 5.42/5.63 thf(fact_1138_power__Suc2,axiom,
% 5.42/5.63 ! [A: nat,N: nat] :
% 5.42/5.63 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc2
% 5.42/5.63 thf(fact_1139_power__Suc2,axiom,
% 5.42/5.63 ! [A: int,N: nat] :
% 5.42/5.63 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.42/5.63 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_Suc2
% 5.42/5.63 thf(fact_1140_lift__Suc__antimono__le,axiom,
% 5.42/5.63 ! [F: nat > set_nat,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_antimono_le
% 5.42/5.63 thf(fact_1141_lift__Suc__antimono__le,axiom,
% 5.42/5.63 ! [F: nat > rat,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_antimono_le
% 5.42/5.63 thf(fact_1142_lift__Suc__antimono__le,axiom,
% 5.42/5.63 ! [F: nat > num,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_antimono_le
% 5.42/5.63 thf(fact_1143_lift__Suc__antimono__le,axiom,
% 5.42/5.63 ! [F: nat > nat,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_antimono_le
% 5.42/5.63 thf(fact_1144_lift__Suc__antimono__le,axiom,
% 5.42/5.63 ! [F: nat > int,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_antimono_le
% 5.42/5.63 thf(fact_1145_lift__Suc__mono__le,axiom,
% 5.42/5.63 ! [F: nat > set_nat,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_le
% 5.42/5.63 thf(fact_1146_lift__Suc__mono__le,axiom,
% 5.42/5.63 ! [F: nat > rat,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_le
% 5.42/5.63 thf(fact_1147_lift__Suc__mono__le,axiom,
% 5.42/5.63 ! [F: nat > num,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_le
% 5.42/5.63 thf(fact_1148_lift__Suc__mono__le,axiom,
% 5.42/5.63 ! [F: nat > nat,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_le
% 5.42/5.63 thf(fact_1149_lift__Suc__mono__le,axiom,
% 5.42/5.63 ! [F: nat > int,N: nat,N5: nat] :
% 5.42/5.63 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.42/5.63 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % lift_Suc_mono_le
% 5.42/5.63 thf(fact_1150_diff__less__mono,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( ord_less_nat @ A @ B )
% 5.42/5.63 => ( ( ord_less_eq_nat @ C @ A )
% 5.42/5.63 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_less_mono
% 5.42/5.63 thf(fact_1151_less__diff__iff,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ M )
% 5.42/5.63 => ( ( ord_less_eq_nat @ K @ N )
% 5.42/5.63 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.42/5.63 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_diff_iff
% 5.42/5.63 thf(fact_1152_add__diff__inverse__nat,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ~ ( ord_less_nat @ M @ N )
% 5.42/5.63 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.42/5.63 = M ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_inverse_nat
% 5.42/5.63 thf(fact_1153_less__diff__conv,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.42/5.63 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_diff_conv
% 5.42/5.63 thf(fact_1154_Nat_Ole__imp__diff__is__add,axiom,
% 5.42/5.63 ! [I: nat,J: nat,K: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 => ( ( ( minus_minus_nat @ J @ I )
% 5.42/5.63 = K )
% 5.42/5.63 = ( J
% 5.42/5.63 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.le_imp_diff_is_add
% 5.42/5.63 thf(fact_1155_Nat_Odiff__add__assoc2,axiom,
% 5.42/5.63 ! [K: nat,J: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.42/5.63 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 5.42/5.63 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.diff_add_assoc2
% 5.42/5.63 thf(fact_1156_Nat_Odiff__add__assoc,axiom,
% 5.42/5.63 ! [K: nat,J: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.42/5.63 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.42/5.63 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.diff_add_assoc
% 5.42/5.63 thf(fact_1157_Nat_Ole__diff__conv2,axiom,
% 5.42/5.63 ! [K: nat,J: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.42/5.63 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.42/5.63 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Nat.le_diff_conv2
% 5.42/5.63 thf(fact_1158_le__diff__conv,axiom,
% 5.42/5.63 ! [J: nat,K: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.42/5.63 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_diff_conv
% 5.42/5.63 thf(fact_1159_le__imp__less__Suc,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_imp_less_Suc
% 5.42/5.63 thf(fact_1160_less__eq__Suc__le,axiom,
% 5.42/5.63 ( ord_less_nat
% 5.42/5.63 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_eq_Suc_le
% 5.42/5.63 thf(fact_1161_less__Suc__eq__le,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.42/5.63 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_Suc_eq_le
% 5.42/5.63 thf(fact_1162_le__less__Suc__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.42/5.63 = ( N = M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % le_less_Suc_eq
% 5.42/5.63 thf(fact_1163_Suc__le__lessD,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.42/5.63 => ( ord_less_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_le_lessD
% 5.42/5.63 thf(fact_1164_inc__induct,axiom,
% 5.42/5.63 ! [I: nat,J: nat,P: nat > $o] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 => ( ( P @ J )
% 5.42/5.63 => ( ! [N3: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ N3 )
% 5.42/5.63 => ( ( ord_less_nat @ N3 @ J )
% 5.42/5.63 => ( ( P @ ( suc @ N3 ) )
% 5.42/5.63 => ( P @ N3 ) ) ) )
% 5.42/5.63 => ( P @ I ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % inc_induct
% 5.42/5.63 thf(fact_1165_dec__induct,axiom,
% 5.42/5.63 ! [I: nat,J: nat,P: nat > $o] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 => ( ( P @ I )
% 5.42/5.63 => ( ! [N3: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ N3 )
% 5.42/5.63 => ( ( ord_less_nat @ N3 @ J )
% 5.42/5.63 => ( ( P @ N3 )
% 5.42/5.63 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.42/5.63 => ( P @ J ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % dec_induct
% 5.42/5.63 thf(fact_1166_Suc__le__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.42/5.63 = ( ord_less_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_le_eq
% 5.42/5.63 thf(fact_1167_Suc__leI,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ N )
% 5.42/5.63 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_leI
% 5.42/5.63 thf(fact_1168_less__imp__Suc__add,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ N )
% 5.42/5.63 => ? [K3: nat] :
% 5.42/5.63 ( N
% 5.42/5.63 = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_imp_Suc_add
% 5.42/5.63 thf(fact_1169_less__iff__Suc__add,axiom,
% 5.42/5.63 ( ord_less_nat
% 5.42/5.63 = ( ^ [M3: nat,N2: nat] :
% 5.42/5.63 ? [K2: nat] :
% 5.42/5.63 ( N2
% 5.42/5.63 = ( suc @ ( plus_plus_nat @ M3 @ K2 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_iff_Suc_add
% 5.42/5.63 thf(fact_1170_less__add__Suc2,axiom,
% 5.42/5.63 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_Suc2
% 5.42/5.63 thf(fact_1171_less__add__Suc1,axiom,
% 5.42/5.63 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_Suc1
% 5.42/5.63 thf(fact_1172_less__natE,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ M @ N )
% 5.42/5.63 => ~ ! [Q3: nat] :
% 5.42/5.63 ( N
% 5.42/5.63 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_natE
% 5.42/5.63 thf(fact_1173_Suc__mult__less__cancel1,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.42/5.63 = ( ord_less_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mult_less_cancel1
% 5.42/5.63 thf(fact_1174_Suc__mult__le__cancel1,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.42/5.63 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_mult_le_cancel1
% 5.42/5.63 thf(fact_1175_Suc__eq__plus1__left,axiom,
% 5.42/5.63 ( suc
% 5.42/5.63 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_eq_plus1_left
% 5.42/5.63 thf(fact_1176_plus__1__eq__Suc,axiom,
% 5.42/5.63 ( ( plus_plus_nat @ one_one_nat )
% 5.42/5.63 = suc ) ).
% 5.42/5.63
% 5.42/5.63 % plus_1_eq_Suc
% 5.42/5.63 thf(fact_1177_Suc__eq__plus1,axiom,
% 5.42/5.63 ( suc
% 5.42/5.63 = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_eq_plus1
% 5.42/5.63 thf(fact_1178_Suc__div__le__mono,axiom,
% 5.42/5.63 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_div_le_mono
% 5.42/5.63 thf(fact_1179_mult__Suc,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.42/5.63 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_Suc
% 5.42/5.63 thf(fact_1180_mult__exp__mod__exp__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat,A: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_exp_mod_exp_eq
% 5.42/5.63 thf(fact_1181_mult__exp__mod__exp__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat,A: int] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_exp_mod_exp_eq
% 5.42/5.63 thf(fact_1182_mult__exp__mod__exp__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat,A: code_integer] :
% 5.42/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.42/5.63 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mult_exp_mod_exp_eq
% 5.42/5.63 thf(fact_1183_cong__exp__iff__simps_I6_J,axiom,
% 5.42/5.63 ! [Q2: num,N: num] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(6)
% 5.42/5.63 thf(fact_1184_cong__exp__iff__simps_I6_J,axiom,
% 5.42/5.63 ! [Q2: num,N: num] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(6)
% 5.42/5.63 thf(fact_1185_cong__exp__iff__simps_I6_J,axiom,
% 5.42/5.63 ! [Q2: num,N: num] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(6)
% 5.42/5.63 thf(fact_1186_cong__exp__iff__simps_I8_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(8)
% 5.42/5.63 thf(fact_1187_cong__exp__iff__simps_I8_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(8)
% 5.42/5.63 thf(fact_1188_cong__exp__iff__simps_I8_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(8)
% 5.42/5.63 thf(fact_1189_mult__div__mod__eq,axiom,
% 5.42/5.63 ! [B: nat,A: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult_div_mod_eq
% 5.42/5.63 thf(fact_1190_mult__div__mod__eq,axiom,
% 5.42/5.63 ! [B: int,A: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult_div_mod_eq
% 5.42/5.63 thf(fact_1191_mult__div__mod__eq,axiom,
% 5.42/5.63 ! [B: code_integer,A: code_integer] :
% 5.42/5.63 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mult_div_mod_eq
% 5.42/5.63 thf(fact_1192_mod__mult__div__eq,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_div_eq
% 5.42/5.63 thf(fact_1193_mod__mult__div__eq,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_div_eq
% 5.42/5.63 thf(fact_1194_mod__mult__div__eq,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult_div_eq
% 5.42/5.63 thf(fact_1195_mod__div__mult__eq,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mod_div_mult_eq
% 5.42/5.63 thf(fact_1196_mod__div__mult__eq,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mod_div_mult_eq
% 5.42/5.63 thf(fact_1197_mod__div__mult__eq,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % mod_div_mult_eq
% 5.42/5.63 thf(fact_1198_div__mult__mod__eq,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % div_mult_mod_eq
% 5.42/5.63 thf(fact_1199_div__mult__mod__eq,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % div_mult_mod_eq
% 5.42/5.63 thf(fact_1200_div__mult__mod__eq,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.42/5.63 = A ) ).
% 5.42/5.63
% 5.42/5.63 % div_mult_mod_eq
% 5.42/5.63 thf(fact_1201_mod__div__decomp,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( A
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_div_decomp
% 5.42/5.63 thf(fact_1202_mod__div__decomp,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( A
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_div_decomp
% 5.42/5.63 thf(fact_1203_mod__div__decomp,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer] :
% 5.42/5.63 ( A
% 5.42/5.63 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_div_decomp
% 5.42/5.63 thf(fact_1204_cancel__div__mod__rules_I1_J,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.42/5.63 = ( plus_plus_nat @ A @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % cancel_div_mod_rules(1)
% 5.42/5.63 thf(fact_1205_cancel__div__mod__rules_I1_J,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.42/5.63 = ( plus_plus_int @ A @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % cancel_div_mod_rules(1)
% 5.42/5.63 thf(fact_1206_cancel__div__mod__rules_I1_J,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.42/5.63 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.42/5.63 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % cancel_div_mod_rules(1)
% 5.42/5.63 thf(fact_1207_cancel__div__mod__rules_I2_J,axiom,
% 5.42/5.63 ! [B: nat,A: nat,C: nat] :
% 5.42/5.63 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.42/5.63 = ( plus_plus_nat @ A @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % cancel_div_mod_rules(2)
% 5.42/5.63 thf(fact_1208_cancel__div__mod__rules_I2_J,axiom,
% 5.42/5.63 ! [B: int,A: int,C: int] :
% 5.42/5.63 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.42/5.63 = ( plus_plus_int @ A @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % cancel_div_mod_rules(2)
% 5.42/5.63 thf(fact_1209_cancel__div__mod__rules_I2_J,axiom,
% 5.42/5.63 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.42/5.63 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.42/5.63 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.42/5.63
% 5.42/5.63 % cancel_div_mod_rules(2)
% 5.42/5.63 thf(fact_1210_div__mult1__eq,axiom,
% 5.42/5.63 ! [A: nat,B: nat,C: nat] :
% 5.42/5.63 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.42/5.63 = ( 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 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_mult1_eq
% 5.42/5.63 thf(fact_1211_div__mult1__eq,axiom,
% 5.42/5.63 ! [A: int,B: int,C: int] :
% 5.42/5.63 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.42/5.63 = ( 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 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_mult1_eq
% 5.42/5.63 thf(fact_1212_div__mult1__eq,axiom,
% 5.42/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.42/5.63 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.42/5.63 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_mult1_eq
% 5.42/5.63 thf(fact_1213_cong__exp__iff__simps_I10_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(10)
% 5.42/5.63 thf(fact_1214_cong__exp__iff__simps_I10_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(10)
% 5.42/5.63 thf(fact_1215_cong__exp__iff__simps_I10_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(10)
% 5.42/5.63 thf(fact_1216_cong__exp__iff__simps_I12_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(12)
% 5.42/5.63 thf(fact_1217_cong__exp__iff__simps_I12_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(12)
% 5.42/5.63 thf(fact_1218_cong__exp__iff__simps_I12_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(12)
% 5.42/5.63 thf(fact_1219_cong__exp__iff__simps_I13_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.42/5.63 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.42/5.63 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(13)
% 5.42/5.63 thf(fact_1220_cong__exp__iff__simps_I13_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.42/5.63 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.42/5.63 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(13)
% 5.42/5.63 thf(fact_1221_cong__exp__iff__simps_I13_J,axiom,
% 5.42/5.63 ! [M: num,Q2: num,N: num] :
% 5.42/5.63 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.42/5.63 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.42/5.63 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % cong_exp_iff_simps(13)
% 5.42/5.63 thf(fact_1222_ordered__ring__class_Ole__add__iff2,axiom,
% 5.42/5.63 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_ring_class.le_add_iff2
% 5.42/5.63 thf(fact_1223_ordered__ring__class_Ole__add__iff2,axiom,
% 5.42/5.63 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_ring_class.le_add_iff2
% 5.42/5.63 thf(fact_1224_ordered__ring__class_Ole__add__iff2,axiom,
% 5.42/5.63 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_ring_class.le_add_iff2
% 5.42/5.63 thf(fact_1225_ordered__ring__class_Ole__add__iff1,axiom,
% 5.42/5.63 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.42/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_ring_class.le_add_iff1
% 5.42/5.63 thf(fact_1226_ordered__ring__class_Ole__add__iff1,axiom,
% 5.42/5.63 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.42/5.63 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_ring_class.le_add_iff1
% 5.42/5.63 thf(fact_1227_ordered__ring__class_Ole__add__iff1,axiom,
% 5.42/5.63 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.42/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % ordered_ring_class.le_add_iff1
% 5.42/5.63 thf(fact_1228_less__add__iff2,axiom,
% 5.42/5.63 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.42/5.63 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_iff2
% 5.42/5.63 thf(fact_1229_less__add__iff2,axiom,
% 5.42/5.63 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.42/5.63 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_iff2
% 5.42/5.63 thf(fact_1230_less__add__iff2,axiom,
% 5.42/5.63 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.42/5.63 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_iff2
% 5.42/5.63 thf(fact_1231_less__add__iff1,axiom,
% 5.42/5.63 ! [A: real,E: real,C: real,B: real,D2: real] :
% 5.42/5.63 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_iff1
% 5.42/5.63 thf(fact_1232_less__add__iff1,axiom,
% 5.42/5.63 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.42/5.63 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_iff1
% 5.42/5.63 thf(fact_1233_less__add__iff1,axiom,
% 5.42/5.63 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.42/5.63 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.42/5.63 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_add_iff1
% 5.42/5.63 thf(fact_1234_square__diff__one__factored,axiom,
% 5.42/5.63 ! [X2: complex] :
% 5.42/5.63 ( ( minus_minus_complex @ ( times_times_complex @ X2 @ X2 ) @ one_one_complex )
% 5.42/5.63 = ( times_times_complex @ ( plus_plus_complex @ X2 @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % square_diff_one_factored
% 5.42/5.63 thf(fact_1235_square__diff__one__factored,axiom,
% 5.42/5.63 ! [X2: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ one_one_real )
% 5.42/5.63 = ( times_times_real @ ( plus_plus_real @ X2 @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % square_diff_one_factored
% 5.42/5.63 thf(fact_1236_square__diff__one__factored,axiom,
% 5.42/5.63 ! [X2: rat] :
% 5.42/5.63 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ one_one_rat )
% 5.42/5.63 = ( times_times_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % square_diff_one_factored
% 5.42/5.63 thf(fact_1237_square__diff__one__factored,axiom,
% 5.42/5.63 ! [X2: int] :
% 5.42/5.63 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ one_one_int )
% 5.42/5.63 = ( times_times_int @ ( plus_plus_int @ X2 @ one_one_int ) @ ( minus_minus_int @ X2 @ one_one_int ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % square_diff_one_factored
% 5.42/5.63 thf(fact_1238_nat__mod__eq__lemma,axiom,
% 5.42/5.63 ! [X2: nat,N: nat,Y2: nat] :
% 5.42/5.63 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.42/5.63 = ( modulo_modulo_nat @ Y2 @ N ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 5.42/5.63 => ? [Q3: nat] :
% 5.42/5.63 ( X2
% 5.42/5.63 = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_mod_eq_lemma
% 5.42/5.63 thf(fact_1239_mod__eq__nat2E,axiom,
% 5.42/5.63 ! [M: nat,Q2: nat,N: nat] :
% 5.42/5.63 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.42/5.63 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.63 => ~ ! [S3: nat] :
% 5.42/5.63 ( N
% 5.42/5.63 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_eq_nat2E
% 5.42/5.63 thf(fact_1240_mod__eq__nat1E,axiom,
% 5.42/5.63 ! [M: nat,Q2: nat,N: nat] :
% 5.42/5.63 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.42/5.63 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ N @ M )
% 5.42/5.63 => ~ ! [S3: nat] :
% 5.42/5.63 ( M
% 5.42/5.63 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_eq_nat1E
% 5.42/5.63 thf(fact_1241_mod__mult2__eq,axiom,
% 5.42/5.63 ! [M: nat,N: nat,Q2: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % mod_mult2_eq
% 5.42/5.63 thf(fact_1242_power__gt1,axiom,
% 5.42/5.63 ! [A: real,N: nat] :
% 5.42/5.63 ( ( ord_less_real @ one_one_real @ A )
% 5.42/5.63 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_gt1
% 5.42/5.63 thf(fact_1243_power__gt1,axiom,
% 5.42/5.63 ! [A: rat,N: nat] :
% 5.42/5.63 ( ( ord_less_rat @ one_one_rat @ A )
% 5.42/5.63 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_gt1
% 5.42/5.63 thf(fact_1244_power__gt1,axiom,
% 5.42/5.63 ! [A: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_nat @ one_one_nat @ A )
% 5.42/5.63 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_gt1
% 5.42/5.63 thf(fact_1245_power__gt1,axiom,
% 5.42/5.63 ! [A: int,N: nat] :
% 5.42/5.63 ( ( ord_less_int @ one_one_int @ A )
% 5.42/5.63 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_gt1
% 5.42/5.63 thf(fact_1246_less__diff__conv2,axiom,
% 5.42/5.63 ! [K: nat,J: nat,I: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.42/5.63 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.42/5.63 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % less_diff_conv2
% 5.42/5.63 thf(fact_1247_eval__nat__numeral_I3_J,axiom,
% 5.42/5.63 ! [N: num] :
% 5.42/5.63 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.42/5.63 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % eval_nat_numeral(3)
% 5.42/5.63 thf(fact_1248_nat__diff__add__eq2,axiom,
% 5.42/5.63 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.42/5.63 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_diff_add_eq2
% 5.42/5.63 thf(fact_1249_nat__diff__add__eq1,axiom,
% 5.42/5.63 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ J @ I )
% 5.42/5.63 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.42/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_diff_add_eq1
% 5.42/5.63 thf(fact_1250_nat__le__add__iff2,axiom,
% 5.42/5.63 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.42/5.63 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_le_add_iff2
% 5.42/5.63 thf(fact_1251_nat__le__add__iff1,axiom,
% 5.42/5.63 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ J @ I )
% 5.42/5.63 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.42/5.63 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_le_add_iff1
% 5.42/5.63 thf(fact_1252_nat__eq__add__iff2,axiom,
% 5.42/5.63 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.42/5.63 = ( M
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_eq_add_iff2
% 5.42/5.63 thf(fact_1253_nat__eq__add__iff1,axiom,
% 5.42/5.63 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ J @ I )
% 5.42/5.63 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.42/5.63 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 5.42/5.63 = N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_eq_add_iff1
% 5.42/5.63 thf(fact_1254_power2__commute,axiom,
% 5.42/5.63 ! [X2: real,Y2: real] :
% 5.42/5.63 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( power_power_real @ ( minus_minus_real @ Y2 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_commute
% 5.42/5.63 thf(fact_1255_power2__commute,axiom,
% 5.42/5.63 ! [X2: complex,Y2: complex] :
% 5.42/5.63 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( power_power_complex @ ( minus_minus_complex @ Y2 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_commute
% 5.42/5.63 thf(fact_1256_power2__commute,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat] :
% 5.42/5.63 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( power_power_rat @ ( minus_minus_rat @ Y2 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_commute
% 5.42/5.63 thf(fact_1257_power2__commute,axiom,
% 5.42/5.63 ! [X2: int,Y2: int] :
% 5.42/5.63 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( power_power_int @ ( minus_minus_int @ Y2 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_commute
% 5.42/5.63 thf(fact_1258_nat__less__add__iff2,axiom,
% 5.42/5.63 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ I @ J )
% 5.42/5.63 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.42/5.63 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_less_add_iff2
% 5.42/5.63 thf(fact_1259_nat__less__add__iff1,axiom,
% 5.42/5.63 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ J @ I )
% 5.42/5.63 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.42/5.63 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % nat_less_add_iff1
% 5.42/5.63 thf(fact_1260_Suc3__eq__add__3,axiom,
% 5.42/5.63 ! [N: nat] :
% 5.42/5.63 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.42/5.63 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc3_eq_add_3
% 5.42/5.63 thf(fact_1261_div__nat__eqI,axiom,
% 5.42/5.63 ! [N: nat,Q2: nat,M: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 5.42/5.63 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 5.42/5.63 => ( ( divide_divide_nat @ M @ N )
% 5.42/5.63 = Q2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_nat_eqI
% 5.42/5.63 thf(fact_1262_Suc__nat__number__of__add,axiom,
% 5.42/5.63 ! [V: num,N: nat] :
% 5.42/5.63 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.42/5.63 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_nat_number_of_add
% 5.42/5.63 thf(fact_1263_diff__le__diff__pow,axiom,
% 5.42/5.63 ! [K: nat,M: nat,N: nat] :
% 5.42/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.42/5.63 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % diff_le_diff_pow
% 5.42/5.63 thf(fact_1264_Suc__div__eq__add3__div,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.42/5.63 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_div_eq_add3_div
% 5.42/5.63 thf(fact_1265_div__exp__mod__exp__eq,axiom,
% 5.42/5.63 ! [A: nat,N: nat,M: nat] :
% 5.42/5.63 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_exp_mod_exp_eq
% 5.42/5.63 thf(fact_1266_div__exp__mod__exp__eq,axiom,
% 5.42/5.63 ! [A: int,N: nat,M: nat] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_exp_mod_exp_eq
% 5.42/5.63 thf(fact_1267_div__exp__mod__exp__eq,axiom,
% 5.42/5.63 ! [A: code_integer,N: nat,M: nat] :
% 5.42/5.63 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_exp_mod_exp_eq
% 5.42/5.63 thf(fact_1268_insersimp,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat,Y2: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 5.42/5.63 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % insersimp
% 5.42/5.63 thf(fact_1269_power__odd__eq,axiom,
% 5.42/5.63 ! [A: complex,N: nat] :
% 5.42/5.63 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.42/5.63 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_odd_eq
% 5.42/5.63 thf(fact_1270_power__odd__eq,axiom,
% 5.42/5.63 ! [A: real,N: nat] :
% 5.42/5.63 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.42/5.63 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_odd_eq
% 5.42/5.63 thf(fact_1271_power__odd__eq,axiom,
% 5.42/5.63 ! [A: rat,N: nat] :
% 5.42/5.63 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.42/5.63 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_odd_eq
% 5.42/5.63 thf(fact_1272_power__odd__eq,axiom,
% 5.42/5.63 ! [A: nat,N: nat] :
% 5.42/5.63 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.42/5.63 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_odd_eq
% 5.42/5.63 thf(fact_1273_power__odd__eq,axiom,
% 5.42/5.63 ! [A: int,N: nat] :
% 5.42/5.63 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.42/5.63 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power_odd_eq
% 5.42/5.63 thf(fact_1274_power2__diff,axiom,
% 5.42/5.63 ! [X2: complex,Y2: complex] :
% 5.42/5.63 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_diff
% 5.42/5.63 thf(fact_1275_power2__diff,axiom,
% 5.42/5.63 ! [X2: real,Y2: real] :
% 5.42/5.63 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_diff
% 5.42/5.63 thf(fact_1276_power2__diff,axiom,
% 5.42/5.63 ! [X2: rat,Y2: rat] :
% 5.42/5.63 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_diff
% 5.42/5.63 thf(fact_1277_power2__diff,axiom,
% 5.42/5.63 ! [X2: int,Y2: int] :
% 5.42/5.63 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.63 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % power2_diff
% 5.42/5.63 thf(fact_1278_in__children__def,axiom,
% 5.42/5.63 ( vEBT_V5917875025757280293ildren
% 5.42/5.63 = ( ^ [N2: nat,TreeList3: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X @ N2 ) ) @ ( vEBT_VEBT_low @ X @ N2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % in_children_def
% 5.42/5.63 thf(fact_1279_invar__vebt_Ointros_I5_J,axiom,
% 5.42/5.63 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.42/5.63 ( ! [X3: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.63 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.42/5.63 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.42/5.63 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.42/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 => ( ( M
% 5.42/5.63 = ( suc @ N ) )
% 5.42/5.63 => ( ( Deg
% 5.42/5.63 = ( plus_plus_nat @ N @ M ) )
% 5.42/5.63 => ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X5 ) )
% 5.42/5.63 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.42/5.63 => ( ( ( Mi = Ma )
% 5.42/5.63 => ! [X3: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.63 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.42/5.63 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.42/5.63 => ( ( ( Mi != Ma )
% 5.42/5.63 => ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.42/5.63 = I2 )
% 5.42/5.63 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.42/5.63 & ! [X3: nat] :
% 5.42/5.63 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.42/5.63 = I2 )
% 5.42/5.63 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.42/5.63 => ( ( ord_less_nat @ Mi @ X3 )
% 5.42/5.63 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.42/5.63 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % invar_vebt.intros(5)
% 5.42/5.63 thf(fact_1280_invar__vebt_Ointros_I4_J,axiom,
% 5.42/5.63 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.42/5.63 ( ! [X3: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.63 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.42/5.63 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.42/5.63 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.42/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 => ( ( M = N )
% 5.42/5.63 => ( ( Deg
% 5.42/5.63 = ( plus_plus_nat @ N @ M ) )
% 5.42/5.63 => ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X5 ) )
% 5.42/5.63 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.42/5.63 => ( ( ( Mi = Ma )
% 5.42/5.63 => ! [X3: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.63 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.42/5.63 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.42/5.63 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.42/5.63 => ( ( ( Mi != Ma )
% 5.42/5.63 => ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.42/5.63 = I2 )
% 5.42/5.63 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.42/5.63 & ! [X3: nat] :
% 5.42/5.63 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.42/5.63 = I2 )
% 5.42/5.63 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.42/5.63 => ( ( ord_less_nat @ Mi @ X3 )
% 5.42/5.63 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.42/5.63 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % invar_vebt.intros(4)
% 5.42/5.63 thf(fact_1281_set__vebt__set__vebt_H__valid,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,N: nat] :
% 5.42/5.63 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.63 => ( ( vEBT_set_vebt @ T )
% 5.42/5.63 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % set_vebt_set_vebt'_valid
% 5.42/5.63 thf(fact_1282_divmod__step__eq,axiom,
% 5.42/5.63 ! [L2: num,R: nat,Q2: nat] :
% 5.42/5.63 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 5.42/5.63 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.42/5.63 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 5.42/5.63 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 5.42/5.63 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.42/5.63 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divmod_step_eq
% 5.42/5.63 thf(fact_1283_divmod__step__eq,axiom,
% 5.42/5.63 ! [L2: num,R: int,Q2: int] :
% 5.42/5.63 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 5.42/5.63 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.42/5.63 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 5.42/5.63 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 5.42/5.63 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.42/5.63 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divmod_step_eq
% 5.42/5.63 thf(fact_1284_divmod__step__eq,axiom,
% 5.42/5.63 ! [L2: num,R: code_integer,Q2: code_integer] :
% 5.42/5.63 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 5.42/5.63 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 5.42/5.63 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 5.42/5.63 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 5.42/5.63 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 5.42/5.63 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % divmod_step_eq
% 5.42/5.63 thf(fact_1285_double__not__eq__Suc__double,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.42/5.63 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % double_not_eq_Suc_double
% 5.42/5.63 thf(fact_1286_Suc__double__not__eq__double,axiom,
% 5.42/5.63 ! [M: nat,N: nat] :
% 5.42/5.63 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.63 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.42/5.63
% 5.42/5.63 % Suc_double_not_eq_double
% 5.42/5.63 thf(fact_1287_div__mod__decomp,axiom,
% 5.42/5.63 ! [A2: nat,N: nat] :
% 5.42/5.63 ( A2
% 5.42/5.63 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_mod_decomp
% 5.42/5.63 thf(fact_1288_unset__bit__Suc,axiom,
% 5.42/5.63 ! [N: nat,A: code_integer] :
% 5.42/5.63 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.42/5.63 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % unset_bit_Suc
% 5.42/5.63 thf(fact_1289_unset__bit__Suc,axiom,
% 5.42/5.63 ! [N: nat,A: int] :
% 5.42/5.63 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.42/5.63 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % unset_bit_Suc
% 5.42/5.63 thf(fact_1290_unset__bit__Suc,axiom,
% 5.42/5.63 ! [N: nat,A: nat] :
% 5.42/5.63 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.42/5.63 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % unset_bit_Suc
% 5.42/5.63 thf(fact_1291_flip__bit__Suc,axiom,
% 5.42/5.63 ! [N: nat,A: code_integer] :
% 5.42/5.63 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.42/5.63 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % flip_bit_Suc
% 5.42/5.63 thf(fact_1292_flip__bit__Suc,axiom,
% 5.42/5.63 ! [N: nat,A: int] :
% 5.42/5.63 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.42/5.63 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % flip_bit_Suc
% 5.42/5.63 thf(fact_1293_flip__bit__Suc,axiom,
% 5.42/5.63 ! [N: nat,A: nat] :
% 5.42/5.63 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.42/5.63 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % flip_bit_Suc
% 5.42/5.63 thf(fact_1294_set__bit__Suc,axiom,
% 5.42/5.63 ! [N: nat,A: code_integer] :
% 5.42/5.63 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.42/5.63 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % set_bit_Suc
% 5.42/5.63 thf(fact_1295_set__bit__Suc,axiom,
% 5.42/5.63 ! [N: nat,A: int] :
% 5.42/5.63 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.42/5.63 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % set_bit_Suc
% 5.42/5.63 thf(fact_1296_set__bit__Suc,axiom,
% 5.42/5.63 ! [N: nat,A: nat] :
% 5.42/5.63 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.42/5.63 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % set_bit_Suc
% 5.42/5.63 thf(fact_1297_verit__eq__simplify_I8_J,axiom,
% 5.42/5.63 ! [X23: num,Y22: num] :
% 5.42/5.63 ( ( ( bit0 @ X23 )
% 5.42/5.63 = ( bit0 @ Y22 ) )
% 5.42/5.63 = ( X23 = Y22 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_eq_simplify(8)
% 5.42/5.63 thf(fact_1298_verit__eq__simplify_I9_J,axiom,
% 5.42/5.63 ! [X33: num,Y32: num] :
% 5.42/5.63 ( ( ( bit1 @ X33 )
% 5.42/5.63 = ( bit1 @ Y32 ) )
% 5.42/5.63 = ( X33 = Y32 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_eq_simplify(9)
% 5.42/5.63 thf(fact_1299_VEBT_Oinject_I1_J,axiom,
% 5.42/5.63 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.42/5.63 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.42/5.63 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.42/5.63 = ( ( X11 = Y11 )
% 5.42/5.63 & ( X12 = Y12 )
% 5.42/5.63 & ( X13 = Y13 )
% 5.42/5.63 & ( X14 = Y14 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % VEBT.inject(1)
% 5.42/5.63 thf(fact_1300_zmod__numeral__Bit0,axiom,
% 5.42/5.63 ! [V: num,W: num] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.42/5.63 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % zmod_numeral_Bit0
% 5.42/5.63 thf(fact_1301_zmod__numeral__Bit1,axiom,
% 5.42/5.63 ! [V: num,W: num] :
% 5.42/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.42/5.63 = ( 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 ) ) ).
% 5.42/5.63
% 5.42/5.63 % zmod_numeral_Bit1
% 5.42/5.63 thf(fact_1302_pred__member,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,X2: nat,Y2: nat] :
% 5.42/5.63 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y2 )
% 5.42/5.63 = ( ( vEBT_vebt_member @ T @ Y2 )
% 5.42/5.63 & ( ord_less_nat @ Y2 @ X2 )
% 5.42/5.63 & ! [Z4: nat] :
% 5.42/5.63 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 5.42/5.63 & ( ord_less_nat @ Z4 @ X2 ) )
% 5.42/5.63 => ( ord_less_eq_nat @ Z4 @ Y2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % pred_member
% 5.42/5.63 thf(fact_1303_succ__member,axiom,
% 5.42/5.63 ! [T: vEBT_VEBT,X2: nat,Y2: nat] :
% 5.42/5.63 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y2 )
% 5.42/5.63 = ( ( vEBT_vebt_member @ T @ Y2 )
% 5.42/5.63 & ( ord_less_nat @ X2 @ Y2 )
% 5.42/5.63 & ! [Z4: nat] :
% 5.42/5.63 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 5.42/5.63 & ( ord_less_nat @ X2 @ Z4 ) )
% 5.42/5.63 => ( ord_less_eq_nat @ Y2 @ Z4 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % succ_member
% 5.42/5.63 thf(fact_1304_div__mod__decomp__int,axiom,
% 5.42/5.63 ! [A2: int,N: int] :
% 5.42/5.63 ( A2
% 5.42/5.63 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % div_mod_decomp_int
% 5.42/5.63 thf(fact_1305_add__diff__assoc__enat,axiom,
% 5.42/5.63 ! [Z: extended_enat,Y2: extended_enat,X2: extended_enat] :
% 5.42/5.63 ( ( ord_le2932123472753598470d_enat @ Z @ Y2 )
% 5.42/5.63 => ( ( plus_p3455044024723400733d_enat @ X2 @ ( minus_3235023915231533773d_enat @ Y2 @ Z ) )
% 5.42/5.63 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % add_diff_assoc_enat
% 5.42/5.63 thf(fact_1306_xor__num_Ocases,axiom,
% 5.42/5.63 ! [X2: product_prod_num_num] :
% 5.42/5.63 ( ( X2
% 5.42/5.63 != ( product_Pair_num_num @ one @ one ) )
% 5.42/5.63 => ( ! [N3: num] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 5.42/5.63 => ( ! [N3: num] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 5.42/5.63 => ( ! [M4: num] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 5.42/5.63 => ( ! [M4: num,N3: num] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
% 5.42/5.63 => ( ! [M4: num,N3: num] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
% 5.42/5.63 => ( ! [M4: num] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 5.42/5.63 => ( ! [M4: num,N3: num] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
% 5.42/5.63 => ~ ! [M4: num,N3: num] :
% 5.42/5.63 ( X2
% 5.42/5.63 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % xor_num.cases
% 5.42/5.63 thf(fact_1307_verit__comp__simplify1_I2_J,axiom,
% 5.42/5.63 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(2)
% 5.42/5.63 thf(fact_1308_verit__comp__simplify1_I2_J,axiom,
% 5.42/5.63 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(2)
% 5.42/5.63 thf(fact_1309_verit__comp__simplify1_I2_J,axiom,
% 5.42/5.63 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(2)
% 5.42/5.63 thf(fact_1310_verit__comp__simplify1_I2_J,axiom,
% 5.42/5.63 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(2)
% 5.42/5.63 thf(fact_1311_verit__comp__simplify1_I2_J,axiom,
% 5.42/5.63 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(2)
% 5.42/5.63 thf(fact_1312_verit__la__disequality,axiom,
% 5.42/5.63 ! [A: rat,B: rat] :
% 5.42/5.63 ( ( A = B )
% 5.42/5.63 | ~ ( ord_less_eq_rat @ A @ B )
% 5.42/5.63 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_la_disequality
% 5.42/5.63 thf(fact_1313_verit__la__disequality,axiom,
% 5.42/5.63 ! [A: num,B: num] :
% 5.42/5.63 ( ( A = B )
% 5.42/5.63 | ~ ( ord_less_eq_num @ A @ B )
% 5.42/5.63 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_la_disequality
% 5.42/5.63 thf(fact_1314_verit__la__disequality,axiom,
% 5.42/5.63 ! [A: nat,B: nat] :
% 5.42/5.63 ( ( A = B )
% 5.42/5.63 | ~ ( ord_less_eq_nat @ A @ B )
% 5.42/5.63 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_la_disequality
% 5.42/5.63 thf(fact_1315_verit__la__disequality,axiom,
% 5.42/5.63 ! [A: int,B: int] :
% 5.42/5.63 ( ( A = B )
% 5.42/5.63 | ~ ( ord_less_eq_int @ A @ B )
% 5.42/5.63 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_la_disequality
% 5.42/5.63 thf(fact_1316_verit__comp__simplify1_I1_J,axiom,
% 5.42/5.63 ! [A: real] :
% 5.42/5.63 ~ ( ord_less_real @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(1)
% 5.42/5.63 thf(fact_1317_verit__comp__simplify1_I1_J,axiom,
% 5.42/5.63 ! [A: rat] :
% 5.42/5.63 ~ ( ord_less_rat @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(1)
% 5.42/5.63 thf(fact_1318_verit__comp__simplify1_I1_J,axiom,
% 5.42/5.63 ! [A: num] :
% 5.42/5.63 ~ ( ord_less_num @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(1)
% 5.42/5.63 thf(fact_1319_verit__comp__simplify1_I1_J,axiom,
% 5.42/5.63 ! [A: nat] :
% 5.42/5.63 ~ ( ord_less_nat @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(1)
% 5.42/5.63 thf(fact_1320_verit__comp__simplify1_I1_J,axiom,
% 5.42/5.63 ! [A: int] :
% 5.42/5.63 ~ ( ord_less_int @ A @ A ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(1)
% 5.42/5.63 thf(fact_1321_verit__comp__simplify1_I3_J,axiom,
% 5.42/5.63 ! [B4: real,A4: real] :
% 5.42/5.63 ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 5.42/5.63 = ( ord_less_real @ A4 @ B4 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(3)
% 5.42/5.63 thf(fact_1322_verit__comp__simplify1_I3_J,axiom,
% 5.42/5.63 ! [B4: rat,A4: rat] :
% 5.42/5.63 ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 5.42/5.63 = ( ord_less_rat @ A4 @ B4 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(3)
% 5.42/5.63 thf(fact_1323_verit__comp__simplify1_I3_J,axiom,
% 5.42/5.63 ! [B4: num,A4: num] :
% 5.42/5.63 ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 5.42/5.63 = ( ord_less_num @ A4 @ B4 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(3)
% 5.42/5.63 thf(fact_1324_verit__comp__simplify1_I3_J,axiom,
% 5.42/5.63 ! [B4: nat,A4: nat] :
% 5.42/5.63 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 5.42/5.63 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(3)
% 5.42/5.63 thf(fact_1325_verit__comp__simplify1_I3_J,axiom,
% 5.42/5.63 ! [B4: int,A4: int] :
% 5.42/5.63 ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 5.42/5.63 = ( ord_less_int @ A4 @ B4 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_comp_simplify1(3)
% 5.42/5.63 thf(fact_1326_verit__eq__simplify_I10_J,axiom,
% 5.42/5.63 ! [X23: num] :
% 5.42/5.63 ( one
% 5.42/5.63 != ( bit0 @ X23 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_eq_simplify(10)
% 5.42/5.63 thf(fact_1327_verit__eq__simplify_I14_J,axiom,
% 5.42/5.63 ! [X23: num,X33: num] :
% 5.42/5.63 ( ( bit0 @ X23 )
% 5.42/5.63 != ( bit1 @ X33 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_eq_simplify(14)
% 5.42/5.63 thf(fact_1328_verit__eq__simplify_I12_J,axiom,
% 5.42/5.63 ! [X33: num] :
% 5.42/5.63 ( one
% 5.42/5.63 != ( bit1 @ X33 ) ) ).
% 5.42/5.63
% 5.42/5.63 % verit_eq_simplify(12)
% 5.42/5.63 thf(fact_1329_real__average__minus__second,axiom,
% 5.42/5.63 ! [B: real,A: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.42/5.63 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % real_average_minus_second
% 5.42/5.63 thf(fact_1330_real__average__minus__first,axiom,
% 5.42/5.63 ! [A: real,B: real] :
% 5.42/5.63 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.42/5.63 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % real_average_minus_first
% 5.42/5.63 thf(fact_1331_all__set__conv__all__nth,axiom,
% 5.42/5.63 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.42/5.63 ( ( ! [X: vEBT_VEBT] :
% 5.42/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X ) ) )
% 5.42/5.63 = ( ! [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_set_conv_all_nth
% 5.42/5.63 thf(fact_1332_all__set__conv__all__nth,axiom,
% 5.42/5.63 ! [Xs2: list_o,P: $o > $o] :
% 5.42/5.63 ( ( ! [X: $o] :
% 5.42/5.63 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X ) ) )
% 5.42/5.63 = ( ! [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_o @ Xs2 @ I4 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_set_conv_all_nth
% 5.42/5.63 thf(fact_1333_all__set__conv__all__nth,axiom,
% 5.42/5.63 ! [Xs2: list_nat,P: nat > $o] :
% 5.42/5.63 ( ( ! [X: nat] :
% 5.42/5.63 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X ) ) )
% 5.42/5.63 = ( ! [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_nat @ Xs2 @ I4 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_set_conv_all_nth
% 5.42/5.63 thf(fact_1334_all__set__conv__all__nth,axiom,
% 5.42/5.63 ! [Xs2: list_int,P: int > $o] :
% 5.42/5.63 ( ( ! [X: int] :
% 5.42/5.63 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X ) ) )
% 5.42/5.63 = ( ! [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_int @ Xs2 @ I4 ) ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_set_conv_all_nth
% 5.42/5.63 thf(fact_1335_all__nth__imp__all__set,axiom,
% 5.42/5.63 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X2: product_prod_nat_nat] :
% 5.42/5.63 ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I2 ) ) )
% 5.42/5.63 => ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.42/5.63 => ( P @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_nth_imp_all_set
% 5.42/5.63 thf(fact_1336_all__nth__imp__all__set,axiom,
% 5.42/5.63 ! [Xs2: list_complex,P: complex > $o,X2: complex] :
% 5.42/5.63 ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_complex @ Xs2 @ I2 ) ) )
% 5.42/5.63 => ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_nth_imp_all_set
% 5.42/5.63 thf(fact_1337_all__nth__imp__all__set,axiom,
% 5.42/5.63 ! [Xs2: list_real,P: real > $o,X2: real] :
% 5.42/5.63 ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_real @ Xs2 @ I2 ) ) )
% 5.42/5.63 => ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_nth_imp_all_set
% 5.42/5.63 thf(fact_1338_all__nth__imp__all__set,axiom,
% 5.42/5.63 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.42/5.63 ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 5.42/5.63 => ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_nth_imp_all_set
% 5.42/5.63 thf(fact_1339_all__nth__imp__all__set,axiom,
% 5.42/5.63 ! [Xs2: list_o,P: $o > $o,X2: $o] :
% 5.42/5.63 ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_o @ Xs2 @ I2 ) ) )
% 5.42/5.63 => ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_nth_imp_all_set
% 5.42/5.63 thf(fact_1340_all__nth__imp__all__set,axiom,
% 5.42/5.63 ! [Xs2: list_nat,P: nat > $o,X2: nat] :
% 5.42/5.63 ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_nat @ Xs2 @ I2 ) ) )
% 5.42/5.63 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_nth_imp_all_set
% 5.42/5.63 thf(fact_1341_all__nth__imp__all__set,axiom,
% 5.42/5.63 ! [Xs2: list_int,P: int > $o,X2: int] :
% 5.42/5.63 ( ! [I2: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.42/5.63 => ( P @ ( nth_int @ Xs2 @ I2 ) ) )
% 5.42/5.63 => ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.42/5.63 => ( P @ X2 ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % all_nth_imp_all_set
% 5.42/5.63 thf(fact_1342_in__set__conv__nth,axiom,
% 5.42/5.63 ! [X2: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.42/5.63 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.42/5.63 = ( ? [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.42/5.63 & ( ( nth_Pr7617993195940197384at_nat @ Xs2 @ I4 )
% 5.42/5.63 = X2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % in_set_conv_nth
% 5.42/5.63 thf(fact_1343_in__set__conv__nth,axiom,
% 5.42/5.63 ! [X2: complex,Xs2: list_complex] :
% 5.42/5.63 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.42/5.63 = ( ? [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.42/5.63 & ( ( nth_complex @ Xs2 @ I4 )
% 5.42/5.63 = X2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % in_set_conv_nth
% 5.42/5.63 thf(fact_1344_in__set__conv__nth,axiom,
% 5.42/5.63 ! [X2: real,Xs2: list_real] :
% 5.42/5.63 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.42/5.63 = ( ? [I4: nat] :
% 5.42/5.63 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 5.42/5.63 & ( ( nth_real @ Xs2 @ I4 )
% 5.42/5.63 = X2 ) ) ) ) ).
% 5.42/5.63
% 5.42/5.63 % in_set_conv_nth
% 5.42/5.64 thf(fact_1345_in__set__conv__nth,axiom,
% 5.42/5.64 ! [X2: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.42/5.64 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.42/5.64 = ( ? [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.42/5.64 & ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 5.42/5.64 = X2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % in_set_conv_nth
% 5.42/5.64 thf(fact_1346_in__set__conv__nth,axiom,
% 5.42/5.64 ! [X2: $o,Xs2: list_o] :
% 5.42/5.64 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.42/5.64 = ( ? [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.42/5.64 & ( ( nth_o @ Xs2 @ I4 )
% 5.42/5.64 = X2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % in_set_conv_nth
% 5.42/5.64 thf(fact_1347_in__set__conv__nth,axiom,
% 5.42/5.64 ! [X2: nat,Xs2: list_nat] :
% 5.42/5.64 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.42/5.64 = ( ? [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.42/5.64 & ( ( nth_nat @ Xs2 @ I4 )
% 5.42/5.64 = X2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % in_set_conv_nth
% 5.42/5.64 thf(fact_1348_in__set__conv__nth,axiom,
% 5.42/5.64 ! [X2: int,Xs2: list_int] :
% 5.42/5.64 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.42/5.64 = ( ? [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.42/5.64 & ( ( nth_int @ Xs2 @ I4 )
% 5.42/5.64 = X2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % in_set_conv_nth
% 5.42/5.64 thf(fact_1349_list__ball__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.42/5.64 => ( ! [X3: vEBT_VEBT] :
% 5.42/5.64 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.42/5.64 => ( P @ X3 ) )
% 5.42/5.64 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % list_ball_nth
% 5.42/5.64 thf(fact_1350_list__ball__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_o,P: $o > $o] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.42/5.64 => ( ! [X3: $o] :
% 5.42/5.64 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.42/5.64 => ( P @ X3 ) )
% 5.42/5.64 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % list_ball_nth
% 5.42/5.64 thf(fact_1351_list__ball__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.42/5.64 => ( ! [X3: nat] :
% 5.42/5.64 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.42/5.64 => ( P @ X3 ) )
% 5.42/5.64 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % list_ball_nth
% 5.42/5.64 thf(fact_1352_list__ball__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_int,P: int > $o] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.42/5.64 => ( ! [X3: int] :
% 5.42/5.64 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.42/5.64 => ( P @ X3 ) )
% 5.42/5.64 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % list_ball_nth
% 5.42/5.64 thf(fact_1353_nth__mem,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_P6011104703257516679at_nat] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.42/5.64 => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_mem
% 5.42/5.64 thf(fact_1354_nth__mem,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_complex] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.42/5.64 => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_mem
% 5.42/5.64 thf(fact_1355_nth__mem,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_real] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.42/5.64 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_mem
% 5.42/5.64 thf(fact_1356_nth__mem,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.42/5.64 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_mem
% 5.42/5.64 thf(fact_1357_nth__mem,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_o] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.42/5.64 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_mem
% 5.42/5.64 thf(fact_1358_nth__mem,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_nat] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.42/5.64 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_mem
% 5.42/5.64 thf(fact_1359_nth__mem,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_int] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.42/5.64 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_mem
% 5.42/5.64 thf(fact_1360_nested__mint,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.42/5.64 => ( ( N
% 5.42/5.64 = ( suc @ ( suc @ Va ) ) )
% 5.42/5.64 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.42/5.64 => ( ( Ma != Mi )
% 5.42/5.64 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nested_mint
% 5.42/5.64 thf(fact_1361_invar__vebt_Ointros_I3_J,axiom,
% 5.42/5.64 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.42/5.64 ( ! [X3: vEBT_VEBT] :
% 5.42/5.64 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.64 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.42/5.64 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.42/5.64 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.42/5.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.64 => ( ( M
% 5.42/5.64 = ( suc @ N ) )
% 5.42/5.64 => ( ( Deg
% 5.42/5.64 = ( plus_plus_nat @ N @ M ) )
% 5.42/5.64 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.42/5.64 => ( ! [X3: vEBT_VEBT] :
% 5.42/5.64 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.64 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.42/5.64 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % invar_vebt.intros(3)
% 5.42/5.64 thf(fact_1362_dbl__inc__simps_I3_J,axiom,
% 5.42/5.64 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.42/5.64 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(3)
% 5.42/5.64 thf(fact_1363_dbl__inc__simps_I3_J,axiom,
% 5.42/5.64 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.42/5.64 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(3)
% 5.42/5.64 thf(fact_1364_dbl__inc__simps_I3_J,axiom,
% 5.42/5.64 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.42/5.64 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(3)
% 5.42/5.64 thf(fact_1365_dbl__inc__simps_I3_J,axiom,
% 5.42/5.64 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.42/5.64 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(3)
% 5.42/5.64 thf(fact_1366_dbl__inc__simps_I5_J,axiom,
% 5.42/5.64 ! [K: num] :
% 5.42/5.64 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.42/5.64 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(5)
% 5.42/5.64 thf(fact_1367_dbl__inc__simps_I5_J,axiom,
% 5.42/5.64 ! [K: num] :
% 5.42/5.64 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.42/5.64 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(5)
% 5.42/5.64 thf(fact_1368_dbl__inc__simps_I5_J,axiom,
% 5.42/5.64 ! [K: num] :
% 5.42/5.64 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.42/5.64 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(5)
% 5.42/5.64 thf(fact_1369_dbl__inc__simps_I5_J,axiom,
% 5.42/5.64 ! [K: num] :
% 5.42/5.64 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.42/5.64 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(5)
% 5.42/5.64 thf(fact_1370_vebt__member_Osimps_I2_J,axiom,
% 5.42/5.64 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_member.simps(2)
% 5.42/5.64 thf(fact_1371_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.42/5.64 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.minNull.simps(4)
% 5.42/5.64 thf(fact_1372_subset__code_I1_J,axiom,
% 5.42/5.64 ! [Xs2: list_P6011104703257516679at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ B3 )
% 5.42/5.64 = ( ! [X: product_prod_nat_nat] :
% 5.42/5.64 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.42/5.64 => ( member8440522571783428010at_nat @ X @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % subset_code(1)
% 5.42/5.64 thf(fact_1373_subset__code_I1_J,axiom,
% 5.42/5.64 ! [Xs2: list_complex,B3: set_complex] :
% 5.42/5.64 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B3 )
% 5.42/5.64 = ( ! [X: complex] :
% 5.42/5.64 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.42/5.64 => ( member_complex @ X @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % subset_code(1)
% 5.42/5.64 thf(fact_1374_subset__code_I1_J,axiom,
% 5.42/5.64 ! [Xs2: list_real,B3: set_real] :
% 5.42/5.64 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B3 )
% 5.42/5.64 = ( ! [X: real] :
% 5.42/5.64 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.42/5.64 => ( member_real @ X @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % subset_code(1)
% 5.42/5.64 thf(fact_1375_subset__code_I1_J,axiom,
% 5.42/5.64 ! [Xs2: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.42/5.64 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B3 )
% 5.42/5.64 = ( ! [X: vEBT_VEBT] :
% 5.42/5.64 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.42/5.64 => ( member_VEBT_VEBT @ X @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % subset_code(1)
% 5.42/5.64 thf(fact_1376_subset__code_I1_J,axiom,
% 5.42/5.64 ! [Xs2: list_int,B3: set_int] :
% 5.42/5.64 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B3 )
% 5.42/5.64 = ( ! [X: int] :
% 5.42/5.64 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.42/5.64 => ( member_int @ X @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % subset_code(1)
% 5.42/5.64 thf(fact_1377_subset__code_I1_J,axiom,
% 5.42/5.64 ! [Xs2: list_nat,B3: set_nat] :
% 5.42/5.64 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B3 )
% 5.42/5.64 = ( ! [X: nat] :
% 5.42/5.64 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.42/5.64 => ( member_nat @ X @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % subset_code(1)
% 5.42/5.64 thf(fact_1378_Ex__list__of__length,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ? [Xs3: list_VEBT_VEBT] :
% 5.42/5.64 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.42/5.64 = N ) ).
% 5.42/5.64
% 5.42/5.64 % Ex_list_of_length
% 5.42/5.64 thf(fact_1379_Ex__list__of__length,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ? [Xs3: list_o] :
% 5.42/5.64 ( ( size_size_list_o @ Xs3 )
% 5.42/5.64 = N ) ).
% 5.42/5.64
% 5.42/5.64 % Ex_list_of_length
% 5.42/5.64 thf(fact_1380_Ex__list__of__length,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ? [Xs3: list_nat] :
% 5.42/5.64 ( ( size_size_list_nat @ Xs3 )
% 5.42/5.64 = N ) ).
% 5.42/5.64
% 5.42/5.64 % Ex_list_of_length
% 5.42/5.64 thf(fact_1381_Ex__list__of__length,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ? [Xs3: list_int] :
% 5.42/5.64 ( ( size_size_list_int @ Xs3 )
% 5.42/5.64 = N ) ).
% 5.42/5.64
% 5.42/5.64 % Ex_list_of_length
% 5.42/5.64 thf(fact_1382_neq__if__length__neq,axiom,
% 5.42/5.64 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.42/5.64 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.42/5.64 => ( Xs2 != Ys ) ) ).
% 5.42/5.64
% 5.42/5.64 % neq_if_length_neq
% 5.42/5.64 thf(fact_1383_neq__if__length__neq,axiom,
% 5.42/5.64 ! [Xs2: list_o,Ys: list_o] :
% 5.42/5.64 ( ( ( size_size_list_o @ Xs2 )
% 5.42/5.64 != ( size_size_list_o @ Ys ) )
% 5.42/5.64 => ( Xs2 != Ys ) ) ).
% 5.42/5.64
% 5.42/5.64 % neq_if_length_neq
% 5.42/5.64 thf(fact_1384_neq__if__length__neq,axiom,
% 5.42/5.64 ! [Xs2: list_nat,Ys: list_nat] :
% 5.42/5.64 ( ( ( size_size_list_nat @ Xs2 )
% 5.42/5.64 != ( size_size_list_nat @ Ys ) )
% 5.42/5.64 => ( Xs2 != Ys ) ) ).
% 5.42/5.64
% 5.42/5.64 % neq_if_length_neq
% 5.42/5.64 thf(fact_1385_neq__if__length__neq,axiom,
% 5.42/5.64 ! [Xs2: list_int,Ys: list_int] :
% 5.42/5.64 ( ( ( size_size_list_int @ Xs2 )
% 5.42/5.64 != ( size_size_list_int @ Ys ) )
% 5.42/5.64 => ( Xs2 != Ys ) ) ).
% 5.42/5.64
% 5.42/5.64 % neq_if_length_neq
% 5.42/5.64 thf(fact_1386_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I4_J,axiom,
% 5.42/5.64 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.42/5.64 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 5.42/5.64 = one_one_nat ) ).
% 5.42/5.64
% 5.42/5.64 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(4)
% 5.42/5.64 thf(fact_1387_dbl__inc__def,axiom,
% 5.42/5.64 ( neg_nu8557863876264182079omplex
% 5.42/5.64 = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_def
% 5.42/5.64 thf(fact_1388_dbl__inc__def,axiom,
% 5.42/5.64 ( neg_nu8295874005876285629c_real
% 5.42/5.64 = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_def
% 5.42/5.64 thf(fact_1389_dbl__inc__def,axiom,
% 5.42/5.64 ( neg_nu5219082963157363817nc_rat
% 5.42/5.64 = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_def
% 5.42/5.64 thf(fact_1390_dbl__inc__def,axiom,
% 5.42/5.64 ( neg_nu5851722552734809277nc_int
% 5.42/5.64 = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_def
% 5.42/5.64 thf(fact_1391_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 5.42/5.64 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 )
% 5.42/5.64 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(2)
% 5.42/5.64 thf(fact_1392_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 5.42/5.64 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(4)
% 5.42/5.64 thf(fact_1393_length__induct,axiom,
% 5.42/5.64 ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.42/5.64 ( ! [Xs3: list_VEBT_VEBT] :
% 5.42/5.64 ( ! [Ys2: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.42/5.64 => ( P @ Ys2 ) )
% 5.42/5.64 => ( P @ Xs3 ) )
% 5.42/5.64 => ( P @ Xs2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_induct
% 5.42/5.64 thf(fact_1394_length__induct,axiom,
% 5.42/5.64 ! [P: list_o > $o,Xs2: list_o] :
% 5.42/5.64 ( ! [Xs3: list_o] :
% 5.42/5.64 ( ! [Ys2: list_o] :
% 5.42/5.64 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.42/5.64 => ( P @ Ys2 ) )
% 5.42/5.64 => ( P @ Xs3 ) )
% 5.42/5.64 => ( P @ Xs2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_induct
% 5.42/5.64 thf(fact_1395_length__induct,axiom,
% 5.42/5.64 ! [P: list_nat > $o,Xs2: list_nat] :
% 5.42/5.64 ( ! [Xs3: list_nat] :
% 5.42/5.64 ( ! [Ys2: list_nat] :
% 5.42/5.64 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.42/5.64 => ( P @ Ys2 ) )
% 5.42/5.64 => ( P @ Xs3 ) )
% 5.42/5.64 => ( P @ Xs2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_induct
% 5.42/5.64 thf(fact_1396_length__induct,axiom,
% 5.42/5.64 ! [P: list_int > $o,Xs2: list_int] :
% 5.42/5.64 ( ! [Xs3: list_int] :
% 5.42/5.64 ( ! [Ys2: list_int] :
% 5.42/5.64 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 5.42/5.64 => ( P @ Ys2 ) )
% 5.42/5.64 => ( P @ Xs3 ) )
% 5.42/5.64 => ( P @ Xs2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_induct
% 5.42/5.64 thf(fact_1397_nth__equalityI,axiom,
% 5.42/5.64 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.42/5.64 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.42/5.64 => ( ! [I2: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.42/5.64 => ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.42/5.64 = ( nth_VEBT_VEBT @ Ys @ I2 ) ) )
% 5.42/5.64 => ( Xs2 = Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_equalityI
% 5.42/5.64 thf(fact_1398_nth__equalityI,axiom,
% 5.42/5.64 ! [Xs2: list_o,Ys: list_o] :
% 5.42/5.64 ( ( ( size_size_list_o @ Xs2 )
% 5.42/5.64 = ( size_size_list_o @ Ys ) )
% 5.42/5.64 => ( ! [I2: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.42/5.64 => ( ( nth_o @ Xs2 @ I2 )
% 5.42/5.64 = ( nth_o @ Ys @ I2 ) ) )
% 5.42/5.64 => ( Xs2 = Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_equalityI
% 5.42/5.64 thf(fact_1399_nth__equalityI,axiom,
% 5.42/5.64 ! [Xs2: list_nat,Ys: list_nat] :
% 5.42/5.64 ( ( ( size_size_list_nat @ Xs2 )
% 5.42/5.64 = ( size_size_list_nat @ Ys ) )
% 5.42/5.64 => ( ! [I2: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.42/5.64 => ( ( nth_nat @ Xs2 @ I2 )
% 5.42/5.64 = ( nth_nat @ Ys @ I2 ) ) )
% 5.42/5.64 => ( Xs2 = Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_equalityI
% 5.42/5.64 thf(fact_1400_nth__equalityI,axiom,
% 5.42/5.64 ! [Xs2: list_int,Ys: list_int] :
% 5.42/5.64 ( ( ( size_size_list_int @ Xs2 )
% 5.42/5.64 = ( size_size_list_int @ Ys ) )
% 5.42/5.64 => ( ! [I2: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.42/5.64 => ( ( nth_int @ Xs2 @ I2 )
% 5.42/5.64 = ( nth_int @ Ys @ I2 ) ) )
% 5.42/5.64 => ( Xs2 = Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nth_equalityI
% 5.42/5.64 thf(fact_1401_Skolem__list__nth,axiom,
% 5.42/5.64 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.42/5.64 ( ( ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ K )
% 5.42/5.64 => ? [X5: vEBT_VEBT] : ( P @ I4 @ X5 ) ) )
% 5.42/5.64 = ( ? [Xs: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.42/5.64 = K )
% 5.42/5.64 & ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ K )
% 5.42/5.64 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Skolem_list_nth
% 5.42/5.64 thf(fact_1402_Skolem__list__nth,axiom,
% 5.42/5.64 ! [K: nat,P: nat > $o > $o] :
% 5.42/5.64 ( ( ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ K )
% 5.42/5.64 => ? [X5: $o] : ( P @ I4 @ X5 ) ) )
% 5.42/5.64 = ( ? [Xs: list_o] :
% 5.42/5.64 ( ( ( size_size_list_o @ Xs )
% 5.42/5.64 = K )
% 5.42/5.64 & ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ K )
% 5.42/5.64 => ( P @ I4 @ ( nth_o @ Xs @ I4 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Skolem_list_nth
% 5.42/5.64 thf(fact_1403_Skolem__list__nth,axiom,
% 5.42/5.64 ! [K: nat,P: nat > nat > $o] :
% 5.42/5.64 ( ( ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ K )
% 5.42/5.64 => ? [X5: nat] : ( P @ I4 @ X5 ) ) )
% 5.42/5.64 = ( ? [Xs: list_nat] :
% 5.42/5.64 ( ( ( size_size_list_nat @ Xs )
% 5.42/5.64 = K )
% 5.42/5.64 & ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ K )
% 5.42/5.64 => ( P @ I4 @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Skolem_list_nth
% 5.42/5.64 thf(fact_1404_Skolem__list__nth,axiom,
% 5.42/5.64 ! [K: nat,P: nat > int > $o] :
% 5.42/5.64 ( ( ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ K )
% 5.42/5.64 => ? [X5: int] : ( P @ I4 @ X5 ) ) )
% 5.42/5.64 = ( ? [Xs: list_int] :
% 5.42/5.64 ( ( ( size_size_list_int @ Xs )
% 5.42/5.64 = K )
% 5.42/5.64 & ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ K )
% 5.42/5.64 => ( P @ I4 @ ( nth_int @ Xs @ I4 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Skolem_list_nth
% 5.42/5.64 thf(fact_1405_list__eq__iff__nth__eq,axiom,
% 5.42/5.64 ( ( ^ [Y5: list_VEBT_VEBT,Z5: list_VEBT_VEBT] : ( Y5 = Z5 ) )
% 5.42/5.64 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.42/5.64 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.42/5.64 & ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.42/5.64 => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 5.42/5.64 = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % list_eq_iff_nth_eq
% 5.42/5.64 thf(fact_1406_list__eq__iff__nth__eq,axiom,
% 5.42/5.64 ( ( ^ [Y5: list_o,Z5: list_o] : ( Y5 = Z5 ) )
% 5.42/5.64 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.42/5.64 ( ( ( size_size_list_o @ Xs )
% 5.42/5.64 = ( size_size_list_o @ Ys3 ) )
% 5.42/5.64 & ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.42/5.64 => ( ( nth_o @ Xs @ I4 )
% 5.42/5.64 = ( nth_o @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % list_eq_iff_nth_eq
% 5.42/5.64 thf(fact_1407_list__eq__iff__nth__eq,axiom,
% 5.42/5.64 ( ( ^ [Y5: list_nat,Z5: list_nat] : ( Y5 = Z5 ) )
% 5.42/5.64 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.42/5.64 ( ( ( size_size_list_nat @ Xs )
% 5.42/5.64 = ( size_size_list_nat @ Ys3 ) )
% 5.42/5.64 & ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.42/5.64 => ( ( nth_nat @ Xs @ I4 )
% 5.42/5.64 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % list_eq_iff_nth_eq
% 5.42/5.64 thf(fact_1408_list__eq__iff__nth__eq,axiom,
% 5.42/5.64 ( ( ^ [Y5: list_int,Z5: list_int] : ( Y5 = Z5 ) )
% 5.42/5.64 = ( ^ [Xs: list_int,Ys3: list_int] :
% 5.42/5.64 ( ( ( size_size_list_int @ Xs )
% 5.42/5.64 = ( size_size_list_int @ Ys3 ) )
% 5.42/5.64 & ! [I4: nat] :
% 5.42/5.64 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.42/5.64 => ( ( nth_int @ Xs @ I4 )
% 5.42/5.64 = ( nth_int @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % list_eq_iff_nth_eq
% 5.42/5.64 thf(fact_1409_invar__vebt_Ointros_I2_J,axiom,
% 5.42/5.64 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.42/5.64 ( ! [X3: vEBT_VEBT] :
% 5.42/5.64 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.64 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.42/5.64 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.42/5.64 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.42/5.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.42/5.64 => ( ( M = N )
% 5.42/5.64 => ( ( Deg
% 5.42/5.64 = ( plus_plus_nat @ N @ M ) )
% 5.42/5.64 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.42/5.64 => ( ! [X3: vEBT_VEBT] :
% 5.42/5.64 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.42/5.64 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.42/5.64 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % invar_vebt.intros(2)
% 5.42/5.64 thf(fact_1410_summaxma,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.42/5.64 => ( ( Mi != Ma )
% 5.42/5.64 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.42/5.64 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % summaxma
% 5.42/5.64 thf(fact_1411_mintlistlength,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.42/5.64 => ( ( Mi != Ma )
% 5.42/5.64 => ( ( ord_less_nat @ Mi @ Ma )
% 5.42/5.64 & ? [M4: nat] :
% 5.42/5.64 ( ( ( some_nat @ M4 )
% 5.42/5.64 = ( vEBT_vebt_mint @ Summary ) )
% 5.42/5.64 & ( ord_less_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mintlistlength
% 5.42/5.64 thf(fact_1412_option_Ocollapse,axiom,
% 5.42/5.64 ! [Option: option4927543243414619207at_nat] :
% 5.42/5.64 ( ( Option != none_P5556105721700978146at_nat )
% 5.42/5.64 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.42/5.64 = Option ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.collapse
% 5.42/5.64 thf(fact_1413_option_Ocollapse,axiom,
% 5.42/5.64 ! [Option: option_nat] :
% 5.42/5.64 ( ( Option != none_nat )
% 5.42/5.64 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.42/5.64 = Option ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.collapse
% 5.42/5.64 thf(fact_1414_option_Ocollapse,axiom,
% 5.42/5.64 ! [Option: option_num] :
% 5.42/5.64 ( ( Option != none_num )
% 5.42/5.64 => ( ( some_num @ ( the_num @ Option ) )
% 5.42/5.64 = Option ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.collapse
% 5.42/5.64 thf(fact_1415_vebt__insert_Osimps_I4_J,axiom,
% 5.42/5.64 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_insert.simps(4)
% 5.42/5.64 thf(fact_1416_zle__add1__eq__le,axiom,
% 5.42/5.64 ! [W: int,Z: int] :
% 5.42/5.64 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.42/5.64 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.42/5.64
% 5.42/5.64 % zle_add1_eq_le
% 5.42/5.64 thf(fact_1417_not__Some__eq,axiom,
% 5.42/5.64 ! [X2: option4927543243414619207at_nat] :
% 5.42/5.64 ( ( ! [Y: product_prod_nat_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( some_P7363390416028606310at_nat @ Y ) ) )
% 5.42/5.64 = ( X2 = none_P5556105721700978146at_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % not_Some_eq
% 5.42/5.64 thf(fact_1418_not__Some__eq,axiom,
% 5.42/5.64 ! [X2: option_nat] :
% 5.42/5.64 ( ( ! [Y: nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( some_nat @ Y ) ) )
% 5.42/5.64 = ( X2 = none_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % not_Some_eq
% 5.42/5.64 thf(fact_1419_not__Some__eq,axiom,
% 5.42/5.64 ! [X2: option_num] :
% 5.42/5.64 ( ( ! [Y: num] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( some_num @ Y ) ) )
% 5.42/5.64 = ( X2 = none_num ) ) ).
% 5.42/5.64
% 5.42/5.64 % not_Some_eq
% 5.42/5.64 thf(fact_1420_not__None__eq,axiom,
% 5.42/5.64 ! [X2: option4927543243414619207at_nat] :
% 5.42/5.64 ( ( X2 != none_P5556105721700978146at_nat )
% 5.42/5.64 = ( ? [Y: product_prod_nat_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % not_None_eq
% 5.42/5.64 thf(fact_1421_not__None__eq,axiom,
% 5.42/5.64 ! [X2: option_nat] :
% 5.42/5.64 ( ( X2 != none_nat )
% 5.42/5.64 = ( ? [Y: nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( some_nat @ Y ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % not_None_eq
% 5.42/5.64 thf(fact_1422_not__None__eq,axiom,
% 5.42/5.64 ! [X2: option_num] :
% 5.42/5.64 ( ( X2 != none_num )
% 5.42/5.64 = ( ? [Y: num] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( some_num @ Y ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % not_None_eq
% 5.42/5.64 thf(fact_1423_misiz,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( some_nat @ M )
% 5.42/5.64 = ( vEBT_vebt_mint @ T ) )
% 5.42/5.64 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % misiz
% 5.42/5.64 thf(fact_1424_mint__corr,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_mint @ T )
% 5.42/5.64 = ( some_nat @ X2 ) )
% 5.42/5.64 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mint_corr
% 5.42/5.64 thf(fact_1425_mint__sound,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.42/5.64 => ( ( vEBT_vebt_mint @ T )
% 5.42/5.64 = ( some_nat @ X2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mint_sound
% 5.42/5.64 thf(fact_1426_minminNull,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT] :
% 5.42/5.64 ( ( ( vEBT_vebt_mint @ T )
% 5.42/5.64 = none_nat )
% 5.42/5.64 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.42/5.64
% 5.42/5.64 % minminNull
% 5.42/5.64 thf(fact_1427_minNullmin,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT] :
% 5.42/5.64 ( ( vEBT_VEBT_minNull @ T )
% 5.42/5.64 => ( ( vEBT_vebt_mint @ T )
% 5.42/5.64 = none_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % minNullmin
% 5.42/5.64 thf(fact_1428_maxbmo,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( ( vEBT_vebt_maxt @ T )
% 5.42/5.64 = ( some_nat @ X2 ) )
% 5.42/5.64 => ( vEBT_V8194947554948674370ptions @ T @ X2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % maxbmo
% 5.42/5.64 thf(fact_1429_power__shift,axiom,
% 5.42/5.64 ! [X2: nat,Y2: nat,Z: nat] :
% 5.42/5.64 ( ( ( power_power_nat @ X2 @ Y2 )
% 5.42/5.64 = Z )
% 5.42/5.64 = ( ( vEBT_VEBT_power @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) )
% 5.42/5.64 = ( some_nat @ Z ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_shift
% 5.42/5.64 thf(fact_1430_mint__member,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_mint @ T )
% 5.42/5.64 = ( some_nat @ Maxi ) )
% 5.42/5.64 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mint_member
% 5.42/5.64 thf(fact_1431_maxt__member,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_maxt @ T )
% 5.42/5.64 = ( some_nat @ Maxi ) )
% 5.42/5.64 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % maxt_member
% 5.42/5.64 thf(fact_1432_option_Oinject,axiom,
% 5.42/5.64 ! [X23: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 5.42/5.64 ( ( ( some_P7363390416028606310at_nat @ X23 )
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ Y22 ) )
% 5.42/5.64 = ( X23 = Y22 ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.inject
% 5.42/5.64 thf(fact_1433_option_Oinject,axiom,
% 5.42/5.64 ! [X23: nat,Y22: nat] :
% 5.42/5.64 ( ( ( some_nat @ X23 )
% 5.42/5.64 = ( some_nat @ Y22 ) )
% 5.42/5.64 = ( X23 = Y22 ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.inject
% 5.42/5.64 thf(fact_1434_option_Oinject,axiom,
% 5.42/5.64 ! [X23: num,Y22: num] :
% 5.42/5.64 ( ( ( some_num @ X23 )
% 5.42/5.64 = ( some_num @ Y22 ) )
% 5.42/5.64 = ( X23 = Y22 ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.inject
% 5.42/5.64 thf(fact_1435_mint__corr__help,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,Mini: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_mint @ T )
% 5.42/5.64 = ( some_nat @ Mini ) )
% 5.42/5.64 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.42/5.64 => ( ord_less_eq_nat @ Mini @ X2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mint_corr_help
% 5.42/5.64 thf(fact_1436_maxt__corr__help,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_maxt @ T )
% 5.42/5.64 = ( some_nat @ Maxi ) )
% 5.42/5.64 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.42/5.64 => ( ord_less_eq_nat @ X2 @ Maxi ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % maxt_corr_help
% 5.42/5.64 thf(fact_1437_maxt__sound,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.42/5.64 => ( ( vEBT_vebt_maxt @ T )
% 5.42/5.64 = ( some_nat @ X2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % maxt_sound
% 5.42/5.64 thf(fact_1438_maxt__corr,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_maxt @ T )
% 5.42/5.64 = ( some_nat @ X2 ) )
% 5.42/5.64 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % maxt_corr
% 5.42/5.64 thf(fact_1439_zle__diff1__eq,axiom,
% 5.42/5.64 ! [W: int,Z: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.42/5.64 = ( ord_less_int @ W @ Z ) ) ).
% 5.42/5.64
% 5.42/5.64 % zle_diff1_eq
% 5.42/5.64 thf(fact_1440_lesseq__shift,axiom,
% 5.42/5.64 ( ord_less_eq_nat
% 5.42/5.64 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % lesseq_shift
% 5.42/5.64 thf(fact_1441_set__bit__greater__eq,axiom,
% 5.42/5.64 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_bit_greater_eq
% 5.42/5.64 thf(fact_1442_unset__bit__less__eq,axiom,
% 5.42/5.64 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.42/5.64
% 5.42/5.64 % unset_bit_less_eq
% 5.42/5.64 thf(fact_1443_int__le__induct,axiom,
% 5.42/5.64 ! [I: int,K: int,P: int > $o] :
% 5.42/5.64 ( ( ord_less_eq_int @ I @ K )
% 5.42/5.64 => ( ( P @ K )
% 5.42/5.64 => ( ! [I2: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ I2 @ K )
% 5.42/5.64 => ( ( P @ I2 )
% 5.42/5.64 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.42/5.64 => ( P @ I ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % int_le_induct
% 5.42/5.64 thf(fact_1444_int__less__induct,axiom,
% 5.42/5.64 ! [I: int,K: int,P: int > $o] :
% 5.42/5.64 ( ( ord_less_int @ I @ K )
% 5.42/5.64 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.42/5.64 => ( ! [I2: int] :
% 5.42/5.64 ( ( ord_less_int @ I2 @ K )
% 5.42/5.64 => ( ( P @ I2 )
% 5.42/5.64 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.42/5.64 => ( P @ I ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % int_less_induct
% 5.42/5.64 thf(fact_1445_int__distrib_I4_J,axiom,
% 5.42/5.64 ! [W: int,Z1: int,Z22: int] :
% 5.42/5.64 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.42/5.64 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % int_distrib(4)
% 5.42/5.64 thf(fact_1446_int__distrib_I3_J,axiom,
% 5.42/5.64 ! [Z1: int,Z22: int,W: int] :
% 5.42/5.64 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.42/5.64 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % int_distrib(3)
% 5.42/5.64 thf(fact_1447_option_Odistinct_I1_J,axiom,
% 5.42/5.64 ! [X23: product_prod_nat_nat] :
% 5.42/5.64 ( none_P5556105721700978146at_nat
% 5.42/5.64 != ( some_P7363390416028606310at_nat @ X23 ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.distinct(1)
% 5.42/5.64 thf(fact_1448_option_Odistinct_I1_J,axiom,
% 5.42/5.64 ! [X23: nat] :
% 5.42/5.64 ( none_nat
% 5.42/5.64 != ( some_nat @ X23 ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.distinct(1)
% 5.42/5.64 thf(fact_1449_option_Odistinct_I1_J,axiom,
% 5.42/5.64 ! [X23: num] :
% 5.42/5.64 ( none_num
% 5.42/5.64 != ( some_num @ X23 ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.distinct(1)
% 5.42/5.64 thf(fact_1450_option_OdiscI,axiom,
% 5.42/5.64 ! [Option: option4927543243414619207at_nat,X23: product_prod_nat_nat] :
% 5.42/5.64 ( ( Option
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ X23 ) )
% 5.42/5.64 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.discI
% 5.42/5.64 thf(fact_1451_option_OdiscI,axiom,
% 5.42/5.64 ! [Option: option_nat,X23: nat] :
% 5.42/5.64 ( ( Option
% 5.42/5.64 = ( some_nat @ X23 ) )
% 5.42/5.64 => ( Option != none_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.discI
% 5.42/5.64 thf(fact_1452_option_OdiscI,axiom,
% 5.42/5.64 ! [Option: option_num,X23: num] :
% 5.42/5.64 ( ( Option
% 5.42/5.64 = ( some_num @ X23 ) )
% 5.42/5.64 => ( Option != none_num ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.discI
% 5.42/5.64 thf(fact_1453_option_Oexhaust,axiom,
% 5.42/5.64 ! [Y2: option4927543243414619207at_nat] :
% 5.42/5.64 ( ( Y2 != none_P5556105721700978146at_nat )
% 5.42/5.64 => ~ ! [X22: product_prod_nat_nat] :
% 5.42/5.64 ( Y2
% 5.42/5.64 != ( some_P7363390416028606310at_nat @ X22 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.exhaust
% 5.42/5.64 thf(fact_1454_option_Oexhaust,axiom,
% 5.42/5.64 ! [Y2: option_nat] :
% 5.42/5.64 ( ( Y2 != none_nat )
% 5.42/5.64 => ~ ! [X22: nat] :
% 5.42/5.64 ( Y2
% 5.42/5.64 != ( some_nat @ X22 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.exhaust
% 5.42/5.64 thf(fact_1455_option_Oexhaust,axiom,
% 5.42/5.64 ! [Y2: option_num] :
% 5.42/5.64 ( ( Y2 != none_num )
% 5.42/5.64 => ~ ! [X22: num] :
% 5.42/5.64 ( Y2
% 5.42/5.64 != ( some_num @ X22 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.exhaust
% 5.42/5.64 thf(fact_1456_split__option__ex,axiom,
% 5.42/5.64 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.42/5.64 ? [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.42/5.64 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.42/5.64 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.42/5.64 | ? [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % split_option_ex
% 5.42/5.64 thf(fact_1457_split__option__ex,axiom,
% 5.42/5.64 ( ( ^ [P3: option_nat > $o] :
% 5.42/5.64 ? [X6: option_nat] : ( P3 @ X6 ) )
% 5.42/5.64 = ( ^ [P4: option_nat > $o] :
% 5.42/5.64 ( ( P4 @ none_nat )
% 5.42/5.64 | ? [X: nat] : ( P4 @ ( some_nat @ X ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % split_option_ex
% 5.42/5.64 thf(fact_1458_split__option__ex,axiom,
% 5.42/5.64 ( ( ^ [P3: option_num > $o] :
% 5.42/5.64 ? [X6: option_num] : ( P3 @ X6 ) )
% 5.42/5.64 = ( ^ [P4: option_num > $o] :
% 5.42/5.64 ( ( P4 @ none_num )
% 5.42/5.64 | ? [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % split_option_ex
% 5.42/5.64 thf(fact_1459_split__option__all,axiom,
% 5.42/5.64 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.42/5.64 ! [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.42/5.64 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.42/5.64 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.42/5.64 & ! [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % split_option_all
% 5.42/5.64 thf(fact_1460_split__option__all,axiom,
% 5.42/5.64 ( ( ^ [P3: option_nat > $o] :
% 5.42/5.64 ! [X6: option_nat] : ( P3 @ X6 ) )
% 5.42/5.64 = ( ^ [P4: option_nat > $o] :
% 5.42/5.64 ( ( P4 @ none_nat )
% 5.42/5.64 & ! [X: nat] : ( P4 @ ( some_nat @ X ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % split_option_all
% 5.42/5.64 thf(fact_1461_split__option__all,axiom,
% 5.42/5.64 ( ( ^ [P3: option_num > $o] :
% 5.42/5.64 ! [X6: option_num] : ( P3 @ X6 ) )
% 5.42/5.64 = ( ^ [P4: option_num > $o] :
% 5.42/5.64 ( ( P4 @ none_num )
% 5.42/5.64 & ! [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % split_option_all
% 5.42/5.64 thf(fact_1462_combine__options__cases,axiom,
% 5.42/5.64 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 5.42/5.64 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ! [A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.42/5.64 => ( ( Y2
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % combine_options_cases
% 5.42/5.64 thf(fact_1463_combine__options__cases,axiom,
% 5.42/5.64 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y2: option_nat] :
% 5.42/5.64 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ( ( Y2 = none_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ! [A5: product_prod_nat_nat,B5: nat] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.42/5.64 => ( ( Y2
% 5.42/5.64 = ( some_nat @ B5 ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % combine_options_cases
% 5.42/5.64 thf(fact_1464_combine__options__cases,axiom,
% 5.42/5.64 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y2: option_num] :
% 5.42/5.64 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ( ( Y2 = none_num )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ! [A5: product_prod_nat_nat,B5: num] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.42/5.64 => ( ( Y2
% 5.42/5.64 = ( some_num @ B5 ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % combine_options_cases
% 5.42/5.64 thf(fact_1465_combine__options__cases,axiom,
% 5.42/5.64 ! [X2: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 5.42/5.64 ( ( ( X2 = none_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ! [A5: nat,B5: product_prod_nat_nat] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( some_nat @ A5 ) )
% 5.42/5.64 => ( ( Y2
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % combine_options_cases
% 5.42/5.64 thf(fact_1466_combine__options__cases,axiom,
% 5.42/5.64 ! [X2: option_nat,P: option_nat > option_nat > $o,Y2: option_nat] :
% 5.42/5.64 ( ( ( X2 = none_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ( ( Y2 = none_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ! [A5: nat,B5: nat] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( some_nat @ A5 ) )
% 5.42/5.64 => ( ( Y2
% 5.42/5.64 = ( some_nat @ B5 ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % combine_options_cases
% 5.42/5.64 thf(fact_1467_combine__options__cases,axiom,
% 5.42/5.64 ! [X2: option_nat,P: option_nat > option_num > $o,Y2: option_num] :
% 5.42/5.64 ( ( ( X2 = none_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ( ( Y2 = none_num )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ! [A5: nat,B5: num] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( some_nat @ A5 ) )
% 5.42/5.64 => ( ( Y2
% 5.42/5.64 = ( some_num @ B5 ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % combine_options_cases
% 5.42/5.64 thf(fact_1468_combine__options__cases,axiom,
% 5.42/5.64 ! [X2: option_num,P: option_num > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 5.42/5.64 ( ( ( X2 = none_num )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ! [A5: num,B5: product_prod_nat_nat] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( some_num @ A5 ) )
% 5.42/5.64 => ( ( Y2
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % combine_options_cases
% 5.42/5.64 thf(fact_1469_combine__options__cases,axiom,
% 5.42/5.64 ! [X2: option_num,P: option_num > option_nat > $o,Y2: option_nat] :
% 5.42/5.64 ( ( ( X2 = none_num )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ( ( Y2 = none_nat )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ! [A5: num,B5: nat] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( some_num @ A5 ) )
% 5.42/5.64 => ( ( Y2
% 5.42/5.64 = ( some_nat @ B5 ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % combine_options_cases
% 5.42/5.64 thf(fact_1470_combine__options__cases,axiom,
% 5.42/5.64 ! [X2: option_num,P: option_num > option_num > $o,Y2: option_num] :
% 5.42/5.64 ( ( ( X2 = none_num )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ( ( Y2 = none_num )
% 5.42/5.64 => ( P @ X2 @ Y2 ) )
% 5.42/5.64 => ( ! [A5: num,B5: num] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( some_num @ A5 ) )
% 5.42/5.64 => ( ( Y2
% 5.42/5.64 = ( some_num @ B5 ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) )
% 5.42/5.64 => ( P @ X2 @ Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % combine_options_cases
% 5.42/5.64 thf(fact_1471_add1__zle__eq,axiom,
% 5.42/5.64 ! [W: int,Z: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.42/5.64 = ( ord_less_int @ W @ Z ) ) ).
% 5.42/5.64
% 5.42/5.64 % add1_zle_eq
% 5.42/5.64 thf(fact_1472_int__gr__induct,axiom,
% 5.42/5.64 ! [K: int,I: int,P: int > $o] :
% 5.42/5.64 ( ( ord_less_int @ K @ I )
% 5.42/5.64 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.42/5.64 => ( ! [I2: int] :
% 5.42/5.64 ( ( ord_less_int @ K @ I2 )
% 5.42/5.64 => ( ( P @ I2 )
% 5.42/5.64 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.42/5.64 => ( P @ I ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % int_gr_induct
% 5.42/5.64 thf(fact_1473_zless__add1__eq,axiom,
% 5.42/5.64 ! [W: int,Z: int] :
% 5.42/5.64 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.42/5.64 = ( ( ord_less_int @ W @ Z )
% 5.42/5.64 | ( W = Z ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % zless_add1_eq
% 5.42/5.64 thf(fact_1474_zless__imp__add1__zle,axiom,
% 5.42/5.64 ! [W: int,Z: int] :
% 5.42/5.64 ( ( ord_less_int @ W @ Z )
% 5.42/5.64 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.42/5.64
% 5.42/5.64 % zless_imp_add1_zle
% 5.42/5.64 thf(fact_1475_int__induct,axiom,
% 5.42/5.64 ! [P: int > $o,K: int,I: int] :
% 5.42/5.64 ( ( P @ K )
% 5.42/5.64 => ( ! [I2: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ K @ I2 )
% 5.42/5.64 => ( ( P @ I2 )
% 5.42/5.64 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.42/5.64 => ( ! [I2: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ I2 @ K )
% 5.42/5.64 => ( ( P @ I2 )
% 5.42/5.64 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.42/5.64 => ( P @ I ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % int_induct
% 5.42/5.64 thf(fact_1476_option_Osel,axiom,
% 5.42/5.64 ! [X23: product_prod_nat_nat] :
% 5.42/5.64 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.42/5.64 = X23 ) ).
% 5.42/5.64
% 5.42/5.64 % option.sel
% 5.42/5.64 thf(fact_1477_option_Osel,axiom,
% 5.42/5.64 ! [X23: nat] :
% 5.42/5.64 ( ( the_nat @ ( some_nat @ X23 ) )
% 5.42/5.64 = X23 ) ).
% 5.42/5.64
% 5.42/5.64 % option.sel
% 5.42/5.64 thf(fact_1478_option_Osel,axiom,
% 5.42/5.64 ! [X23: num] :
% 5.42/5.64 ( ( the_num @ ( some_num @ X23 ) )
% 5.42/5.64 = X23 ) ).
% 5.42/5.64
% 5.42/5.64 % option.sel
% 5.42/5.64 thf(fact_1479_option_Oexhaust__sel,axiom,
% 5.42/5.64 ! [Option: option4927543243414619207at_nat] :
% 5.42/5.64 ( ( Option != none_P5556105721700978146at_nat )
% 5.42/5.64 => ( Option
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.exhaust_sel
% 5.42/5.64 thf(fact_1480_option_Oexhaust__sel,axiom,
% 5.42/5.64 ! [Option: option_nat] :
% 5.42/5.64 ( ( Option != none_nat )
% 5.42/5.64 => ( Option
% 5.42/5.64 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.exhaust_sel
% 5.42/5.64 thf(fact_1481_option_Oexhaust__sel,axiom,
% 5.42/5.64 ! [Option: option_num] :
% 5.42/5.64 ( ( Option != none_num )
% 5.42/5.64 => ( Option
% 5.42/5.64 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % option.exhaust_sel
% 5.42/5.64 thf(fact_1482_pred__list__to__short,axiom,
% 5.42/5.64 ! [Deg: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.64 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.42/5.64 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = none_nat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % pred_list_to_short
% 5.42/5.64 thf(fact_1483_succ__list__to__short,axiom,
% 5.42/5.64 ! [Deg: nat,Mi: nat,X2: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.64 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.42/5.64 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = none_nat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % succ_list_to_short
% 5.42/5.64 thf(fact_1484_pred__max,axiom,
% 5.42/5.64 ! [Deg: nat,Ma: nat,X2: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.64 => ( ( ord_less_nat @ Ma @ X2 )
% 5.42/5.64 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( some_nat @ Ma ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % pred_max
% 5.42/5.64 thf(fact_1485_succ__min,axiom,
% 5.42/5.64 ! [Deg: nat,X2: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.64 => ( ( ord_less_nat @ X2 @ Mi )
% 5.42/5.64 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( some_nat @ Mi ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % succ_min
% 5.42/5.64 thf(fact_1486_less__shift,axiom,
% 5.42/5.64 ( ord_less_nat
% 5.42/5.64 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_shift
% 5.42/5.64 thf(fact_1487_greater__shift,axiom,
% 5.42/5.64 ( ord_less_nat
% 5.42/5.64 = ( ^ [Y: nat,X: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % greater_shift
% 5.42/5.64 thf(fact_1488_helpyd,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat,Y2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.42/5.64 = ( some_nat @ Y2 ) )
% 5.42/5.64 => ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % helpyd
% 5.42/5.64 thf(fact_1489_helpypredd,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat,Y2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.42/5.64 = ( some_nat @ Y2 ) )
% 5.42/5.64 => ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % helpypredd
% 5.42/5.64 thf(fact_1490_succ__correct,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.42/5.64 = ( some_nat @ Sx ) )
% 5.42/5.64 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % succ_correct
% 5.42/5.64 thf(fact_1491_pred__correct,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.42/5.64 = ( some_nat @ Sx ) )
% 5.42/5.64 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % pred_correct
% 5.42/5.64 thf(fact_1492_succ__corr,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.42/5.64 = ( some_nat @ Sx ) )
% 5.42/5.64 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % succ_corr
% 5.42/5.64 thf(fact_1493_pred__corr,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat,Px: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.42/5.64 = ( some_nat @ Px ) )
% 5.42/5.64 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Px ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % pred_corr
% 5.42/5.64 thf(fact_1494_geqmaxNone,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.42/5.64 => ( ( ord_less_eq_nat @ Ma @ X2 )
% 5.42/5.64 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = none_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % geqmaxNone
% 5.42/5.64 thf(fact_1495_local_Opower__def,axiom,
% 5.42/5.64 ( vEBT_VEBT_power
% 5.42/5.64 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % local.power_def
% 5.42/5.64 thf(fact_1496_vebt__maxt_Osimps_I3_J,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.42/5.64 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.42/5.64 = ( some_nat @ Ma ) ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_maxt.simps(3)
% 5.42/5.64 thf(fact_1497_vebt__mint_Osimps_I3_J,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.42/5.64 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.42/5.64 = ( some_nat @ Mi ) ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_mint.simps(3)
% 5.42/5.64 thf(fact_1498_mul__shift,axiom,
% 5.42/5.64 ! [X2: nat,Y2: nat,Z: nat] :
% 5.42/5.64 ( ( ( times_times_nat @ X2 @ Y2 )
% 5.42/5.64 = Z )
% 5.42/5.64 = ( ( vEBT_VEBT_mul @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) )
% 5.42/5.64 = ( some_nat @ Z ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mul_shift
% 5.42/5.64 thf(fact_1499_add__shift,axiom,
% 5.42/5.64 ! [X2: nat,Y2: nat,Z: nat] :
% 5.42/5.64 ( ( ( plus_plus_nat @ X2 @ Y2 )
% 5.42/5.64 = Z )
% 5.42/5.64 = ( ( vEBT_VEBT_add @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) )
% 5.42/5.64 = ( some_nat @ Z ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_shift
% 5.42/5.64 thf(fact_1500_vebt__maxt_Osimps_I2_J,axiom,
% 5.42/5.64 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.42/5.64 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.42/5.64 = none_nat ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_maxt.simps(2)
% 5.42/5.64 thf(fact_1501_vebt__pred_Osimps_I4_J,axiom,
% 5.42/5.64 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.42/5.64 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.42/5.64 = none_nat ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_pred.simps(4)
% 5.42/5.64 thf(fact_1502_vebt__succ_Osimps_I3_J,axiom,
% 5.42/5.64 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.42/5.64 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.42/5.64 = none_nat ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_succ.simps(3)
% 5.42/5.64 thf(fact_1503_vebt__mint_Osimps_I2_J,axiom,
% 5.42/5.64 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.42/5.64 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.42/5.64 = none_nat ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_mint.simps(2)
% 5.42/5.64 thf(fact_1504_maxt__corr__help__empty,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_maxt @ T )
% 5.42/5.64 = none_nat )
% 5.42/5.64 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.42/5.64 = bot_bot_set_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % maxt_corr_help_empty
% 5.42/5.64 thf(fact_1505_mint__corr__help__empty,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_mint @ T )
% 5.42/5.64 = none_nat )
% 5.42/5.64 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.42/5.64 = bot_bot_set_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mint_corr_help_empty
% 5.42/5.64 thf(fact_1506_add__def,axiom,
% 5.42/5.64 ( vEBT_VEBT_add
% 5.42/5.64 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_def
% 5.42/5.64 thf(fact_1507_mul__def,axiom,
% 5.42/5.64 ( vEBT_VEBT_mul
% 5.42/5.64 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % mul_def
% 5.42/5.64 thf(fact_1508_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.42/5.64 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.42/5.64 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.simps(3)
% 5.42/5.64 thf(fact_1509_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.42/5.64 ! [F: num > num > num,A: num,B: num] :
% 5.42/5.64 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.42/5.64 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.simps(3)
% 5.42/5.64 thf(fact_1510_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.42/5.64 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.42/5.64 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.42/5.64 = ( some_nat @ ( F @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.simps(3)
% 5.42/5.64 thf(fact_1511_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.42/5.64 ! [X2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y2: option4927543243414619207at_nat] :
% 5.42/5.64 ( ( ( vEBT_V1502963449132264192at_nat @ X2 @ Xa2 @ Xb )
% 5.42/5.64 = Y2 )
% 5.42/5.64 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.42/5.64 => ( Y2 != none_P5556105721700978146at_nat ) )
% 5.42/5.64 => ( ( ? [V2: product_prod_nat_nat] :
% 5.42/5.64 ( Xa2
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.42/5.64 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.42/5.64 => ( Y2 != none_P5556105721700978146at_nat ) ) )
% 5.42/5.64 => ~ ! [A5: product_prod_nat_nat] :
% 5.42/5.64 ( ( Xa2
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.42/5.64 => ! [B5: product_prod_nat_nat] :
% 5.42/5.64 ( ( Xb
% 5.42/5.64 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.42/5.64 => ( Y2
% 5.42/5.64 != ( some_P7363390416028606310at_nat @ ( X2 @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.elims
% 5.42/5.64 thf(fact_1512_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.42/5.64 ! [X2: num > num > num,Xa2: option_num,Xb: option_num,Y2: option_num] :
% 5.42/5.64 ( ( ( vEBT_V819420779217536731ft_num @ X2 @ Xa2 @ Xb )
% 5.42/5.64 = Y2 )
% 5.42/5.64 => ( ( ( Xa2 = none_num )
% 5.42/5.64 => ( Y2 != none_num ) )
% 5.42/5.64 => ( ( ? [V2: num] :
% 5.42/5.64 ( Xa2
% 5.42/5.64 = ( some_num @ V2 ) )
% 5.42/5.64 => ( ( Xb = none_num )
% 5.42/5.64 => ( Y2 != none_num ) ) )
% 5.42/5.64 => ~ ! [A5: num] :
% 5.42/5.64 ( ( Xa2
% 5.42/5.64 = ( some_num @ A5 ) )
% 5.42/5.64 => ! [B5: num] :
% 5.42/5.64 ( ( Xb
% 5.42/5.64 = ( some_num @ B5 ) )
% 5.42/5.64 => ( Y2
% 5.42/5.64 != ( some_num @ ( X2 @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.elims
% 5.42/5.64 thf(fact_1513_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.42/5.64 ! [X2: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y2: option_nat] :
% 5.42/5.64 ( ( ( vEBT_V4262088993061758097ft_nat @ X2 @ Xa2 @ Xb )
% 5.42/5.64 = Y2 )
% 5.42/5.64 => ( ( ( Xa2 = none_nat )
% 5.42/5.64 => ( Y2 != none_nat ) )
% 5.42/5.64 => ( ( ? [V2: nat] :
% 5.42/5.64 ( Xa2
% 5.42/5.64 = ( some_nat @ V2 ) )
% 5.42/5.64 => ( ( Xb = none_nat )
% 5.42/5.64 => ( Y2 != none_nat ) ) )
% 5.42/5.64 => ~ ! [A5: nat] :
% 5.42/5.64 ( ( Xa2
% 5.42/5.64 = ( some_nat @ A5 ) )
% 5.42/5.64 => ! [B5: nat] :
% 5.42/5.64 ( ( Xb
% 5.42/5.64 = ( some_nat @ B5 ) )
% 5.42/5.64 => ( Y2
% 5.42/5.64 != ( some_nat @ ( X2 @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.elims
% 5.42/5.64 thf(fact_1514_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.42/5.64 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.42/5.64 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.42/5.64 = none_P5556105721700978146at_nat ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.simps(2)
% 5.42/5.64 thf(fact_1515_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.42/5.64 ! [Uw: num > num > num,V: num] :
% 5.42/5.64 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 5.42/5.64 = none_num ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.simps(2)
% 5.42/5.64 thf(fact_1516_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.42/5.64 ! [Uw: nat > nat > nat,V: nat] :
% 5.42/5.64 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.42/5.64 = none_nat ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.simps(2)
% 5.42/5.64 thf(fact_1517_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.42/5.64 ! [X2: produc5491161045314408544at_nat] :
% 5.42/5.64 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.42/5.64 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.42/5.64 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_comp_shift.cases
% 5.42/5.64 thf(fact_1518_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.42/5.64 ! [X2: produc2233624965454879586on_nat] :
% 5.42/5.64 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.42/5.64 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.42/5.64 => ~ ! [F2: nat > nat > $o,X3: nat,Y3: nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_comp_shift.cases
% 5.42/5.64 thf(fact_1519_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.42/5.64 ! [X2: produc7036089656553540234on_num] :
% 5.42/5.64 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.42/5.64 => ( ! [Uw2: num > num > $o,V2: num] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.42/5.64 => ~ ! [F2: num > num > $o,X3: num,Y3: num] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_comp_shift.cases
% 5.42/5.64 thf(fact_1520_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.42/5.64 ! [X2: produc5542196010084753463at_nat] :
% 5.42/5.64 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.42/5.64 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.42/5.64 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A5 ) @ ( some_P7363390416028606310at_nat @ B5 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.cases
% 5.42/5.64 thf(fact_1521_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.42/5.64 ! [X2: produc8306885398267862888on_nat] :
% 5.42/5.64 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.42/5.64 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.42/5.64 => ~ ! [F2: nat > nat > nat,A5: nat,B5: nat] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A5 ) @ ( some_nat @ B5 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.cases
% 5.42/5.64 thf(fact_1522_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.42/5.64 ! [X2: produc1193250871479095198on_num] :
% 5.42/5.64 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.42/5.64 => ( ! [Uw2: num > num > num,V2: num] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.42/5.64 => ~ ! [F2: num > num > num,A5: num,B5: num] :
% 5.42/5.64 ( X2
% 5.42/5.64 != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A5 ) @ ( some_num @ B5 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.option_shift.cases
% 5.42/5.64 thf(fact_1523_is__pred__in__set__def,axiom,
% 5.42/5.64 ( vEBT_is_pred_in_set
% 5.42/5.64 = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 5.42/5.64 ( ( member_nat @ Y @ Xs )
% 5.42/5.64 & ( ord_less_nat @ Y @ X )
% 5.42/5.64 & ! [Z4: nat] :
% 5.42/5.64 ( ( member_nat @ Z4 @ Xs )
% 5.42/5.64 => ( ( ord_less_nat @ Z4 @ X )
% 5.42/5.64 => ( ord_less_eq_nat @ Z4 @ Y ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % is_pred_in_set_def
% 5.42/5.64 thf(fact_1524_is__succ__in__set__def,axiom,
% 5.42/5.64 ( vEBT_is_succ_in_set
% 5.42/5.64 = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 5.42/5.64 ( ( member_nat @ Y @ Xs )
% 5.42/5.64 & ( ord_less_nat @ X @ Y )
% 5.42/5.64 & ! [Z4: nat] :
% 5.42/5.64 ( ( member_nat @ Z4 @ Xs )
% 5.42/5.64 => ( ( ord_less_nat @ X @ Z4 )
% 5.42/5.64 => ( ord_less_eq_nat @ Y @ Z4 ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % is_succ_in_set_def
% 5.42/5.64 thf(fact_1525_buildup__gives__empty,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.42/5.64 = bot_bot_set_nat ) ).
% 5.42/5.64
% 5.42/5.64 % buildup_gives_empty
% 5.42/5.64 thf(fact_1526_Diff__eq__empty__iff,axiom,
% 5.42/5.64 ! [A2: set_int,B3: set_int] :
% 5.42/5.64 ( ( ( minus_minus_set_int @ A2 @ B3 )
% 5.42/5.64 = bot_bot_set_int )
% 5.42/5.64 = ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_eq_empty_iff
% 5.42/5.64 thf(fact_1527_Diff__eq__empty__iff,axiom,
% 5.42/5.64 ! [A2: set_real,B3: set_real] :
% 5.42/5.64 ( ( ( minus_minus_set_real @ A2 @ B3 )
% 5.42/5.64 = bot_bot_set_real )
% 5.42/5.64 = ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_eq_empty_iff
% 5.42/5.64 thf(fact_1528_Diff__eq__empty__iff,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( ( minus_1356011639430497352at_nat @ A2 @ B3 )
% 5.42/5.64 = bot_bo2099793752762293965at_nat )
% 5.42/5.64 = ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_eq_empty_iff
% 5.42/5.64 thf(fact_1529_Diff__eq__empty__iff,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( ( minus_minus_set_nat @ A2 @ B3 )
% 5.42/5.64 = bot_bot_set_nat )
% 5.42/5.64 = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_eq_empty_iff
% 5.42/5.64 thf(fact_1530_succ__less__length__list,axiom,
% 5.42/5.64 ! [Deg: nat,Mi: nat,X2: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.64 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.42/5.64 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( if_option_nat
% 5.42/5.64 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 != none_nat )
% 5.42/5.64 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 = none_nat )
% 5.42/5.64 @ none_nat
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % succ_less_length_list
% 5.42/5.64 thf(fact_1531_succ__greatereq__min,axiom,
% 5.42/5.64 ! [Deg: nat,Mi: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.64 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.42/5.64 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 != none_nat )
% 5.42/5.64 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 = none_nat )
% 5.42/5.64 @ none_nat
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.42/5.64 @ none_nat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % succ_greatereq_min
% 5.42/5.64 thf(fact_1532_pred__lesseq__max,axiom,
% 5.42/5.64 ! [Deg: nat,X2: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.64 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.42/5.64 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 != none_nat )
% 5.42/5.64 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 = none_nat )
% 5.42/5.64 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.42/5.64 @ none_nat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % pred_lesseq_max
% 5.42/5.64 thf(fact_1533_pred__less__length__list,axiom,
% 5.42/5.64 ! [Deg: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.42/5.64 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.42/5.64 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( if_option_nat
% 5.42/5.64 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 != none_nat )
% 5.42/5.64 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 = none_nat )
% 5.42/5.64 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % pred_less_length_list
% 5.42/5.64 thf(fact_1534_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_num,Ys: list_num] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1535_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_Code_integer,Ys: list_o] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1536_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1537_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1538_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1539_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1540_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1541_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_o,Ys: list_o] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1542_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1543_product__nth,axiom,
% 5.42/5.64 ! [N: nat,Xs2: list_o,Ys: list_int] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.42/5.64 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 5.42/5.64 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % product_nth
% 5.42/5.64 thf(fact_1544_obtain__set__succ,axiom,
% 5.42/5.64 ! [X2: nat,Z: nat,A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( ord_less_nat @ X2 @ Z )
% 5.42/5.64 => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 5.42/5.64 => ( ( finite_finite_nat @ B3 )
% 5.42/5.64 => ( ( A2 = B3 )
% 5.42/5.64 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X2 @ X_1 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % obtain_set_succ
% 5.42/5.64 thf(fact_1545_obtain__set__pred,axiom,
% 5.42/5.64 ! [Z: nat,X2: nat,A2: set_nat] :
% 5.42/5.64 ( ( ord_less_nat @ Z @ X2 )
% 5.42/5.64 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 5.42/5.64 => ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X2 @ X_1 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % obtain_set_pred
% 5.42/5.64 thf(fact_1546_vebt__succ_Osimps_I6_J,axiom,
% 5.42/5.64 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ( ord_less_nat @ X2 @ Mi )
% 5.42/5.64 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( some_nat @ Mi ) ) )
% 5.42/5.64 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.42/5.64 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 != none_nat )
% 5.42/5.64 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 = none_nat )
% 5.42/5.64 @ none_nat
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.42/5.64 @ none_nat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_succ.simps(6)
% 5.42/5.64 thf(fact_1547_set__vebt_H__def,axiom,
% 5.42/5.64 ( vEBT_VEBT_set_vebt
% 5.42/5.64 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_vebt'_def
% 5.42/5.64 thf(fact_1548_set__vebt__finite,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_vebt_finite
% 5.42/5.64 thf(fact_1549_pred__none__empty,axiom,
% 5.42/5.64 ! [Xs2: set_nat,A: nat] :
% 5.42/5.64 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 5.42/5.64 => ( ( finite_finite_nat @ Xs2 )
% 5.42/5.64 => ~ ? [X4: nat] :
% 5.42/5.64 ( ( member_nat @ X4 @ Xs2 )
% 5.42/5.64 & ( ord_less_nat @ X4 @ A ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % pred_none_empty
% 5.42/5.64 thf(fact_1550_succ__none__empty,axiom,
% 5.42/5.64 ! [Xs2: set_nat,A: nat] :
% 5.42/5.64 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_1 )
% 5.42/5.64 => ( ( finite_finite_nat @ Xs2 )
% 5.42/5.64 => ~ ? [X4: nat] :
% 5.42/5.64 ( ( member_nat @ X4 @ Xs2 )
% 5.42/5.64 & ( ord_less_nat @ A @ X4 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % succ_none_empty
% 5.42/5.64 thf(fact_1551_psubsetI,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.42/5.64 => ( ( A2 != B3 )
% 5.42/5.64 => ( ord_less_set_nat @ A2 @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubsetI
% 5.42/5.64 thf(fact_1552_DiffI,axiom,
% 5.42/5.64 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.42/5.64 ( ( member_complex @ C @ A2 )
% 5.42/5.64 => ( ~ ( member_complex @ C @ B3 )
% 5.42/5.64 => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffI
% 5.42/5.64 thf(fact_1553_DiffI,axiom,
% 5.42/5.64 ! [C: real,A2: set_real,B3: set_real] :
% 5.42/5.64 ( ( member_real @ C @ A2 )
% 5.42/5.64 => ( ~ ( member_real @ C @ B3 )
% 5.42/5.64 => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffI
% 5.42/5.64 thf(fact_1554_DiffI,axiom,
% 5.42/5.64 ! [C: int,A2: set_int,B3: set_int] :
% 5.42/5.64 ( ( member_int @ C @ A2 )
% 5.42/5.64 => ( ~ ( member_int @ C @ B3 )
% 5.42/5.64 => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffI
% 5.42/5.64 thf(fact_1555_DiffI,axiom,
% 5.42/5.64 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.42/5.64 => ( ~ ( member8440522571783428010at_nat @ C @ B3 )
% 5.42/5.64 => ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffI
% 5.42/5.64 thf(fact_1556_DiffI,axiom,
% 5.42/5.64 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( member_nat @ C @ A2 )
% 5.42/5.64 => ( ~ ( member_nat @ C @ B3 )
% 5.42/5.64 => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffI
% 5.42/5.64 thf(fact_1557_Diff__iff,axiom,
% 5.42/5.64 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.42/5.64 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.42/5.64 = ( ( member_complex @ C @ A2 )
% 5.42/5.64 & ~ ( member_complex @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_iff
% 5.42/5.64 thf(fact_1558_Diff__iff,axiom,
% 5.42/5.64 ! [C: real,A2: set_real,B3: set_real] :
% 5.42/5.64 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.42/5.64 = ( ( member_real @ C @ A2 )
% 5.42/5.64 & ~ ( member_real @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_iff
% 5.42/5.64 thf(fact_1559_Diff__iff,axiom,
% 5.42/5.64 ! [C: int,A2: set_int,B3: set_int] :
% 5.42/5.64 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.42/5.64 = ( ( member_int @ C @ A2 )
% 5.42/5.64 & ~ ( member_int @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_iff
% 5.42/5.64 thf(fact_1560_Diff__iff,axiom,
% 5.42/5.64 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) )
% 5.42/5.64 = ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.42/5.64 & ~ ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_iff
% 5.42/5.64 thf(fact_1561_Diff__iff,axiom,
% 5.42/5.64 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.42/5.64 = ( ( member_nat @ C @ A2 )
% 5.42/5.64 & ~ ( member_nat @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_iff
% 5.42/5.64 thf(fact_1562_Diff__idemp,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) @ B3 )
% 5.42/5.64 = ( minus_1356011639430497352at_nat @ A2 @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_idemp
% 5.42/5.64 thf(fact_1563_Diff__idemp,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ B3 )
% 5.42/5.64 = ( minus_minus_set_nat @ A2 @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_idemp
% 5.42/5.64 thf(fact_1564_succ__empty,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.42/5.64 = none_nat )
% 5.42/5.64 = ( ( collect_nat
% 5.42/5.64 @ ^ [Y: nat] :
% 5.42/5.64 ( ( vEBT_vebt_member @ T @ Y )
% 5.42/5.64 & ( ord_less_nat @ X2 @ Y ) ) )
% 5.42/5.64 = bot_bot_set_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % succ_empty
% 5.42/5.64 thf(fact_1565_pred__empty,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.42/5.64 = none_nat )
% 5.42/5.64 = ( ( collect_nat
% 5.42/5.64 @ ^ [Y: nat] :
% 5.42/5.64 ( ( vEBT_vebt_member @ T @ Y )
% 5.42/5.64 & ( ord_less_nat @ Y @ X2 ) ) )
% 5.42/5.64 = bot_bot_set_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % pred_empty
% 5.42/5.64 thf(fact_1566_List_Ofinite__set,axiom,
% 5.42/5.64 ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % List.finite_set
% 5.42/5.64 thf(fact_1567_List_Ofinite__set,axiom,
% 5.42/5.64 ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % List.finite_set
% 5.42/5.64 thf(fact_1568_List_Ofinite__set,axiom,
% 5.42/5.64 ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % List.finite_set
% 5.42/5.64 thf(fact_1569_List_Ofinite__set,axiom,
% 5.42/5.64 ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % List.finite_set
% 5.42/5.64 thf(fact_1570_Diff__empty,axiom,
% 5.42/5.64 ! [A2: set_int] :
% 5.42/5.64 ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 5.42/5.64 = A2 ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_empty
% 5.42/5.64 thf(fact_1571_Diff__empty,axiom,
% 5.42/5.64 ! [A2: set_real] :
% 5.42/5.64 ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 5.42/5.64 = A2 ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_empty
% 5.42/5.64 thf(fact_1572_Diff__empty,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( minus_1356011639430497352at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 5.42/5.64 = A2 ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_empty
% 5.42/5.64 thf(fact_1573_Diff__empty,axiom,
% 5.42/5.64 ! [A2: set_nat] :
% 5.42/5.64 ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 5.42/5.64 = A2 ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_empty
% 5.42/5.64 thf(fact_1574_empty__Diff,axiom,
% 5.42/5.64 ! [A2: set_int] :
% 5.42/5.64 ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 5.42/5.64 = bot_bot_set_int ) ).
% 5.42/5.64
% 5.42/5.64 % empty_Diff
% 5.42/5.64 thf(fact_1575_empty__Diff,axiom,
% 5.42/5.64 ! [A2: set_real] :
% 5.42/5.64 ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 5.42/5.64 = bot_bot_set_real ) ).
% 5.42/5.64
% 5.42/5.64 % empty_Diff
% 5.42/5.64 thf(fact_1576_empty__Diff,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( minus_1356011639430497352at_nat @ bot_bo2099793752762293965at_nat @ A2 )
% 5.42/5.64 = bot_bo2099793752762293965at_nat ) ).
% 5.42/5.64
% 5.42/5.64 % empty_Diff
% 5.42/5.64 thf(fact_1577_empty__Diff,axiom,
% 5.42/5.64 ! [A2: set_nat] :
% 5.42/5.64 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 5.42/5.64 = bot_bot_set_nat ) ).
% 5.42/5.64
% 5.42/5.64 % empty_Diff
% 5.42/5.64 thf(fact_1578_Diff__cancel,axiom,
% 5.42/5.64 ! [A2: set_int] :
% 5.42/5.64 ( ( minus_minus_set_int @ A2 @ A2 )
% 5.42/5.64 = bot_bot_set_int ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_cancel
% 5.42/5.64 thf(fact_1579_Diff__cancel,axiom,
% 5.42/5.64 ! [A2: set_real] :
% 5.42/5.64 ( ( minus_minus_set_real @ A2 @ A2 )
% 5.42/5.64 = bot_bot_set_real ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_cancel
% 5.42/5.64 thf(fact_1580_Diff__cancel,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( minus_1356011639430497352at_nat @ A2 @ A2 )
% 5.42/5.64 = bot_bo2099793752762293965at_nat ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_cancel
% 5.42/5.64 thf(fact_1581_Diff__cancel,axiom,
% 5.42/5.64 ! [A2: set_nat] :
% 5.42/5.64 ( ( minus_minus_set_nat @ A2 @ A2 )
% 5.42/5.64 = bot_bot_set_nat ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_cancel
% 5.42/5.64 thf(fact_1582_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.42/5.64 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1583_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.42/5.64 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1584_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.42/5.64 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1585_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.42/5.64 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1586_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.42/5.64 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1587_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_o,Ys: list_o] :
% 5.42/5.64 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1588_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_o,Ys: list_nat] :
% 5.42/5.64 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1589_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_o,Ys: list_int] :
% 5.42/5.64 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1590_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.42/5.64 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1591_length__product,axiom,
% 5.42/5.64 ! [Xs2: list_nat,Ys: list_o] :
% 5.42/5.64 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 5.42/5.64 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % length_product
% 5.42/5.64 thf(fact_1592_mult__commute__abs,axiom,
% 5.42/5.64 ! [C: real] :
% 5.42/5.64 ( ( ^ [X: real] : ( times_times_real @ X @ C ) )
% 5.42/5.64 = ( times_times_real @ C ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_commute_abs
% 5.42/5.64 thf(fact_1593_mult__commute__abs,axiom,
% 5.42/5.64 ! [C: rat] :
% 5.42/5.64 ( ( ^ [X: rat] : ( times_times_rat @ X @ C ) )
% 5.42/5.64 = ( times_times_rat @ C ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_commute_abs
% 5.42/5.64 thf(fact_1594_mult__commute__abs,axiom,
% 5.42/5.64 ! [C: nat] :
% 5.42/5.64 ( ( ^ [X: nat] : ( times_times_nat @ X @ C ) )
% 5.42/5.64 = ( times_times_nat @ C ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_commute_abs
% 5.42/5.64 thf(fact_1595_mult__commute__abs,axiom,
% 5.42/5.64 ! [C: int] :
% 5.42/5.64 ( ( ^ [X: int] : ( times_times_int @ X @ C ) )
% 5.42/5.64 = ( times_times_int @ C ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_commute_abs
% 5.42/5.64 thf(fact_1596_DiffE,axiom,
% 5.42/5.64 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.42/5.64 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( ( member_complex @ C @ A2 )
% 5.42/5.64 => ( member_complex @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffE
% 5.42/5.64 thf(fact_1597_DiffE,axiom,
% 5.42/5.64 ! [C: real,A2: set_real,B3: set_real] :
% 5.42/5.64 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( ( member_real @ C @ A2 )
% 5.42/5.64 => ( member_real @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffE
% 5.42/5.64 thf(fact_1598_DiffE,axiom,
% 5.42/5.64 ! [C: int,A2: set_int,B3: set_int] :
% 5.42/5.64 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( ( member_int @ C @ A2 )
% 5.42/5.64 => ( member_int @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffE
% 5.42/5.64 thf(fact_1599_DiffE,axiom,
% 5.42/5.64 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.42/5.64 => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffE
% 5.42/5.64 thf(fact_1600_DiffE,axiom,
% 5.42/5.64 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( ( member_nat @ C @ A2 )
% 5.42/5.64 => ( member_nat @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffE
% 5.42/5.64 thf(fact_1601_DiffD1,axiom,
% 5.42/5.64 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.42/5.64 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.42/5.64 => ( member_complex @ C @ A2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD1
% 5.42/5.64 thf(fact_1602_DiffD1,axiom,
% 5.42/5.64 ! [C: real,A2: set_real,B3: set_real] :
% 5.42/5.64 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.42/5.64 => ( member_real @ C @ A2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD1
% 5.42/5.64 thf(fact_1603_DiffD1,axiom,
% 5.42/5.64 ! [C: int,A2: set_int,B3: set_int] :
% 5.42/5.64 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.42/5.64 => ( member_int @ C @ A2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD1
% 5.42/5.64 thf(fact_1604_DiffD1,axiom,
% 5.42/5.64 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) )
% 5.42/5.64 => ( member8440522571783428010at_nat @ C @ A2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD1
% 5.42/5.64 thf(fact_1605_DiffD1,axiom,
% 5.42/5.64 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.42/5.64 => ( member_nat @ C @ A2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD1
% 5.42/5.64 thf(fact_1606_DiffD2,axiom,
% 5.42/5.64 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.42/5.64 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( member_complex @ C @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD2
% 5.42/5.64 thf(fact_1607_DiffD2,axiom,
% 5.42/5.64 ! [C: real,A2: set_real,B3: set_real] :
% 5.42/5.64 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( member_real @ C @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD2
% 5.42/5.64 thf(fact_1608_DiffD2,axiom,
% 5.42/5.64 ! [C: int,A2: set_int,B3: set_int] :
% 5.42/5.64 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( member_int @ C @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD2
% 5.42/5.64 thf(fact_1609_DiffD2,axiom,
% 5.42/5.64 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( member8440522571783428010at_nat @ C @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD2
% 5.42/5.64 thf(fact_1610_DiffD2,axiom,
% 5.42/5.64 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.42/5.64 => ~ ( member_nat @ C @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % DiffD2
% 5.42/5.64 thf(fact_1611_set__diff__eq,axiom,
% 5.42/5.64 ( minus_811609699411566653omplex
% 5.42/5.64 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.42/5.64 ( collect_complex
% 5.42/5.64 @ ^ [X: complex] :
% 5.42/5.64 ( ( member_complex @ X @ A6 )
% 5.42/5.64 & ~ ( member_complex @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_diff_eq
% 5.42/5.64 thf(fact_1612_set__diff__eq,axiom,
% 5.42/5.64 ( minus_minus_set_real
% 5.42/5.64 = ( ^ [A6: set_real,B6: set_real] :
% 5.42/5.64 ( collect_real
% 5.42/5.64 @ ^ [X: real] :
% 5.42/5.64 ( ( member_real @ X @ A6 )
% 5.42/5.64 & ~ ( member_real @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_diff_eq
% 5.42/5.64 thf(fact_1613_set__diff__eq,axiom,
% 5.42/5.64 ( minus_7954133019191499631st_nat
% 5.42/5.64 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.42/5.64 ( collect_list_nat
% 5.42/5.64 @ ^ [X: list_nat] :
% 5.42/5.64 ( ( member_list_nat @ X @ A6 )
% 5.42/5.64 & ~ ( member_list_nat @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_diff_eq
% 5.42/5.64 thf(fact_1614_set__diff__eq,axiom,
% 5.42/5.64 ( minus_minus_set_int
% 5.42/5.64 = ( ^ [A6: set_int,B6: set_int] :
% 5.42/5.64 ( collect_int
% 5.42/5.64 @ ^ [X: int] :
% 5.42/5.64 ( ( member_int @ X @ A6 )
% 5.42/5.64 & ~ ( member_int @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_diff_eq
% 5.42/5.64 thf(fact_1615_set__diff__eq,axiom,
% 5.42/5.64 ( minus_1356011639430497352at_nat
% 5.42/5.64 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( collec3392354462482085612at_nat
% 5.42/5.64 @ ^ [X: product_prod_nat_nat] :
% 5.42/5.64 ( ( member8440522571783428010at_nat @ X @ A6 )
% 5.42/5.64 & ~ ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_diff_eq
% 5.42/5.64 thf(fact_1616_set__diff__eq,axiom,
% 5.42/5.64 ( minus_minus_set_nat
% 5.42/5.64 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.42/5.64 ( collect_nat
% 5.42/5.64 @ ^ [X: nat] :
% 5.42/5.64 ( ( member_nat @ X @ A6 )
% 5.42/5.64 & ~ ( member_nat @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_diff_eq
% 5.42/5.64 thf(fact_1617_minus__set__def,axiom,
% 5.42/5.64 ( minus_811609699411566653omplex
% 5.42/5.64 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.42/5.64 ( collect_complex
% 5.42/5.64 @ ( minus_8727706125548526216plex_o
% 5.42/5.64 @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 5.42/5.64 @ ^ [X: complex] : ( member_complex @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % minus_set_def
% 5.42/5.64 thf(fact_1618_minus__set__def,axiom,
% 5.42/5.64 ( minus_minus_set_real
% 5.42/5.64 = ( ^ [A6: set_real,B6: set_real] :
% 5.42/5.64 ( collect_real
% 5.42/5.64 @ ( minus_minus_real_o
% 5.42/5.64 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.42/5.64 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % minus_set_def
% 5.42/5.64 thf(fact_1619_minus__set__def,axiom,
% 5.42/5.64 ( minus_7954133019191499631st_nat
% 5.42/5.64 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.42/5.64 ( collect_list_nat
% 5.42/5.64 @ ( minus_1139252259498527702_nat_o
% 5.42/5.64 @ ^ [X: list_nat] : ( member_list_nat @ X @ A6 )
% 5.42/5.64 @ ^ [X: list_nat] : ( member_list_nat @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % minus_set_def
% 5.42/5.64 thf(fact_1620_minus__set__def,axiom,
% 5.42/5.64 ( minus_minus_set_int
% 5.42/5.64 = ( ^ [A6: set_int,B6: set_int] :
% 5.42/5.64 ( collect_int
% 5.42/5.64 @ ( minus_minus_int_o
% 5.42/5.64 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.42/5.64 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % minus_set_def
% 5.42/5.64 thf(fact_1621_minus__set__def,axiom,
% 5.42/5.64 ( minus_1356011639430497352at_nat
% 5.42/5.64 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( collec3392354462482085612at_nat
% 5.42/5.64 @ ( minus_2270307095948843157_nat_o
% 5.42/5.64 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 5.42/5.64 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % minus_set_def
% 5.42/5.64 thf(fact_1622_minus__set__def,axiom,
% 5.42/5.64 ( minus_minus_set_nat
% 5.42/5.64 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.42/5.64 ( collect_nat
% 5.42/5.64 @ ( minus_minus_nat_o
% 5.42/5.64 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.42/5.64 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % minus_set_def
% 5.42/5.64 thf(fact_1623_psubset__imp__ex__mem,axiom,
% 5.42/5.64 ! [A2: set_complex,B3: set_complex] :
% 5.42/5.64 ( ( ord_less_set_complex @ A2 @ B3 )
% 5.42/5.64 => ? [B5: complex] : ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubset_imp_ex_mem
% 5.42/5.64 thf(fact_1624_psubset__imp__ex__mem,axiom,
% 5.42/5.64 ! [A2: set_real,B3: set_real] :
% 5.42/5.64 ( ( ord_less_set_real @ A2 @ B3 )
% 5.42/5.64 => ? [B5: real] : ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubset_imp_ex_mem
% 5.42/5.64 thf(fact_1625_psubset__imp__ex__mem,axiom,
% 5.42/5.64 ! [A2: set_int,B3: set_int] :
% 5.42/5.64 ( ( ord_less_set_int @ A2 @ B3 )
% 5.42/5.64 => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubset_imp_ex_mem
% 5.42/5.64 thf(fact_1626_psubset__imp__ex__mem,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 5.42/5.64 => ? [B5: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B5 @ ( minus_1356011639430497352at_nat @ B3 @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubset_imp_ex_mem
% 5.42/5.64 thf(fact_1627_psubset__imp__ex__mem,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.42/5.64 => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubset_imp_ex_mem
% 5.42/5.64 thf(fact_1628_finite__lists__length__eq,axiom,
% 5.42/5.64 ! [A2: set_complex,N: nat] :
% 5.42/5.64 ( ( finite3207457112153483333omplex @ A2 )
% 5.42/5.64 => ( finite8712137658972009173omplex
% 5.42/5.64 @ ( collect_list_complex
% 5.42/5.64 @ ^ [Xs: list_complex] :
% 5.42/5.64 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.42/5.64 = N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_eq
% 5.42/5.64 thf(fact_1629_finite__lists__length__eq,axiom,
% 5.42/5.64 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.42/5.64 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.42/5.64 => ( finite3004134309566078307T_VEBT
% 5.42/5.64 @ ( collec5608196760682091941T_VEBT
% 5.42/5.64 @ ^ [Xs: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.42/5.64 = N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_eq
% 5.42/5.64 thf(fact_1630_finite__lists__length__eq,axiom,
% 5.42/5.64 ! [A2: set_o,N: nat] :
% 5.42/5.64 ( ( finite_finite_o @ A2 )
% 5.42/5.64 => ( finite_finite_list_o
% 5.42/5.64 @ ( collect_list_o
% 5.42/5.64 @ ^ [Xs: list_o] :
% 5.42/5.64 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ( size_size_list_o @ Xs )
% 5.42/5.64 = N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_eq
% 5.42/5.64 thf(fact_1631_finite__lists__length__eq,axiom,
% 5.42/5.64 ! [A2: set_int,N: nat] :
% 5.42/5.64 ( ( finite_finite_int @ A2 )
% 5.42/5.64 => ( finite3922522038869484883st_int
% 5.42/5.64 @ ( collect_list_int
% 5.42/5.64 @ ^ [Xs: list_int] :
% 5.42/5.64 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ( size_size_list_int @ Xs )
% 5.42/5.64 = N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_eq
% 5.42/5.64 thf(fact_1632_finite__lists__length__eq,axiom,
% 5.42/5.64 ! [A2: set_nat,N: nat] :
% 5.42/5.64 ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ( finite8100373058378681591st_nat
% 5.42/5.64 @ ( collect_list_nat
% 5.42/5.64 @ ^ [Xs: list_nat] :
% 5.42/5.64 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ( size_size_list_nat @ Xs )
% 5.42/5.64 = N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_eq
% 5.42/5.64 thf(fact_1633_finite__lists__length__le,axiom,
% 5.42/5.64 ! [A2: set_complex,N: nat] :
% 5.42/5.64 ( ( finite3207457112153483333omplex @ A2 )
% 5.42/5.64 => ( finite8712137658972009173omplex
% 5.42/5.64 @ ( collect_list_complex
% 5.42/5.64 @ ^ [Xs: list_complex] :
% 5.42/5.64 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_le
% 5.42/5.64 thf(fact_1634_finite__lists__length__le,axiom,
% 5.42/5.64 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.42/5.64 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.42/5.64 => ( finite3004134309566078307T_VEBT
% 5.42/5.64 @ ( collec5608196760682091941T_VEBT
% 5.42/5.64 @ ^ [Xs: list_VEBT_VEBT] :
% 5.42/5.64 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_le
% 5.42/5.64 thf(fact_1635_finite__lists__length__le,axiom,
% 5.42/5.64 ! [A2: set_o,N: nat] :
% 5.42/5.64 ( ( finite_finite_o @ A2 )
% 5.42/5.64 => ( finite_finite_list_o
% 5.42/5.64 @ ( collect_list_o
% 5.42/5.64 @ ^ [Xs: list_o] :
% 5.42/5.64 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_le
% 5.42/5.64 thf(fact_1636_finite__lists__length__le,axiom,
% 5.42/5.64 ! [A2: set_int,N: nat] :
% 5.42/5.64 ( ( finite_finite_int @ A2 )
% 5.42/5.64 => ( finite3922522038869484883st_int
% 5.42/5.64 @ ( collect_list_int
% 5.42/5.64 @ ^ [Xs: list_int] :
% 5.42/5.64 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_le
% 5.42/5.64 thf(fact_1637_finite__lists__length__le,axiom,
% 5.42/5.64 ! [A2: set_nat,N: nat] :
% 5.42/5.64 ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ( finite8100373058378681591st_nat
% 5.42/5.64 @ ( collect_list_nat
% 5.42/5.64 @ ^ [Xs: list_nat] :
% 5.42/5.64 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.42/5.64 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_lists_length_le
% 5.42/5.64 thf(fact_1638_lambda__one,axiom,
% 5.42/5.64 ( ( ^ [X: complex] : X )
% 5.42/5.64 = ( times_times_complex @ one_one_complex ) ) ).
% 5.42/5.64
% 5.42/5.64 % lambda_one
% 5.42/5.64 thf(fact_1639_lambda__one,axiom,
% 5.42/5.64 ( ( ^ [X: real] : X )
% 5.42/5.64 = ( times_times_real @ one_one_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % lambda_one
% 5.42/5.64 thf(fact_1640_lambda__one,axiom,
% 5.42/5.64 ( ( ^ [X: rat] : X )
% 5.42/5.64 = ( times_times_rat @ one_one_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % lambda_one
% 5.42/5.64 thf(fact_1641_lambda__one,axiom,
% 5.42/5.64 ( ( ^ [X: nat] : X )
% 5.42/5.64 = ( times_times_nat @ one_one_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % lambda_one
% 5.42/5.64 thf(fact_1642_lambda__one,axiom,
% 5.42/5.64 ( ( ^ [X: int] : X )
% 5.42/5.64 = ( times_times_int @ one_one_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % lambda_one
% 5.42/5.64 thf(fact_1643_finite__list,axiom,
% 5.42/5.64 ! [A2: set_VEBT_VEBT] :
% 5.42/5.64 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.42/5.64 => ? [Xs3: list_VEBT_VEBT] :
% 5.42/5.64 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.42/5.64 = A2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_list
% 5.42/5.64 thf(fact_1644_finite__list,axiom,
% 5.42/5.64 ! [A2: set_nat] :
% 5.42/5.64 ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ? [Xs3: list_nat] :
% 5.42/5.64 ( ( set_nat2 @ Xs3 )
% 5.42/5.64 = A2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_list
% 5.42/5.64 thf(fact_1645_finite__list,axiom,
% 5.42/5.64 ! [A2: set_int] :
% 5.42/5.64 ( ( finite_finite_int @ A2 )
% 5.42/5.64 => ? [Xs3: list_int] :
% 5.42/5.64 ( ( set_int2 @ Xs3 )
% 5.42/5.64 = A2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_list
% 5.42/5.64 thf(fact_1646_finite__list,axiom,
% 5.42/5.64 ! [A2: set_complex] :
% 5.42/5.64 ( ( finite3207457112153483333omplex @ A2 )
% 5.42/5.64 => ? [Xs3: list_complex] :
% 5.42/5.64 ( ( set_complex2 @ Xs3 )
% 5.42/5.64 = A2 ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_list
% 5.42/5.64 thf(fact_1647_set__vebt__def,axiom,
% 5.42/5.64 ( vEBT_set_vebt
% 5.42/5.64 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_vebt_def
% 5.42/5.64 thf(fact_1648_numeral__code_I2_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.42/5.64 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(2)
% 5.42/5.64 thf(fact_1649_numeral__code_I2_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.42/5.64 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(2)
% 5.42/5.64 thf(fact_1650_numeral__code_I2_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.42/5.64 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(2)
% 5.42/5.64 thf(fact_1651_numeral__code_I2_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.42/5.64 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(2)
% 5.42/5.64 thf(fact_1652_numeral__code_I2_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.42/5.64 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(2)
% 5.42/5.64 thf(fact_1653_numeral__code_I3_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.42/5.64 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(3)
% 5.42/5.64 thf(fact_1654_numeral__code_I3_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.42/5.64 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(3)
% 5.42/5.64 thf(fact_1655_numeral__code_I3_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.42/5.64 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(3)
% 5.42/5.64 thf(fact_1656_numeral__code_I3_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.42/5.64 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(3)
% 5.42/5.64 thf(fact_1657_numeral__code_I3_J,axiom,
% 5.42/5.64 ! [N: num] :
% 5.42/5.64 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.42/5.64 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % numeral_code(3)
% 5.42/5.64 thf(fact_1658_power__numeral__even,axiom,
% 5.42/5.64 ! [Z: complex,W: num] :
% 5.42/5.64 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.42/5.64 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_even
% 5.42/5.64 thf(fact_1659_power__numeral__even,axiom,
% 5.42/5.64 ! [Z: real,W: num] :
% 5.42/5.64 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.42/5.64 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_even
% 5.42/5.64 thf(fact_1660_power__numeral__even,axiom,
% 5.42/5.64 ! [Z: rat,W: num] :
% 5.42/5.64 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.42/5.64 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_even
% 5.42/5.64 thf(fact_1661_power__numeral__even,axiom,
% 5.42/5.64 ! [Z: nat,W: num] :
% 5.42/5.64 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.42/5.64 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_even
% 5.42/5.64 thf(fact_1662_power__numeral__even,axiom,
% 5.42/5.64 ! [Z: int,W: num] :
% 5.42/5.64 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.42/5.64 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_even
% 5.42/5.64 thf(fact_1663_power__numeral__odd,axiom,
% 5.42/5.64 ! [Z: complex,W: num] :
% 5.42/5.64 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.42/5.64 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_odd
% 5.42/5.64 thf(fact_1664_power__numeral__odd,axiom,
% 5.42/5.64 ! [Z: real,W: num] :
% 5.42/5.64 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.42/5.64 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_odd
% 5.42/5.64 thf(fact_1665_power__numeral__odd,axiom,
% 5.42/5.64 ! [Z: rat,W: num] :
% 5.42/5.64 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.42/5.64 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_odd
% 5.42/5.64 thf(fact_1666_power__numeral__odd,axiom,
% 5.42/5.64 ! [Z: nat,W: num] :
% 5.42/5.64 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.42/5.64 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_odd
% 5.42/5.64 thf(fact_1667_power__numeral__odd,axiom,
% 5.42/5.64 ! [Z: int,W: num] :
% 5.42/5.64 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.42/5.64 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_numeral_odd
% 5.42/5.64 thf(fact_1668_not__psubset__empty,axiom,
% 5.42/5.64 ! [A2: set_nat] :
% 5.42/5.64 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 5.42/5.64
% 5.42/5.64 % not_psubset_empty
% 5.42/5.64 thf(fact_1669_not__psubset__empty,axiom,
% 5.42/5.64 ! [A2: set_int] :
% 5.42/5.64 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 5.42/5.64
% 5.42/5.64 % not_psubset_empty
% 5.42/5.64 thf(fact_1670_not__psubset__empty,axiom,
% 5.42/5.64 ! [A2: set_real] :
% 5.42/5.64 ~ ( ord_less_set_real @ A2 @ bot_bot_set_real ) ).
% 5.42/5.64
% 5.42/5.64 % not_psubset_empty
% 5.42/5.64 thf(fact_1671_subset__iff__psubset__eq,axiom,
% 5.42/5.64 ( ord_less_eq_set_nat
% 5.42/5.64 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.42/5.64 ( ( ord_less_set_nat @ A6 @ B6 )
% 5.42/5.64 | ( A6 = B6 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % subset_iff_psubset_eq
% 5.42/5.64 thf(fact_1672_subset__psubset__trans,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat,C4: set_nat] :
% 5.42/5.64 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.42/5.64 => ( ( ord_less_set_nat @ B3 @ C4 )
% 5.42/5.64 => ( ord_less_set_nat @ A2 @ C4 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % subset_psubset_trans
% 5.42/5.64 thf(fact_1673_subset__not__subset__eq,axiom,
% 5.42/5.64 ( ord_less_set_nat
% 5.42/5.64 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.42/5.64 ( ( ord_less_eq_set_nat @ A6 @ B6 )
% 5.42/5.64 & ~ ( ord_less_eq_set_nat @ B6 @ A6 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % subset_not_subset_eq
% 5.42/5.64 thf(fact_1674_psubset__subset__trans,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat,C4: set_nat] :
% 5.42/5.64 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.42/5.64 => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 5.42/5.64 => ( ord_less_set_nat @ A2 @ C4 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubset_subset_trans
% 5.42/5.64 thf(fact_1675_psubset__imp__subset,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.42/5.64 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubset_imp_subset
% 5.42/5.64 thf(fact_1676_psubset__eq,axiom,
% 5.42/5.64 ( ord_less_set_nat
% 5.42/5.64 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.42/5.64 ( ( ord_less_eq_set_nat @ A6 @ B6 )
% 5.42/5.64 & ( A6 != B6 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubset_eq
% 5.42/5.64 thf(fact_1677_psubsetE,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.42/5.64 => ~ ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.42/5.64 => ( ord_less_eq_set_nat @ B3 @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubsetE
% 5.42/5.64 thf(fact_1678_Diff__mono,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,D4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( ord_le3146513528884898305at_nat @ A2 @ C4 )
% 5.42/5.64 => ( ( ord_le3146513528884898305at_nat @ D4 @ B3 )
% 5.42/5.64 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) @ ( minus_1356011639430497352at_nat @ C4 @ D4 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_mono
% 5.42/5.64 thf(fact_1679_Diff__mono,axiom,
% 5.42/5.64 ! [A2: set_nat,C4: set_nat,D4: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.42/5.64 => ( ( ord_less_eq_set_nat @ D4 @ B3 )
% 5.42/5.64 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_mono
% 5.42/5.64 thf(fact_1680_Diff__subset,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) @ A2 ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_subset
% 5.42/5.64 thf(fact_1681_Diff__subset,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ A2 ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_subset
% 5.42/5.64 thf(fact_1682_double__diff,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.42/5.64 => ( ( ord_le3146513528884898305at_nat @ B3 @ C4 )
% 5.42/5.64 => ( ( minus_1356011639430497352at_nat @ B3 @ ( minus_1356011639430497352at_nat @ C4 @ A2 ) )
% 5.42/5.64 = A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_diff
% 5.42/5.64 thf(fact_1683_double__diff,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat,C4: set_nat] :
% 5.42/5.64 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.42/5.64 => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 5.42/5.64 => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.42/5.64 = A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_diff
% 5.42/5.64 thf(fact_1684_vebt__member_Osimps_I5_J,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( ( X2 != Mi )
% 5.42/5.64 => ( ( X2 != Ma )
% 5.42/5.64 => ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.42/5.64 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.42/5.64 => ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.42/5.64 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.42/5.64 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_member.simps(5)
% 5.42/5.64 thf(fact_1685_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X2 = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X2 = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(5)
% 5.42/5.64 thf(fact_1686_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 @ ( if_nat
% 5.42/5.64 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 & ~ ( ( X2 = Mi )
% 5.42/5.64 | ( X2 = Ma ) ) )
% 5.42/5.64 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.42/5.64 @ one_one_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(5)
% 5.42/5.64 thf(fact_1687_vebt__pred_Osimps_I7_J,axiom,
% 5.42/5.64 ! [Ma: nat,X2: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.42/5.64 ( ( ( ord_less_nat @ Ma @ X2 )
% 5.42/5.64 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( some_nat @ Ma ) ) )
% 5.42/5.64 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.42/5.64 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 != none_nat )
% 5.42/5.64 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 = none_nat )
% 5.42/5.64 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.42/5.64 @ none_nat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_pred.simps(7)
% 5.42/5.64 thf(fact_1688_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = ( if_nat
% 5.42/5.64 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 & ~ ( ( X2 = Mi )
% 5.42/5.64 | ( X2 = Ma ) ) )
% 5.42/5.64 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.42/5.64 @ one_one_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(5)
% 5.42/5.64 thf(fact_1689_finite__Collect__le__nat,axiom,
% 5.42/5.64 ! [K: nat] :
% 5.42/5.64 ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Collect_le_nat
% 5.42/5.64 thf(fact_1690_finite__Collect__less__nat,axiom,
% 5.42/5.64 ! [K: nat] :
% 5.42/5.64 ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Collect_less_nat
% 5.42/5.64 thf(fact_1691_finite__roots__unity,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.42/5.64 => ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [Z4: real] :
% 5.42/5.64 ( ( power_power_real @ Z4 @ N )
% 5.42/5.64 = one_one_real ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_roots_unity
% 5.42/5.64 thf(fact_1692_finite__roots__unity,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.42/5.64 => ( finite3207457112153483333omplex
% 5.42/5.64 @ ( collect_complex
% 5.42/5.64 @ ^ [Z4: complex] :
% 5.42/5.64 ( ( power_power_complex @ Z4 @ N )
% 5.42/5.64 = one_one_complex ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_roots_unity
% 5.42/5.64 thf(fact_1693_finite__Diff,axiom,
% 5.42/5.64 ! [A2: set_int,B3: set_int] :
% 5.42/5.64 ( ( finite_finite_int @ A2 )
% 5.42/5.64 => ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Diff
% 5.42/5.64 thf(fact_1694_finite__Diff,axiom,
% 5.42/5.64 ! [A2: set_complex,B3: set_complex] :
% 5.42/5.64 ( ( finite3207457112153483333omplex @ A2 )
% 5.42/5.64 => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Diff
% 5.42/5.64 thf(fact_1695_finite__Diff,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( finite6177210948735845034at_nat @ A2 )
% 5.42/5.64 => ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Diff
% 5.42/5.64 thf(fact_1696_finite__Diff,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat] :
% 5.42/5.64 ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Diff
% 5.42/5.64 thf(fact_1697_finite__Diff2,axiom,
% 5.42/5.64 ! [B3: set_int,A2: set_int] :
% 5.42/5.64 ( ( finite_finite_int @ B3 )
% 5.42/5.64 => ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.42/5.64 = ( finite_finite_int @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Diff2
% 5.42/5.64 thf(fact_1698_finite__Diff2,axiom,
% 5.42/5.64 ! [B3: set_complex,A2: set_complex] :
% 5.42/5.64 ( ( finite3207457112153483333omplex @ B3 )
% 5.42/5.64 => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.42/5.64 = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Diff2
% 5.42/5.64 thf(fact_1699_finite__Diff2,axiom,
% 5.42/5.64 ! [B3: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( finite6177210948735845034at_nat @ B3 )
% 5.42/5.64 => ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) )
% 5.42/5.64 = ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Diff2
% 5.42/5.64 thf(fact_1700_finite__Diff2,axiom,
% 5.42/5.64 ! [B3: set_nat,A2: set_nat] :
% 5.42/5.64 ( ( finite_finite_nat @ B3 )
% 5.42/5.64 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.42/5.64 = ( finite_finite_nat @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_Diff2
% 5.42/5.64 thf(fact_1701_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.42/5.64 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X2 )
% 5.42/5.64 = ( ( X2 = Mi )
% 5.42/5.64 | ( X2 = Ma )
% 5.42/5.64 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.membermima.simps(4)
% 5.42/5.64 thf(fact_1702_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.42/5.64 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ X2 )
% 5.42/5.64 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.naive_member.simps(3)
% 5.42/5.64 thf(fact_1703_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.42/5.64 ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X2 )
% 5.42/5.64 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.42/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.membermima.simps(5)
% 5.42/5.64 thf(fact_1704_buildup__nothing__in__leaf,axiom,
% 5.42/5.64 ! [N: nat,X2: nat] :
% 5.42/5.64 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.42/5.64
% 5.42/5.64 % buildup_nothing_in_leaf
% 5.42/5.64 thf(fact_1705_buildup__nothing__in__min__max,axiom,
% 5.42/5.64 ! [N: nat,X2: nat] :
% 5.42/5.64 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.42/5.64
% 5.42/5.64 % buildup_nothing_in_min_max
% 5.42/5.64 thf(fact_1706_both__member__options__def,axiom,
% 5.42/5.64 ( vEBT_V8194947554948674370ptions
% 5.42/5.64 = ( ^ [T2: vEBT_VEBT,X: nat] :
% 5.42/5.64 ( ( vEBT_V5719532721284313246member @ T2 @ X )
% 5.42/5.64 | ( vEBT_VEBT_membermima @ T2 @ X ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % both_member_options_def
% 5.42/5.64 thf(fact_1707_member__valid__both__member__options,axiom,
% 5.42/5.64 ! [Tree: vEBT_VEBT,N: nat,X2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.42/5.64 => ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.42/5.64 => ( ( vEBT_V5719532721284313246member @ Tree @ X2 )
% 5.42/5.64 | ( vEBT_VEBT_membermima @ Tree @ X2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % member_valid_both_member_options
% 5.42/5.64 thf(fact_1708_finite__interval__int4,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( finite_finite_int
% 5.42/5.64 @ ( collect_int
% 5.42/5.64 @ ^ [I4: int] :
% 5.42/5.64 ( ( ord_less_int @ A @ I4 )
% 5.42/5.64 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_interval_int4
% 5.42/5.64 thf(fact_1709_finite__interval__int2,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( finite_finite_int
% 5.42/5.64 @ ( collect_int
% 5.42/5.64 @ ^ [I4: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ A @ I4 )
% 5.42/5.64 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_interval_int2
% 5.42/5.64 thf(fact_1710_finite__interval__int3,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( finite_finite_int
% 5.42/5.64 @ ( collect_int
% 5.42/5.64 @ ^ [I4: int] :
% 5.42/5.64 ( ( ord_less_int @ A @ I4 )
% 5.42/5.64 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_interval_int3
% 5.42/5.64 thf(fact_1711_less__set__def,axiom,
% 5.42/5.64 ( ord_le7866589430770878221at_nat
% 5.42/5.64 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ord_le549003669493604880_nat_o
% 5.42/5.64 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 5.42/5.64 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_set_def
% 5.42/5.64 thf(fact_1712_less__set__def,axiom,
% 5.42/5.64 ( ord_less_set_complex
% 5.42/5.64 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.42/5.64 ( ord_less_complex_o
% 5.42/5.64 @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 5.42/5.64 @ ^ [X: complex] : ( member_complex @ X @ B6 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_set_def
% 5.42/5.64 thf(fact_1713_less__set__def,axiom,
% 5.42/5.64 ( ord_less_set_real
% 5.42/5.64 = ( ^ [A6: set_real,B6: set_real] :
% 5.42/5.64 ( ord_less_real_o
% 5.42/5.64 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.42/5.64 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_set_def
% 5.42/5.64 thf(fact_1714_less__set__def,axiom,
% 5.42/5.64 ( ord_less_set_nat
% 5.42/5.64 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.42/5.64 ( ord_less_nat_o
% 5.42/5.64 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.42/5.64 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_set_def
% 5.42/5.64 thf(fact_1715_less__set__def,axiom,
% 5.42/5.64 ( ord_less_set_int
% 5.42/5.64 = ( ^ [A6: set_int,B6: set_int] :
% 5.42/5.64 ( ord_less_int_o
% 5.42/5.64 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.42/5.64 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_set_def
% 5.42/5.64 thf(fact_1716_psubsetD,axiom,
% 5.42/5.64 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 5.42/5.64 ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 5.42/5.64 => ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.42/5.64 => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubsetD
% 5.42/5.64 thf(fact_1717_psubsetD,axiom,
% 5.42/5.64 ! [A2: set_complex,B3: set_complex,C: complex] :
% 5.42/5.64 ( ( ord_less_set_complex @ A2 @ B3 )
% 5.42/5.64 => ( ( member_complex @ C @ A2 )
% 5.42/5.64 => ( member_complex @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubsetD
% 5.42/5.64 thf(fact_1718_psubsetD,axiom,
% 5.42/5.64 ! [A2: set_real,B3: set_real,C: real] :
% 5.42/5.64 ( ( ord_less_set_real @ A2 @ B3 )
% 5.42/5.64 => ( ( member_real @ C @ A2 )
% 5.42/5.64 => ( member_real @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubsetD
% 5.42/5.64 thf(fact_1719_psubsetD,axiom,
% 5.42/5.64 ! [A2: set_nat,B3: set_nat,C: nat] :
% 5.42/5.64 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.42/5.64 => ( ( member_nat @ C @ A2 )
% 5.42/5.64 => ( member_nat @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubsetD
% 5.42/5.64 thf(fact_1720_psubsetD,axiom,
% 5.42/5.64 ! [A2: set_int,B3: set_int,C: int] :
% 5.42/5.64 ( ( ord_less_set_int @ A2 @ B3 )
% 5.42/5.64 => ( ( member_int @ C @ A2 )
% 5.42/5.64 => ( member_int @ C @ B3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % psubsetD
% 5.42/5.64 thf(fact_1721_finite__maxlen,axiom,
% 5.42/5.64 ! [M7: set_list_VEBT_VEBT] :
% 5.42/5.64 ( ( finite3004134309566078307T_VEBT @ M7 )
% 5.42/5.64 => ? [N3: nat] :
% 5.42/5.64 ! [X4: list_VEBT_VEBT] :
% 5.42/5.64 ( ( member2936631157270082147T_VEBT @ X4 @ M7 )
% 5.42/5.64 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X4 ) @ N3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_maxlen
% 5.42/5.64 thf(fact_1722_finite__maxlen,axiom,
% 5.42/5.64 ! [M7: set_list_o] :
% 5.42/5.64 ( ( finite_finite_list_o @ M7 )
% 5.42/5.64 => ? [N3: nat] :
% 5.42/5.64 ! [X4: list_o] :
% 5.42/5.64 ( ( member_list_o @ X4 @ M7 )
% 5.42/5.64 => ( ord_less_nat @ ( size_size_list_o @ X4 ) @ N3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_maxlen
% 5.42/5.64 thf(fact_1723_finite__maxlen,axiom,
% 5.42/5.64 ! [M7: set_list_nat] :
% 5.42/5.64 ( ( finite8100373058378681591st_nat @ M7 )
% 5.42/5.64 => ? [N3: nat] :
% 5.42/5.64 ! [X4: list_nat] :
% 5.42/5.64 ( ( member_list_nat @ X4 @ M7 )
% 5.42/5.64 => ( ord_less_nat @ ( size_size_list_nat @ X4 ) @ N3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_maxlen
% 5.42/5.64 thf(fact_1724_finite__maxlen,axiom,
% 5.42/5.64 ! [M7: set_list_int] :
% 5.42/5.64 ( ( finite3922522038869484883st_int @ M7 )
% 5.42/5.64 => ? [N3: nat] :
% 5.42/5.64 ! [X4: list_int] :
% 5.42/5.64 ( ( member_list_int @ X4 @ M7 )
% 5.42/5.64 => ( ord_less_nat @ ( size_size_list_int @ X4 ) @ N3 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_maxlen
% 5.42/5.64 thf(fact_1725_finite__psubset__induct,axiom,
% 5.42/5.64 ! [A2: set_nat,P: set_nat > $o] :
% 5.42/5.64 ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ( ! [A7: set_nat] :
% 5.42/5.64 ( ( finite_finite_nat @ A7 )
% 5.42/5.64 => ( ! [B7: set_nat] :
% 5.42/5.64 ( ( ord_less_set_nat @ B7 @ A7 )
% 5.42/5.64 => ( P @ B7 ) )
% 5.42/5.64 => ( P @ A7 ) ) )
% 5.42/5.64 => ( P @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_psubset_induct
% 5.42/5.64 thf(fact_1726_finite__psubset__induct,axiom,
% 5.42/5.64 ! [A2: set_int,P: set_int > $o] :
% 5.42/5.64 ( ( finite_finite_int @ A2 )
% 5.42/5.64 => ( ! [A7: set_int] :
% 5.42/5.64 ( ( finite_finite_int @ A7 )
% 5.42/5.64 => ( ! [B7: set_int] :
% 5.42/5.64 ( ( ord_less_set_int @ B7 @ A7 )
% 5.42/5.64 => ( P @ B7 ) )
% 5.42/5.64 => ( P @ A7 ) ) )
% 5.42/5.64 => ( P @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_psubset_induct
% 5.42/5.64 thf(fact_1727_finite__psubset__induct,axiom,
% 5.42/5.64 ! [A2: set_complex,P: set_complex > $o] :
% 5.42/5.64 ( ( finite3207457112153483333omplex @ A2 )
% 5.42/5.64 => ( ! [A7: set_complex] :
% 5.42/5.64 ( ( finite3207457112153483333omplex @ A7 )
% 5.42/5.64 => ( ! [B7: set_complex] :
% 5.42/5.64 ( ( ord_less_set_complex @ B7 @ A7 )
% 5.42/5.64 => ( P @ B7 ) )
% 5.42/5.64 => ( P @ A7 ) ) )
% 5.42/5.64 => ( P @ A2 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_psubset_induct
% 5.42/5.64 thf(fact_1728_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I4_J,axiom,
% 5.42/5.64 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.42/5.64 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.42/5.64 = one_one_nat ) ).
% 5.42/5.64
% 5.42/5.64 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(4)
% 5.42/5.64 thf(fact_1729_insersimp_H,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,Y2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 5.42/5.64 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y2 ) @ one_one_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % insersimp'
% 5.42/5.64 thf(fact_1730_finite__has__maximal2,axiom,
% 5.42/5.64 ! [A2: set_real,A: real] :
% 5.42/5.64 ( ( finite_finite_real @ A2 )
% 5.42/5.64 => ( ( member_real @ A @ A2 )
% 5.42/5.64 => ? [X3: real] :
% 5.42/5.64 ( ( member_real @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_real @ A @ X3 )
% 5.42/5.64 & ! [Xa: real] :
% 5.42/5.64 ( ( member_real @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal2
% 5.42/5.64 thf(fact_1731_finite__has__maximal2,axiom,
% 5.42/5.64 ! [A2: set_set_nat,A: set_nat] :
% 5.42/5.64 ( ( finite1152437895449049373et_nat @ A2 )
% 5.42/5.64 => ( ( member_set_nat @ A @ A2 )
% 5.42/5.64 => ? [X3: set_nat] :
% 5.42/5.64 ( ( member_set_nat @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_set_nat @ A @ X3 )
% 5.42/5.64 & ! [Xa: set_nat] :
% 5.42/5.64 ( ( member_set_nat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal2
% 5.42/5.64 thf(fact_1732_finite__has__maximal2,axiom,
% 5.42/5.64 ! [A2: set_rat,A: rat] :
% 5.42/5.64 ( ( finite_finite_rat @ A2 )
% 5.42/5.64 => ( ( member_rat @ A @ A2 )
% 5.42/5.64 => ? [X3: rat] :
% 5.42/5.64 ( ( member_rat @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_rat @ A @ X3 )
% 5.42/5.64 & ! [Xa: rat] :
% 5.42/5.64 ( ( member_rat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal2
% 5.42/5.64 thf(fact_1733_finite__has__maximal2,axiom,
% 5.42/5.64 ! [A2: set_num,A: num] :
% 5.42/5.64 ( ( finite_finite_num @ A2 )
% 5.42/5.64 => ( ( member_num @ A @ A2 )
% 5.42/5.64 => ? [X3: num] :
% 5.42/5.64 ( ( member_num @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_num @ A @ X3 )
% 5.42/5.64 & ! [Xa: num] :
% 5.42/5.64 ( ( member_num @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal2
% 5.42/5.64 thf(fact_1734_finite__has__maximal2,axiom,
% 5.42/5.64 ! [A2: set_nat,A: nat] :
% 5.42/5.64 ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ( ( member_nat @ A @ A2 )
% 5.42/5.64 => ? [X3: nat] :
% 5.42/5.64 ( ( member_nat @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_nat @ A @ X3 )
% 5.42/5.64 & ! [Xa: nat] :
% 5.42/5.64 ( ( member_nat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal2
% 5.42/5.64 thf(fact_1735_finite__has__maximal2,axiom,
% 5.42/5.64 ! [A2: set_int,A: int] :
% 5.42/5.64 ( ( finite_finite_int @ A2 )
% 5.42/5.64 => ( ( member_int @ A @ A2 )
% 5.42/5.64 => ? [X3: int] :
% 5.42/5.64 ( ( member_int @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_int @ A @ X3 )
% 5.42/5.64 & ! [Xa: int] :
% 5.42/5.64 ( ( member_int @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal2
% 5.42/5.64 thf(fact_1736_finite__has__minimal2,axiom,
% 5.42/5.64 ! [A2: set_real,A: real] :
% 5.42/5.64 ( ( finite_finite_real @ A2 )
% 5.42/5.64 => ( ( member_real @ A @ A2 )
% 5.42/5.64 => ? [X3: real] :
% 5.42/5.64 ( ( member_real @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_real @ X3 @ A )
% 5.42/5.64 & ! [Xa: real] :
% 5.42/5.64 ( ( member_real @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal2
% 5.42/5.64 thf(fact_1737_finite__has__minimal2,axiom,
% 5.42/5.64 ! [A2: set_set_nat,A: set_nat] :
% 5.42/5.64 ( ( finite1152437895449049373et_nat @ A2 )
% 5.42/5.64 => ( ( member_set_nat @ A @ A2 )
% 5.42/5.64 => ? [X3: set_nat] :
% 5.42/5.64 ( ( member_set_nat @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_set_nat @ X3 @ A )
% 5.42/5.64 & ! [Xa: set_nat] :
% 5.42/5.64 ( ( member_set_nat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal2
% 5.42/5.64 thf(fact_1738_finite__has__minimal2,axiom,
% 5.42/5.64 ! [A2: set_rat,A: rat] :
% 5.42/5.64 ( ( finite_finite_rat @ A2 )
% 5.42/5.64 => ( ( member_rat @ A @ A2 )
% 5.42/5.64 => ? [X3: rat] :
% 5.42/5.64 ( ( member_rat @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_rat @ X3 @ A )
% 5.42/5.64 & ! [Xa: rat] :
% 5.42/5.64 ( ( member_rat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal2
% 5.42/5.64 thf(fact_1739_finite__has__minimal2,axiom,
% 5.42/5.64 ! [A2: set_num,A: num] :
% 5.42/5.64 ( ( finite_finite_num @ A2 )
% 5.42/5.64 => ( ( member_num @ A @ A2 )
% 5.42/5.64 => ? [X3: num] :
% 5.42/5.64 ( ( member_num @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_num @ X3 @ A )
% 5.42/5.64 & ! [Xa: num] :
% 5.42/5.64 ( ( member_num @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal2
% 5.42/5.64 thf(fact_1740_finite__has__minimal2,axiom,
% 5.42/5.64 ! [A2: set_nat,A: nat] :
% 5.42/5.64 ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ( ( member_nat @ A @ A2 )
% 5.42/5.64 => ? [X3: nat] :
% 5.42/5.64 ( ( member_nat @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_nat @ X3 @ A )
% 5.42/5.64 & ! [Xa: nat] :
% 5.42/5.64 ( ( member_nat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal2
% 5.42/5.64 thf(fact_1741_finite__has__minimal2,axiom,
% 5.42/5.64 ! [A2: set_int,A: int] :
% 5.42/5.64 ( ( finite_finite_int @ A2 )
% 5.42/5.64 => ( ( member_int @ A @ A2 )
% 5.42/5.64 => ? [X3: int] :
% 5.42/5.64 ( ( member_int @ X3 @ A2 )
% 5.42/5.64 & ( ord_less_eq_int @ X3 @ A )
% 5.42/5.64 & ! [Xa: int] :
% 5.42/5.64 ( ( member_int @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal2
% 5.42/5.64 thf(fact_1742_insertsimp_H,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat,L2: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( vEBT_VEBT_minNull @ T )
% 5.42/5.64 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L2 ) @ one_one_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % insertsimp'
% 5.42/5.64 thf(fact_1743_Diff__infinite__finite,axiom,
% 5.42/5.64 ! [T3: set_int,S2: set_int] :
% 5.42/5.64 ( ( finite_finite_int @ T3 )
% 5.42/5.64 => ( ~ ( finite_finite_int @ S2 )
% 5.42/5.64 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ T3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_infinite_finite
% 5.42/5.64 thf(fact_1744_Diff__infinite__finite,axiom,
% 5.42/5.64 ! [T3: set_complex,S2: set_complex] :
% 5.42/5.64 ( ( finite3207457112153483333omplex @ T3 )
% 5.42/5.64 => ( ~ ( finite3207457112153483333omplex @ S2 )
% 5.42/5.64 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_infinite_finite
% 5.42/5.64 thf(fact_1745_Diff__infinite__finite,axiom,
% 5.42/5.64 ! [T3: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 5.42/5.64 ( ( finite6177210948735845034at_nat @ T3 )
% 5.42/5.64 => ( ~ ( finite6177210948735845034at_nat @ S2 )
% 5.42/5.64 => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S2 @ T3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_infinite_finite
% 5.42/5.64 thf(fact_1746_Diff__infinite__finite,axiom,
% 5.42/5.64 ! [T3: set_nat,S2: set_nat] :
% 5.42/5.64 ( ( finite_finite_nat @ T3 )
% 5.42/5.64 => ( ~ ( finite_finite_nat @ S2 )
% 5.42/5.64 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T3 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % Diff_infinite_finite
% 5.42/5.64 thf(fact_1747_finite__has__minimal,axiom,
% 5.42/5.64 ! [A2: set_real] :
% 5.42/5.64 ( ( finite_finite_real @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_real )
% 5.42/5.64 => ? [X3: real] :
% 5.42/5.64 ( ( member_real @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: real] :
% 5.42/5.64 ( ( member_real @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal
% 5.42/5.64 thf(fact_1748_finite__has__minimal,axiom,
% 5.42/5.64 ! [A2: set_set_nat] :
% 5.42/5.64 ( ( finite1152437895449049373et_nat @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_set_nat )
% 5.42/5.64 => ? [X3: set_nat] :
% 5.42/5.64 ( ( member_set_nat @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: set_nat] :
% 5.42/5.64 ( ( member_set_nat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal
% 5.42/5.64 thf(fact_1749_finite__has__minimal,axiom,
% 5.42/5.64 ! [A2: set_rat] :
% 5.42/5.64 ( ( finite_finite_rat @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_rat )
% 5.42/5.64 => ? [X3: rat] :
% 5.42/5.64 ( ( member_rat @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: rat] :
% 5.42/5.64 ( ( member_rat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal
% 5.42/5.64 thf(fact_1750_finite__has__minimal,axiom,
% 5.42/5.64 ! [A2: set_num] :
% 5.42/5.64 ( ( finite_finite_num @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_num )
% 5.42/5.64 => ? [X3: num] :
% 5.42/5.64 ( ( member_num @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: num] :
% 5.42/5.64 ( ( member_num @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal
% 5.42/5.64 thf(fact_1751_finite__has__minimal,axiom,
% 5.42/5.64 ! [A2: set_nat] :
% 5.42/5.64 ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_nat )
% 5.42/5.64 => ? [X3: nat] :
% 5.42/5.64 ( ( member_nat @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: nat] :
% 5.42/5.64 ( ( member_nat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal
% 5.42/5.64 thf(fact_1752_finite__has__minimal,axiom,
% 5.42/5.64 ! [A2: set_int] :
% 5.42/5.64 ( ( finite_finite_int @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_int )
% 5.42/5.64 => ? [X3: int] :
% 5.42/5.64 ( ( member_int @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: int] :
% 5.42/5.64 ( ( member_int @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_minimal
% 5.42/5.64 thf(fact_1753_finite__has__maximal,axiom,
% 5.42/5.64 ! [A2: set_real] :
% 5.42/5.64 ( ( finite_finite_real @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_real )
% 5.42/5.64 => ? [X3: real] :
% 5.42/5.64 ( ( member_real @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: real] :
% 5.42/5.64 ( ( member_real @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal
% 5.42/5.64 thf(fact_1754_finite__has__maximal,axiom,
% 5.42/5.64 ! [A2: set_set_nat] :
% 5.42/5.64 ( ( finite1152437895449049373et_nat @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_set_nat )
% 5.42/5.64 => ? [X3: set_nat] :
% 5.42/5.64 ( ( member_set_nat @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: set_nat] :
% 5.42/5.64 ( ( member_set_nat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal
% 5.42/5.64 thf(fact_1755_finite__has__maximal,axiom,
% 5.42/5.64 ! [A2: set_rat] :
% 5.42/5.64 ( ( finite_finite_rat @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_rat )
% 5.42/5.64 => ? [X3: rat] :
% 5.42/5.64 ( ( member_rat @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: rat] :
% 5.42/5.64 ( ( member_rat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal
% 5.42/5.64 thf(fact_1756_finite__has__maximal,axiom,
% 5.42/5.64 ! [A2: set_num] :
% 5.42/5.64 ( ( finite_finite_num @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_num )
% 5.42/5.64 => ? [X3: num] :
% 5.42/5.64 ( ( member_num @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: num] :
% 5.42/5.64 ( ( member_num @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal
% 5.42/5.64 thf(fact_1757_finite__has__maximal,axiom,
% 5.42/5.64 ! [A2: set_nat] :
% 5.42/5.64 ( ( finite_finite_nat @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_nat )
% 5.42/5.64 => ? [X3: nat] :
% 5.42/5.64 ( ( member_nat @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: nat] :
% 5.42/5.64 ( ( member_nat @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal
% 5.42/5.64 thf(fact_1758_finite__has__maximal,axiom,
% 5.42/5.64 ! [A2: set_int] :
% 5.42/5.64 ( ( finite_finite_int @ A2 )
% 5.42/5.64 => ( ( A2 != bot_bot_set_int )
% 5.42/5.64 => ? [X3: int] :
% 5.42/5.64 ( ( member_int @ X3 @ A2 )
% 5.42/5.64 & ! [Xa: int] :
% 5.42/5.64 ( ( member_int @ Xa @ A2 )
% 5.42/5.64 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.42/5.64 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % finite_has_maximal
% 5.42/5.64 thf(fact_1759_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.42/5.64 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.42/5.64 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.42/5.64 => ( ! [Mi2: nat,Ma2: nat] :
% 5.42/5.64 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.42/5.64 => ~ ( ( Xa2 = Mi2 )
% 5.42/5.64 | ( Xa2 = Ma2 ) ) )
% 5.42/5.64 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.42/5.64 ( ? [Vc2: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.42/5.64 => ~ ( ( Xa2 = Mi2 )
% 5.42/5.64 | ( Xa2 = Ma2 )
% 5.42/5.64 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.42/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.42/5.64 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.42/5.64 ( ? [Vd2: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.42/5.64 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.42/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % VEBT_internal.membermima.elims(2)
% 5.42/5.64 thf(fact_1760_vebt__succ_Oelims,axiom,
% 5.42/5.64 ! [X2: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.42/5.64 ( ( ( vEBT_vebt_succ @ X2 @ Xa2 )
% 5.42/5.64 = Y2 )
% 5.42/5.64 => ( ! [Uu2: $o,B5: $o] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 5.42/5.64 => ( ( Xa2 = zero_zero_nat )
% 5.42/5.64 => ~ ( ( B5
% 5.42/5.64 => ( Y2
% 5.42/5.64 = ( some_nat @ one_one_nat ) ) )
% 5.42/5.64 & ( ~ B5
% 5.42/5.64 => ( Y2 = none_nat ) ) ) ) )
% 5.42/5.64 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.42/5.64 => ( ? [N3: nat] :
% 5.42/5.64 ( Xa2
% 5.42/5.64 = ( suc @ N3 ) )
% 5.42/5.64 => ( Y2 != none_nat ) ) )
% 5.42/5.64 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.42/5.64 => ( Y2 != none_nat ) )
% 5.42/5.64 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.42/5.64 => ( Y2 != none_nat ) )
% 5.42/5.64 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.42/5.64 => ( Y2 != none_nat ) )
% 5.42/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.42/5.64 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.42/5.64 => ( Y2
% 5.42/5.64 = ( some_nat @ Mi2 ) ) )
% 5.42/5.64 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.42/5.64 => ( Y2
% 5.42/5.64 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 != none_nat )
% 5.42/5.64 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 = none_nat )
% 5.42/5.64 @ none_nat
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.42/5.64 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_succ.elims
% 5.42/5.64 thf(fact_1761_vebt__pred_Oelims,axiom,
% 5.42/5.64 ! [X2: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.42/5.64 ( ( ( vEBT_vebt_pred @ X2 @ Xa2 )
% 5.42/5.64 = Y2 )
% 5.42/5.64 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.42/5.64 => ( ( Xa2 = zero_zero_nat )
% 5.42/5.64 => ( Y2 != none_nat ) ) )
% 5.42/5.64 => ( ! [A5: $o] :
% 5.42/5.64 ( ? [Uw2: $o] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 5.42/5.64 => ( ( Xa2
% 5.42/5.64 = ( suc @ zero_zero_nat ) )
% 5.42/5.64 => ~ ( ( A5
% 5.42/5.64 => ( Y2
% 5.42/5.64 = ( some_nat @ zero_zero_nat ) ) )
% 5.42/5.64 & ( ~ A5
% 5.42/5.64 => ( Y2 = none_nat ) ) ) ) )
% 5.42/5.64 => ( ! [A5: $o,B5: $o] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.42/5.64 => ( ? [Va3: nat] :
% 5.42/5.64 ( Xa2
% 5.42/5.64 = ( suc @ ( suc @ Va3 ) ) )
% 5.42/5.64 => ~ ( ( B5
% 5.42/5.64 => ( Y2
% 5.42/5.64 = ( some_nat @ one_one_nat ) ) )
% 5.42/5.64 & ( ~ B5
% 5.42/5.64 => ( ( A5
% 5.42/5.64 => ( Y2
% 5.42/5.64 = ( some_nat @ zero_zero_nat ) ) )
% 5.42/5.64 & ( ~ A5
% 5.42/5.64 => ( Y2 = none_nat ) ) ) ) ) ) )
% 5.42/5.64 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.42/5.64 => ( Y2 != none_nat ) )
% 5.42/5.64 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.42/5.64 => ( Y2 != none_nat ) )
% 5.42/5.64 => ( ( ? [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.42/5.64 => ( Y2 != none_nat ) )
% 5.42/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.42/5.64 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.42/5.64 => ( Y2
% 5.42/5.64 = ( some_nat @ Ma2 ) ) )
% 5.42/5.64 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.42/5.64 => ( Y2
% 5.42/5.64 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 != none_nat )
% 5.42/5.64 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.42/5.64 @ ( if_option_nat
% 5.42/5.64 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 = none_nat )
% 5.42/5.64 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.42/5.64 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.42/5.64 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % vebt_pred.elims
% 5.42/5.64 thf(fact_1762_buildup__gives__valid,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.64 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.42/5.64
% 5.42/5.64 % buildup_gives_valid
% 5.42/5.64 thf(fact_1763_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_real,X2: real > complex,Y2: real > complex] :
% 5.42/5.64 ( ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [I4: real] :
% 5.42/5.64 ( ( member_real @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_complex ) ) ) )
% 5.42/5.64 => ( ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [I4: real] :
% 5.42/5.64 ( ( member_real @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_complex ) ) ) )
% 5.42/5.64 => ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [I4: real] :
% 5.42/5.64 ( ( member_real @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_complex ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1764_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_nat,X2: nat > complex,Y2: nat > complex] :
% 5.42/5.64 ( ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [I4: nat] :
% 5.42/5.64 ( ( member_nat @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_complex ) ) ) )
% 5.42/5.64 => ( ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [I4: nat] :
% 5.42/5.64 ( ( member_nat @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_complex ) ) ) )
% 5.42/5.64 => ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [I4: nat] :
% 5.42/5.64 ( ( member_nat @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_complex ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1765_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_int,X2: int > complex,Y2: int > complex] :
% 5.42/5.64 ( ( finite_finite_int
% 5.42/5.64 @ ( collect_int
% 5.42/5.64 @ ^ [I4: int] :
% 5.42/5.64 ( ( member_int @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_complex ) ) ) )
% 5.42/5.64 => ( ( finite_finite_int
% 5.42/5.64 @ ( collect_int
% 5.42/5.64 @ ^ [I4: int] :
% 5.42/5.64 ( ( member_int @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_complex ) ) ) )
% 5.42/5.64 => ( finite_finite_int
% 5.42/5.64 @ ( collect_int
% 5.42/5.64 @ ^ [I4: int] :
% 5.42/5.64 ( ( member_int @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_complex ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1766_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_complex,X2: complex > complex,Y2: complex > complex] :
% 5.42/5.64 ( ( finite3207457112153483333omplex
% 5.42/5.64 @ ( collect_complex
% 5.42/5.64 @ ^ [I4: complex] :
% 5.42/5.64 ( ( member_complex @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_complex ) ) ) )
% 5.42/5.64 => ( ( finite3207457112153483333omplex
% 5.42/5.64 @ ( collect_complex
% 5.42/5.64 @ ^ [I4: complex] :
% 5.42/5.64 ( ( member_complex @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_complex ) ) ) )
% 5.42/5.64 => ( finite3207457112153483333omplex
% 5.42/5.64 @ ( collect_complex
% 5.42/5.64 @ ^ [I4: complex] :
% 5.42/5.64 ( ( member_complex @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_complex ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1767_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_real,X2: real > real,Y2: real > real] :
% 5.42/5.64 ( ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [I4: real] :
% 5.42/5.64 ( ( member_real @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_real ) ) ) )
% 5.42/5.64 => ( ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [I4: real] :
% 5.42/5.64 ( ( member_real @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_real ) ) ) )
% 5.42/5.64 => ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [I4: real] :
% 5.42/5.64 ( ( member_real @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_real ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1768_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_nat,X2: nat > real,Y2: nat > real] :
% 5.42/5.64 ( ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [I4: nat] :
% 5.42/5.64 ( ( member_nat @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_real ) ) ) )
% 5.42/5.64 => ( ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [I4: nat] :
% 5.42/5.64 ( ( member_nat @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_real ) ) ) )
% 5.42/5.64 => ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [I4: nat] :
% 5.42/5.64 ( ( member_nat @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_real ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1769_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_int,X2: int > real,Y2: int > real] :
% 5.42/5.64 ( ( finite_finite_int
% 5.42/5.64 @ ( collect_int
% 5.42/5.64 @ ^ [I4: int] :
% 5.42/5.64 ( ( member_int @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_real ) ) ) )
% 5.42/5.64 => ( ( finite_finite_int
% 5.42/5.64 @ ( collect_int
% 5.42/5.64 @ ^ [I4: int] :
% 5.42/5.64 ( ( member_int @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_real ) ) ) )
% 5.42/5.64 => ( finite_finite_int
% 5.42/5.64 @ ( collect_int
% 5.42/5.64 @ ^ [I4: int] :
% 5.42/5.64 ( ( member_int @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_real ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1770_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_complex,X2: complex > real,Y2: complex > real] :
% 5.42/5.64 ( ( finite3207457112153483333omplex
% 5.42/5.64 @ ( collect_complex
% 5.42/5.64 @ ^ [I4: complex] :
% 5.42/5.64 ( ( member_complex @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_real ) ) ) )
% 5.42/5.64 => ( ( finite3207457112153483333omplex
% 5.42/5.64 @ ( collect_complex
% 5.42/5.64 @ ^ [I4: complex] :
% 5.42/5.64 ( ( member_complex @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_real ) ) ) )
% 5.42/5.64 => ( finite3207457112153483333omplex
% 5.42/5.64 @ ( collect_complex
% 5.42/5.64 @ ^ [I4: complex] :
% 5.42/5.64 ( ( member_complex @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_real ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1771_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_real,X2: real > rat,Y2: real > rat] :
% 5.42/5.64 ( ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [I4: real] :
% 5.42/5.64 ( ( member_real @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_rat ) ) ) )
% 5.42/5.64 => ( ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [I4: real] :
% 5.42/5.64 ( ( member_real @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_rat ) ) ) )
% 5.42/5.64 => ( finite_finite_real
% 5.42/5.64 @ ( collect_real
% 5.42/5.64 @ ^ [I4: real] :
% 5.42/5.64 ( ( member_real @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_rat @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_rat ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1772_prod_Ofinite__Collect__op,axiom,
% 5.42/5.64 ! [I5: set_nat,X2: nat > rat,Y2: nat > rat] :
% 5.42/5.64 ( ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [I4: nat] :
% 5.42/5.64 ( ( member_nat @ I4 @ I5 )
% 5.42/5.64 & ( ( X2 @ I4 )
% 5.42/5.64 != one_one_rat ) ) ) )
% 5.42/5.64 => ( ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [I4: nat] :
% 5.42/5.64 ( ( member_nat @ I4 @ I5 )
% 5.42/5.64 & ( ( Y2 @ I4 )
% 5.42/5.64 != one_one_rat ) ) ) )
% 5.42/5.64 => ( finite_finite_nat
% 5.42/5.64 @ ( collect_nat
% 5.42/5.64 @ ^ [I4: nat] :
% 5.42/5.64 ( ( member_nat @ I4 @ I5 )
% 5.42/5.64 & ( ( times_times_rat @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.64 != one_one_rat ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % prod.finite_Collect_op
% 5.42/5.64 thf(fact_1773_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 5.42/5.64 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.42/5.64 ( ( ( vEBT_T_i_n_s_e_r_t @ X2 @ Xa2 )
% 5.42/5.64 = Y2 )
% 5.42/5.64 => ( ( ? [A5: $o,B5: $o] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.42/5.64 => ( Y2
% 5.42/5.64 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.42/5.64 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 5.42/5.64 => ( Y2 != one_one_nat ) )
% 5.42/5.64 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.42/5.64 => ( Y2 != one_one_nat ) )
% 5.42/5.64 => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.42/5.64 ( X2
% 5.42/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.42/5.64 => ( Y2
% 5.42/5.64 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.42/5.64 ( ( X2
% 5.42/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.42/5.64 => ( Y2
% 5.42/5.64 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.42/5.64 @ ( if_nat
% 5.42/5.64 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.42/5.64 & ~ ( ( Xa2 = Mi2 )
% 5.42/5.64 | ( Xa2 = Ma2 ) ) )
% 5.42/5.64 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.42/5.64 @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.elims
% 5.42/5.64 thf(fact_1774_set__bit__0,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.42/5.64 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_bit_0
% 5.42/5.64 thf(fact_1775_set__bit__0,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.42/5.64 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % set_bit_0
% 5.42/5.64 thf(fact_1776_valid__0__not,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT] :
% 5.42/5.64 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % valid_0_not
% 5.42/5.64 thf(fact_1777_valid__tree__deg__neq__0,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT] :
% 5.42/5.64 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % valid_tree_deg_neq_0
% 5.42/5.64 thf(fact_1778_deg__not__0,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.42/5.64
% 5.42/5.64 % deg_not_0
% 5.42/5.64 thf(fact_1779_Leaf__0__not,axiom,
% 5.42/5.64 ! [A: $o,B: $o] :
% 5.42/5.64 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % Leaf_0_not
% 5.42/5.64 thf(fact_1780_deg__1__Leafy,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT,N: nat] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ N )
% 5.42/5.64 => ( ( N = one_one_nat )
% 5.42/5.64 => ? [A5: $o,B5: $o] :
% 5.42/5.64 ( T
% 5.42/5.64 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % deg_1_Leafy
% 5.42/5.64 thf(fact_1781_deg__1__Leaf,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.42/5.64 => ? [A5: $o,B5: $o] :
% 5.42/5.64 ( T
% 5.42/5.64 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % deg_1_Leaf
% 5.42/5.64 thf(fact_1782_deg1Leaf,axiom,
% 5.42/5.64 ! [T: vEBT_VEBT] :
% 5.42/5.64 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.42/5.64 = ( ? [A3: $o,B2: $o] :
% 5.42/5.64 ( T
% 5.42/5.64 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % deg1Leaf
% 5.42/5.64 thf(fact_1783_le__zero__eq,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.42/5.64 = ( N = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_zero_eq
% 5.42/5.64 thf(fact_1784_not__gr__zero,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.42/5.64 = ( N = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % not_gr_zero
% 5.42/5.64 thf(fact_1785_mult__cancel__right,axiom,
% 5.42/5.64 ! [A: complex,C: complex,B: complex] :
% 5.42/5.64 ( ( ( times_times_complex @ A @ C )
% 5.42/5.64 = ( times_times_complex @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_complex )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right
% 5.42/5.64 thf(fact_1786_mult__cancel__right,axiom,
% 5.42/5.64 ! [A: real,C: real,B: real] :
% 5.42/5.64 ( ( ( times_times_real @ A @ C )
% 5.42/5.64 = ( times_times_real @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_real )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right
% 5.42/5.64 thf(fact_1787_mult__cancel__right,axiom,
% 5.42/5.64 ! [A: rat,C: rat,B: rat] :
% 5.42/5.64 ( ( ( times_times_rat @ A @ C )
% 5.42/5.64 = ( times_times_rat @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_rat )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right
% 5.42/5.64 thf(fact_1788_mult__cancel__right,axiom,
% 5.42/5.64 ! [A: nat,C: nat,B: nat] :
% 5.42/5.64 ( ( ( times_times_nat @ A @ C )
% 5.42/5.64 = ( times_times_nat @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_nat )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right
% 5.42/5.64 thf(fact_1789_mult__cancel__right,axiom,
% 5.42/5.64 ! [A: int,C: int,B: int] :
% 5.42/5.64 ( ( ( times_times_int @ A @ C )
% 5.42/5.64 = ( times_times_int @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_int )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right
% 5.42/5.64 thf(fact_1790_mult__cancel__left,axiom,
% 5.42/5.64 ! [C: complex,A: complex,B: complex] :
% 5.42/5.64 ( ( ( times_times_complex @ C @ A )
% 5.42/5.64 = ( times_times_complex @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_complex )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left
% 5.42/5.64 thf(fact_1791_mult__cancel__left,axiom,
% 5.42/5.64 ! [C: real,A: real,B: real] :
% 5.42/5.64 ( ( ( times_times_real @ C @ A )
% 5.42/5.64 = ( times_times_real @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_real )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left
% 5.42/5.64 thf(fact_1792_mult__cancel__left,axiom,
% 5.42/5.64 ! [C: rat,A: rat,B: rat] :
% 5.42/5.64 ( ( ( times_times_rat @ C @ A )
% 5.42/5.64 = ( times_times_rat @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_rat )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left
% 5.42/5.64 thf(fact_1793_mult__cancel__left,axiom,
% 5.42/5.64 ! [C: nat,A: nat,B: nat] :
% 5.42/5.64 ( ( ( times_times_nat @ C @ A )
% 5.42/5.64 = ( times_times_nat @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_nat )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left
% 5.42/5.64 thf(fact_1794_mult__cancel__left,axiom,
% 5.42/5.64 ! [C: int,A: int,B: int] :
% 5.42/5.64 ( ( ( times_times_int @ C @ A )
% 5.42/5.64 = ( times_times_int @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_int )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left
% 5.42/5.64 thf(fact_1795_mult__eq__0__iff,axiom,
% 5.42/5.64 ! [A: complex,B: complex] :
% 5.42/5.64 ( ( ( times_times_complex @ A @ B )
% 5.42/5.64 = zero_zero_complex )
% 5.42/5.64 = ( ( A = zero_zero_complex )
% 5.42/5.64 | ( B = zero_zero_complex ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_eq_0_iff
% 5.42/5.64 thf(fact_1796_mult__eq__0__iff,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ( times_times_real @ A @ B )
% 5.42/5.64 = zero_zero_real )
% 5.42/5.64 = ( ( A = zero_zero_real )
% 5.42/5.64 | ( B = zero_zero_real ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_eq_0_iff
% 5.42/5.64 thf(fact_1797_mult__eq__0__iff,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ( times_times_rat @ A @ B )
% 5.42/5.64 = zero_zero_rat )
% 5.42/5.64 = ( ( A = zero_zero_rat )
% 5.42/5.64 | ( B = zero_zero_rat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_eq_0_iff
% 5.42/5.64 thf(fact_1798_mult__eq__0__iff,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( ( times_times_nat @ A @ B )
% 5.42/5.64 = zero_zero_nat )
% 5.42/5.64 = ( ( A = zero_zero_nat )
% 5.42/5.64 | ( B = zero_zero_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_eq_0_iff
% 5.42/5.64 thf(fact_1799_mult__eq__0__iff,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ( times_times_int @ A @ B )
% 5.42/5.64 = zero_zero_int )
% 5.42/5.64 = ( ( A = zero_zero_int )
% 5.42/5.64 | ( B = zero_zero_int ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_eq_0_iff
% 5.42/5.64 thf(fact_1800_mult__zero__right,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_right
% 5.42/5.64 thf(fact_1801_mult__zero__right,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( times_times_real @ A @ zero_zero_real )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_right
% 5.42/5.64 thf(fact_1802_mult__zero__right,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_right
% 5.42/5.64 thf(fact_1803_mult__zero__right,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_right
% 5.42/5.64 thf(fact_1804_mult__zero__right,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( times_times_int @ A @ zero_zero_int )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_right
% 5.42/5.64 thf(fact_1805_mult__zero__left,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_left
% 5.42/5.64 thf(fact_1806_mult__zero__left,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( times_times_real @ zero_zero_real @ A )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_left
% 5.42/5.64 thf(fact_1807_mult__zero__left,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_left
% 5.42/5.64 thf(fact_1808_mult__zero__left,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_left
% 5.42/5.64 thf(fact_1809_mult__zero__left,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( times_times_int @ zero_zero_int @ A )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % mult_zero_left
% 5.42/5.64 thf(fact_1810_add__0,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add_0
% 5.42/5.64 thf(fact_1811_add__0,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add_0
% 5.42/5.64 thf(fact_1812_add__0,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add_0
% 5.42/5.64 thf(fact_1813_add__0,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add_0
% 5.42/5.64 thf(fact_1814_add__0,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add_0
% 5.42/5.64 thf(fact_1815_zero__eq__add__iff__both__eq__0,axiom,
% 5.42/5.64 ! [X2: nat,Y2: nat] :
% 5.42/5.64 ( ( zero_zero_nat
% 5.42/5.64 = ( plus_plus_nat @ X2 @ Y2 ) )
% 5.42/5.64 = ( ( X2 = zero_zero_nat )
% 5.42/5.64 & ( Y2 = zero_zero_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_eq_add_iff_both_eq_0
% 5.42/5.64 thf(fact_1816_add__eq__0__iff__both__eq__0,axiom,
% 5.42/5.64 ! [X2: nat,Y2: nat] :
% 5.42/5.64 ( ( ( plus_plus_nat @ X2 @ Y2 )
% 5.42/5.64 = zero_zero_nat )
% 5.42/5.64 = ( ( X2 = zero_zero_nat )
% 5.42/5.64 & ( Y2 = zero_zero_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_eq_0_iff_both_eq_0
% 5.42/5.64 thf(fact_1817_add__cancel__right__right,axiom,
% 5.42/5.64 ! [A: complex,B: complex] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_complex @ A @ B ) )
% 5.42/5.64 = ( B = zero_zero_complex ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_right
% 5.42/5.64 thf(fact_1818_add__cancel__right__right,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_real @ A @ B ) )
% 5.42/5.64 = ( B = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_right
% 5.42/5.64 thf(fact_1819_add__cancel__right__right,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_rat @ A @ B ) )
% 5.42/5.64 = ( B = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_right
% 5.42/5.64 thf(fact_1820_add__cancel__right__right,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_nat @ A @ B ) )
% 5.42/5.64 = ( B = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_right
% 5.42/5.64 thf(fact_1821_add__cancel__right__right,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_int @ A @ B ) )
% 5.42/5.64 = ( B = zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_right
% 5.42/5.64 thf(fact_1822_add__cancel__right__left,axiom,
% 5.42/5.64 ! [A: complex,B: complex] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_complex @ B @ A ) )
% 5.42/5.64 = ( B = zero_zero_complex ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_left
% 5.42/5.64 thf(fact_1823_add__cancel__right__left,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_real @ B @ A ) )
% 5.42/5.64 = ( B = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_left
% 5.42/5.64 thf(fact_1824_add__cancel__right__left,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_rat @ B @ A ) )
% 5.42/5.64 = ( B = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_left
% 5.42/5.64 thf(fact_1825_add__cancel__right__left,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_nat @ B @ A ) )
% 5.42/5.64 = ( B = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_left
% 5.42/5.64 thf(fact_1826_add__cancel__right__left,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( plus_plus_int @ B @ A ) )
% 5.42/5.64 = ( B = zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_right_left
% 5.42/5.64 thf(fact_1827_add__cancel__left__right,axiom,
% 5.42/5.64 ! [A: complex,B: complex] :
% 5.42/5.64 ( ( ( plus_plus_complex @ A @ B )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_complex ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_right
% 5.42/5.64 thf(fact_1828_add__cancel__left__right,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ( plus_plus_real @ A @ B )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_right
% 5.42/5.64 thf(fact_1829_add__cancel__left__right,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ( plus_plus_rat @ A @ B )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_right
% 5.42/5.64 thf(fact_1830_add__cancel__left__right,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( ( plus_plus_nat @ A @ B )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_right
% 5.42/5.64 thf(fact_1831_add__cancel__left__right,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ( plus_plus_int @ A @ B )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_right
% 5.42/5.64 thf(fact_1832_add__cancel__left__left,axiom,
% 5.42/5.64 ! [B: complex,A: complex] :
% 5.42/5.64 ( ( ( plus_plus_complex @ B @ A )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_complex ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_left
% 5.42/5.64 thf(fact_1833_add__cancel__left__left,axiom,
% 5.42/5.64 ! [B: real,A: real] :
% 5.42/5.64 ( ( ( plus_plus_real @ B @ A )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_left
% 5.42/5.64 thf(fact_1834_add__cancel__left__left,axiom,
% 5.42/5.64 ! [B: rat,A: rat] :
% 5.42/5.64 ( ( ( plus_plus_rat @ B @ A )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_left
% 5.42/5.64 thf(fact_1835_add__cancel__left__left,axiom,
% 5.42/5.64 ! [B: nat,A: nat] :
% 5.42/5.64 ( ( ( plus_plus_nat @ B @ A )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_left
% 5.42/5.64 thf(fact_1836_add__cancel__left__left,axiom,
% 5.42/5.64 ! [B: int,A: int] :
% 5.42/5.64 ( ( ( plus_plus_int @ B @ A )
% 5.42/5.64 = A )
% 5.42/5.64 = ( B = zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_cancel_left_left
% 5.42/5.64 thf(fact_1837_double__zero__sym,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( zero_zero_real
% 5.42/5.64 = ( plus_plus_real @ A @ A ) )
% 5.42/5.64 = ( A = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_zero_sym
% 5.42/5.64 thf(fact_1838_double__zero__sym,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( zero_zero_rat
% 5.42/5.64 = ( plus_plus_rat @ A @ A ) )
% 5.42/5.64 = ( A = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_zero_sym
% 5.42/5.64 thf(fact_1839_double__zero__sym,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( zero_zero_int
% 5.42/5.64 = ( plus_plus_int @ A @ A ) )
% 5.42/5.64 = ( A = zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_zero_sym
% 5.42/5.64 thf(fact_1840_add_Oright__neutral,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add.right_neutral
% 5.42/5.64 thf(fact_1841_add_Oright__neutral,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add.right_neutral
% 5.42/5.64 thf(fact_1842_add_Oright__neutral,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add.right_neutral
% 5.42/5.64 thf(fact_1843_add_Oright__neutral,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add.right_neutral
% 5.42/5.64 thf(fact_1844_add_Oright__neutral,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % add.right_neutral
% 5.42/5.64 thf(fact_1845_double__eq__0__iff,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ( plus_plus_real @ A @ A )
% 5.42/5.64 = zero_zero_real )
% 5.42/5.64 = ( A = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_eq_0_iff
% 5.42/5.64 thf(fact_1846_double__eq__0__iff,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ( plus_plus_rat @ A @ A )
% 5.42/5.64 = zero_zero_rat )
% 5.42/5.64 = ( A = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_eq_0_iff
% 5.42/5.64 thf(fact_1847_double__eq__0__iff,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( ( plus_plus_int @ A @ A )
% 5.42/5.64 = zero_zero_int )
% 5.42/5.64 = ( A = zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_eq_0_iff
% 5.42/5.64 thf(fact_1848_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( minus_minus_complex @ A @ A )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % cancel_comm_monoid_add_class.diff_cancel
% 5.42/5.64 thf(fact_1849_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( minus_minus_real @ A @ A )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % cancel_comm_monoid_add_class.diff_cancel
% 5.42/5.64 thf(fact_1850_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( minus_minus_rat @ A @ A )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % cancel_comm_monoid_add_class.diff_cancel
% 5.42/5.64 thf(fact_1851_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( minus_minus_nat @ A @ A )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % cancel_comm_monoid_add_class.diff_cancel
% 5.42/5.64 thf(fact_1852_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( minus_minus_int @ A @ A )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % cancel_comm_monoid_add_class.diff_cancel
% 5.42/5.64 thf(fact_1853_diff__zero,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % diff_zero
% 5.42/5.64 thf(fact_1854_diff__zero,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % diff_zero
% 5.42/5.64 thf(fact_1855_diff__zero,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % diff_zero
% 5.42/5.64 thf(fact_1856_diff__zero,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % diff_zero
% 5.42/5.64 thf(fact_1857_diff__zero,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % diff_zero
% 5.42/5.64 thf(fact_1858_zero__diff,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % zero_diff
% 5.42/5.64 thf(fact_1859_diff__0__right,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % diff_0_right
% 5.42/5.64 thf(fact_1860_diff__0__right,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % diff_0_right
% 5.42/5.64 thf(fact_1861_diff__0__right,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % diff_0_right
% 5.42/5.64 thf(fact_1862_diff__0__right,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % diff_0_right
% 5.42/5.64 thf(fact_1863_diff__self,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( minus_minus_complex @ A @ A )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % diff_self
% 5.42/5.64 thf(fact_1864_diff__self,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( minus_minus_real @ A @ A )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % diff_self
% 5.42/5.64 thf(fact_1865_diff__self,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( minus_minus_rat @ A @ A )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % diff_self
% 5.42/5.64 thf(fact_1866_diff__self,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( minus_minus_int @ A @ A )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % diff_self
% 5.42/5.64 thf(fact_1867_div__0,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % div_0
% 5.42/5.64 thf(fact_1868_div__0,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % div_0
% 5.42/5.64 thf(fact_1869_div__0,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % div_0
% 5.42/5.64 thf(fact_1870_div__0,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % div_0
% 5.42/5.64 thf(fact_1871_div__0,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % div_0
% 5.42/5.64 thf(fact_1872_divide__eq__0__iff,axiom,
% 5.42/5.64 ! [A: complex,B: complex] :
% 5.42/5.64 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.42/5.64 = zero_zero_complex )
% 5.42/5.64 = ( ( A = zero_zero_complex )
% 5.42/5.64 | ( B = zero_zero_complex ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_0_iff
% 5.42/5.64 thf(fact_1873_divide__eq__0__iff,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ( divide_divide_real @ A @ B )
% 5.42/5.64 = zero_zero_real )
% 5.42/5.64 = ( ( A = zero_zero_real )
% 5.42/5.64 | ( B = zero_zero_real ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_0_iff
% 5.42/5.64 thf(fact_1874_divide__eq__0__iff,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ( divide_divide_rat @ A @ B )
% 5.42/5.64 = zero_zero_rat )
% 5.42/5.64 = ( ( A = zero_zero_rat )
% 5.42/5.64 | ( B = zero_zero_rat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_0_iff
% 5.42/5.64 thf(fact_1875_div__by__0,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % div_by_0
% 5.42/5.64 thf(fact_1876_div__by__0,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % div_by_0
% 5.42/5.64 thf(fact_1877_div__by__0,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % div_by_0
% 5.42/5.64 thf(fact_1878_div__by__0,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % div_by_0
% 5.42/5.64 thf(fact_1879_div__by__0,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % div_by_0
% 5.42/5.64 thf(fact_1880_divide__cancel__left,axiom,
% 5.42/5.64 ! [C: complex,A: complex,B: complex] :
% 5.42/5.64 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.42/5.64 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_complex )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_cancel_left
% 5.42/5.64 thf(fact_1881_divide__cancel__left,axiom,
% 5.42/5.64 ! [C: real,A: real,B: real] :
% 5.42/5.64 ( ( ( divide_divide_real @ C @ A )
% 5.42/5.64 = ( divide_divide_real @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_real )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_cancel_left
% 5.42/5.64 thf(fact_1882_divide__cancel__left,axiom,
% 5.42/5.64 ! [C: rat,A: rat,B: rat] :
% 5.42/5.64 ( ( ( divide_divide_rat @ C @ A )
% 5.42/5.64 = ( divide_divide_rat @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_rat )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_cancel_left
% 5.42/5.64 thf(fact_1883_divide__cancel__right,axiom,
% 5.42/5.64 ! [A: complex,C: complex,B: complex] :
% 5.42/5.64 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.42/5.64 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_complex )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_cancel_right
% 5.42/5.64 thf(fact_1884_divide__cancel__right,axiom,
% 5.42/5.64 ! [A: real,C: real,B: real] :
% 5.42/5.64 ( ( ( divide_divide_real @ A @ C )
% 5.42/5.64 = ( divide_divide_real @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_real )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_cancel_right
% 5.42/5.64 thf(fact_1885_divide__cancel__right,axiom,
% 5.42/5.64 ! [A: rat,C: rat,B: rat] :
% 5.42/5.64 ( ( ( divide_divide_rat @ A @ C )
% 5.42/5.64 = ( divide_divide_rat @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_rat )
% 5.42/5.64 | ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_cancel_right
% 5.42/5.64 thf(fact_1886_bits__div__0,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % bits_div_0
% 5.42/5.64 thf(fact_1887_bits__div__0,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % bits_div_0
% 5.42/5.64 thf(fact_1888_bits__div__by__0,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % bits_div_by_0
% 5.42/5.64 thf(fact_1889_bits__div__by__0,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % bits_div_by_0
% 5.42/5.64 thf(fact_1890_division__ring__divide__zero,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % division_ring_divide_zero
% 5.42/5.64 thf(fact_1891_division__ring__divide__zero,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % division_ring_divide_zero
% 5.42/5.64 thf(fact_1892_division__ring__divide__zero,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % division_ring_divide_zero
% 5.42/5.64 thf(fact_1893_bits__mod__0,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % bits_mod_0
% 5.42/5.64 thf(fact_1894_bits__mod__0,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % bits_mod_0
% 5.42/5.64 thf(fact_1895_bits__mod__0,axiom,
% 5.42/5.64 ! [A: code_integer] :
% 5.42/5.64 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.42/5.64 = zero_z3403309356797280102nteger ) ).
% 5.42/5.64
% 5.42/5.64 % bits_mod_0
% 5.42/5.64 thf(fact_1896_mod__self,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( modulo_modulo_nat @ A @ A )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mod_self
% 5.42/5.64 thf(fact_1897_mod__self,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( modulo_modulo_int @ A @ A )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % mod_self
% 5.42/5.64 thf(fact_1898_mod__self,axiom,
% 5.42/5.64 ! [A: code_integer] :
% 5.42/5.64 ( ( modulo364778990260209775nteger @ A @ A )
% 5.42/5.64 = zero_z3403309356797280102nteger ) ).
% 5.42/5.64
% 5.42/5.64 % mod_self
% 5.42/5.64 thf(fact_1899_mod__by__0,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % mod_by_0
% 5.42/5.64 thf(fact_1900_mod__by__0,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % mod_by_0
% 5.42/5.64 thf(fact_1901_mod__by__0,axiom,
% 5.42/5.64 ! [A: code_integer] :
% 5.42/5.64 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % mod_by_0
% 5.42/5.64 thf(fact_1902_mod__0,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mod_0
% 5.42/5.64 thf(fact_1903_mod__0,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % mod_0
% 5.42/5.64 thf(fact_1904_mod__0,axiom,
% 5.42/5.64 ! [A: code_integer] :
% 5.42/5.64 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.42/5.64 = zero_z3403309356797280102nteger ) ).
% 5.42/5.64
% 5.42/5.64 % mod_0
% 5.42/5.64 thf(fact_1905_bot__nat__0_Onot__eq__extremum,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( A != zero_zero_nat )
% 5.42/5.64 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % bot_nat_0.not_eq_extremum
% 5.42/5.64 thf(fact_1906_neq0__conv,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( N != zero_zero_nat )
% 5.42/5.64 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.42/5.64
% 5.42/5.64 % neq0_conv
% 5.42/5.64 thf(fact_1907_less__nat__zero__code,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % less_nat_zero_code
% 5.42/5.64 thf(fact_1908_le0,axiom,
% 5.42/5.64 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.42/5.64
% 5.42/5.64 % le0
% 5.42/5.64 thf(fact_1909_bot__nat__0_Oextremum,axiom,
% 5.42/5.64 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.42/5.64
% 5.42/5.64 % bot_nat_0.extremum
% 5.42/5.64 thf(fact_1910_Nat_Oadd__0__right,axiom,
% 5.42/5.64 ! [M: nat] :
% 5.42/5.64 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.42/5.64 = M ) ).
% 5.42/5.64
% 5.42/5.64 % Nat.add_0_right
% 5.42/5.64 thf(fact_1911_add__is__0,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ( plus_plus_nat @ M @ N )
% 5.42/5.64 = zero_zero_nat )
% 5.42/5.64 = ( ( M = zero_zero_nat )
% 5.42/5.64 & ( N = zero_zero_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_is_0
% 5.42/5.64 thf(fact_1912_diff__self__eq__0,axiom,
% 5.42/5.64 ! [M: nat] :
% 5.42/5.64 ( ( minus_minus_nat @ M @ M )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % diff_self_eq_0
% 5.42/5.64 thf(fact_1913_diff__0__eq__0,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % diff_0_eq_0
% 5.42/5.64 thf(fact_1914_mult__cancel2,axiom,
% 5.42/5.64 ! [M: nat,K: nat,N: nat] :
% 5.42/5.64 ( ( ( times_times_nat @ M @ K )
% 5.42/5.64 = ( times_times_nat @ N @ K ) )
% 5.42/5.64 = ( ( M = N )
% 5.42/5.64 | ( K = zero_zero_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel2
% 5.42/5.64 thf(fact_1915_mult__cancel1,axiom,
% 5.42/5.64 ! [K: nat,M: nat,N: nat] :
% 5.42/5.64 ( ( ( times_times_nat @ K @ M )
% 5.42/5.64 = ( times_times_nat @ K @ N ) )
% 5.42/5.64 = ( ( M = N )
% 5.42/5.64 | ( K = zero_zero_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel1
% 5.42/5.64 thf(fact_1916_mult__0__right,axiom,
% 5.42/5.64 ! [M: nat] :
% 5.42/5.64 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mult_0_right
% 5.42/5.64 thf(fact_1917_mult__is__0,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ( times_times_nat @ M @ N )
% 5.42/5.64 = zero_zero_nat )
% 5.42/5.64 = ( ( M = zero_zero_nat )
% 5.42/5.64 | ( N = zero_zero_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_is_0
% 5.42/5.64 thf(fact_1918_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.42/5.64 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_le_double_add_iff_zero_le_single_add
% 5.42/5.64 thf(fact_1919_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.42/5.64 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_le_double_add_iff_zero_le_single_add
% 5.42/5.64 thf(fact_1920_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.42/5.64 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_le_double_add_iff_zero_le_single_add
% 5.42/5.64 thf(fact_1921_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.42/5.64 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_add_le_zero_iff_single_add_le_zero
% 5.42/5.64 thf(fact_1922_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.42/5.64 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_add_le_zero_iff_single_add_le_zero
% 5.42/5.64 thf(fact_1923_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.42/5.64 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_add_le_zero_iff_single_add_le_zero
% 5.42/5.64 thf(fact_1924_le__add__same__cancel2,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.42/5.64 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_add_same_cancel2
% 5.42/5.64 thf(fact_1925_le__add__same__cancel2,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.42/5.64 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_add_same_cancel2
% 5.42/5.64 thf(fact_1926_le__add__same__cancel2,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.42/5.64 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_add_same_cancel2
% 5.42/5.64 thf(fact_1927_le__add__same__cancel2,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.42/5.64 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_add_same_cancel2
% 5.42/5.64 thf(fact_1928_le__add__same__cancel1,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.42/5.64 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_add_same_cancel1
% 5.42/5.64 thf(fact_1929_le__add__same__cancel1,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.42/5.64 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_add_same_cancel1
% 5.42/5.64 thf(fact_1930_le__add__same__cancel1,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.42/5.64 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_add_same_cancel1
% 5.42/5.64 thf(fact_1931_le__add__same__cancel1,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.42/5.64 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_add_same_cancel1
% 5.42/5.64 thf(fact_1932_add__le__same__cancel2,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.42/5.64 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_le_same_cancel2
% 5.42/5.64 thf(fact_1933_add__le__same__cancel2,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.42/5.64 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_le_same_cancel2
% 5.42/5.64 thf(fact_1934_add__le__same__cancel2,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.42/5.64 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_le_same_cancel2
% 5.42/5.64 thf(fact_1935_add__le__same__cancel2,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.42/5.64 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_le_same_cancel2
% 5.42/5.64 thf(fact_1936_add__le__same__cancel1,axiom,
% 5.42/5.64 ! [B: real,A: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.42/5.64 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_le_same_cancel1
% 5.42/5.64 thf(fact_1937_add__le__same__cancel1,axiom,
% 5.42/5.64 ! [B: rat,A: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.42/5.64 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_le_same_cancel1
% 5.42/5.64 thf(fact_1938_add__le__same__cancel1,axiom,
% 5.42/5.64 ! [B: nat,A: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.42/5.64 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_le_same_cancel1
% 5.42/5.64 thf(fact_1939_add__le__same__cancel1,axiom,
% 5.42/5.64 ! [B: int,A: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.42/5.64 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_le_same_cancel1
% 5.42/5.64 thf(fact_1940_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.42/5.64 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_double_add_iff_zero_less_single_add
% 5.42/5.64 thf(fact_1941_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.42/5.64 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_double_add_iff_zero_less_single_add
% 5.42/5.64 thf(fact_1942_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.42/5.64 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_double_add_iff_zero_less_single_add
% 5.42/5.64 thf(fact_1943_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.42/5.64 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_add_less_zero_iff_single_add_less_zero
% 5.42/5.64 thf(fact_1944_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.42/5.64 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_add_less_zero_iff_single_add_less_zero
% 5.42/5.64 thf(fact_1945_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.42/5.64 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % double_add_less_zero_iff_single_add_less_zero
% 5.42/5.64 thf(fact_1946_less__add__same__cancel2,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.42/5.64 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_add_same_cancel2
% 5.42/5.64 thf(fact_1947_less__add__same__cancel2,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.42/5.64 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_add_same_cancel2
% 5.42/5.64 thf(fact_1948_less__add__same__cancel2,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.42/5.64 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_add_same_cancel2
% 5.42/5.64 thf(fact_1949_less__add__same__cancel2,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.42/5.64 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_add_same_cancel2
% 5.42/5.64 thf(fact_1950_less__add__same__cancel1,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.42/5.64 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_add_same_cancel1
% 5.42/5.64 thf(fact_1951_less__add__same__cancel1,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.42/5.64 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_add_same_cancel1
% 5.42/5.64 thf(fact_1952_less__add__same__cancel1,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.42/5.64 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_add_same_cancel1
% 5.42/5.64 thf(fact_1953_less__add__same__cancel1,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.42/5.64 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_add_same_cancel1
% 5.42/5.64 thf(fact_1954_add__less__same__cancel2,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.42/5.64 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_less_same_cancel2
% 5.42/5.64 thf(fact_1955_add__less__same__cancel2,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.42/5.64 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_less_same_cancel2
% 5.42/5.64 thf(fact_1956_add__less__same__cancel2,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.42/5.64 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_less_same_cancel2
% 5.42/5.64 thf(fact_1957_add__less__same__cancel2,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.42/5.64 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_less_same_cancel2
% 5.42/5.64 thf(fact_1958_add__less__same__cancel1,axiom,
% 5.42/5.64 ! [B: real,A: real] :
% 5.42/5.64 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.42/5.64 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_less_same_cancel1
% 5.42/5.64 thf(fact_1959_add__less__same__cancel1,axiom,
% 5.42/5.64 ! [B: rat,A: rat] :
% 5.42/5.64 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.42/5.64 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_less_same_cancel1
% 5.42/5.64 thf(fact_1960_add__less__same__cancel1,axiom,
% 5.42/5.64 ! [B: nat,A: nat] :
% 5.42/5.64 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.42/5.64 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_less_same_cancel1
% 5.42/5.64 thf(fact_1961_add__less__same__cancel1,axiom,
% 5.42/5.64 ! [B: int,A: int] :
% 5.42/5.64 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.42/5.64 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_less_same_cancel1
% 5.42/5.64 thf(fact_1962_diff__ge__0__iff__ge,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.42/5.64 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % diff_ge_0_iff_ge
% 5.42/5.64 thf(fact_1963_diff__ge__0__iff__ge,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.42/5.64 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % diff_ge_0_iff_ge
% 5.42/5.64 thf(fact_1964_diff__ge__0__iff__ge,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.42/5.64 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % diff_ge_0_iff_ge
% 5.42/5.64 thf(fact_1965_diff__gt__0__iff__gt,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.42/5.64 = ( ord_less_real @ B @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % diff_gt_0_iff_gt
% 5.42/5.64 thf(fact_1966_diff__gt__0__iff__gt,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.42/5.64 = ( ord_less_rat @ B @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % diff_gt_0_iff_gt
% 5.42/5.64 thf(fact_1967_diff__gt__0__iff__gt,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.42/5.64 = ( ord_less_int @ B @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % diff_gt_0_iff_gt
% 5.42/5.64 thf(fact_1968_mult__cancel__right2,axiom,
% 5.42/5.64 ! [A: complex,C: complex] :
% 5.42/5.64 ( ( ( times_times_complex @ A @ C )
% 5.42/5.64 = C )
% 5.42/5.64 = ( ( C = zero_zero_complex )
% 5.42/5.64 | ( A = one_one_complex ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right2
% 5.42/5.64 thf(fact_1969_mult__cancel__right2,axiom,
% 5.42/5.64 ! [A: real,C: real] :
% 5.42/5.64 ( ( ( times_times_real @ A @ C )
% 5.42/5.64 = C )
% 5.42/5.64 = ( ( C = zero_zero_real )
% 5.42/5.64 | ( A = one_one_real ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right2
% 5.42/5.64 thf(fact_1970_mult__cancel__right2,axiom,
% 5.42/5.64 ! [A: rat,C: rat] :
% 5.42/5.64 ( ( ( times_times_rat @ A @ C )
% 5.42/5.64 = C )
% 5.42/5.64 = ( ( C = zero_zero_rat )
% 5.42/5.64 | ( A = one_one_rat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right2
% 5.42/5.64 thf(fact_1971_mult__cancel__right2,axiom,
% 5.42/5.64 ! [A: int,C: int] :
% 5.42/5.64 ( ( ( times_times_int @ A @ C )
% 5.42/5.64 = C )
% 5.42/5.64 = ( ( C = zero_zero_int )
% 5.42/5.64 | ( A = one_one_int ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right2
% 5.42/5.64 thf(fact_1972_mult__cancel__right1,axiom,
% 5.42/5.64 ! [C: complex,B: complex] :
% 5.42/5.64 ( ( C
% 5.42/5.64 = ( times_times_complex @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_complex )
% 5.42/5.64 | ( B = one_one_complex ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right1
% 5.42/5.64 thf(fact_1973_mult__cancel__right1,axiom,
% 5.42/5.64 ! [C: real,B: real] :
% 5.42/5.64 ( ( C
% 5.42/5.64 = ( times_times_real @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_real )
% 5.42/5.64 | ( B = one_one_real ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right1
% 5.42/5.64 thf(fact_1974_mult__cancel__right1,axiom,
% 5.42/5.64 ! [C: rat,B: rat] :
% 5.42/5.64 ( ( C
% 5.42/5.64 = ( times_times_rat @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_rat )
% 5.42/5.64 | ( B = one_one_rat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right1
% 5.42/5.64 thf(fact_1975_mult__cancel__right1,axiom,
% 5.42/5.64 ! [C: int,B: int] :
% 5.42/5.64 ( ( C
% 5.42/5.64 = ( times_times_int @ B @ C ) )
% 5.42/5.64 = ( ( C = zero_zero_int )
% 5.42/5.64 | ( B = one_one_int ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_right1
% 5.42/5.64 thf(fact_1976_mult__cancel__left2,axiom,
% 5.42/5.64 ! [C: complex,A: complex] :
% 5.42/5.64 ( ( ( times_times_complex @ C @ A )
% 5.42/5.64 = C )
% 5.42/5.64 = ( ( C = zero_zero_complex )
% 5.42/5.64 | ( A = one_one_complex ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left2
% 5.42/5.64 thf(fact_1977_mult__cancel__left2,axiom,
% 5.42/5.64 ! [C: real,A: real] :
% 5.42/5.64 ( ( ( times_times_real @ C @ A )
% 5.42/5.64 = C )
% 5.42/5.64 = ( ( C = zero_zero_real )
% 5.42/5.64 | ( A = one_one_real ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left2
% 5.42/5.64 thf(fact_1978_mult__cancel__left2,axiom,
% 5.42/5.64 ! [C: rat,A: rat] :
% 5.42/5.64 ( ( ( times_times_rat @ C @ A )
% 5.42/5.64 = C )
% 5.42/5.64 = ( ( C = zero_zero_rat )
% 5.42/5.64 | ( A = one_one_rat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left2
% 5.42/5.64 thf(fact_1979_mult__cancel__left2,axiom,
% 5.42/5.64 ! [C: int,A: int] :
% 5.42/5.64 ( ( ( times_times_int @ C @ A )
% 5.42/5.64 = C )
% 5.42/5.64 = ( ( C = zero_zero_int )
% 5.42/5.64 | ( A = one_one_int ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left2
% 5.42/5.64 thf(fact_1980_mult__cancel__left1,axiom,
% 5.42/5.64 ! [C: complex,B: complex] :
% 5.42/5.64 ( ( C
% 5.42/5.64 = ( times_times_complex @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_complex )
% 5.42/5.64 | ( B = one_one_complex ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left1
% 5.42/5.64 thf(fact_1981_mult__cancel__left1,axiom,
% 5.42/5.64 ! [C: real,B: real] :
% 5.42/5.64 ( ( C
% 5.42/5.64 = ( times_times_real @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_real )
% 5.42/5.64 | ( B = one_one_real ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left1
% 5.42/5.64 thf(fact_1982_mult__cancel__left1,axiom,
% 5.42/5.64 ! [C: rat,B: rat] :
% 5.42/5.64 ( ( C
% 5.42/5.64 = ( times_times_rat @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_rat )
% 5.42/5.64 | ( B = one_one_rat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left1
% 5.42/5.64 thf(fact_1983_mult__cancel__left1,axiom,
% 5.42/5.64 ! [C: int,B: int] :
% 5.42/5.64 ( ( C
% 5.42/5.64 = ( times_times_int @ C @ B ) )
% 5.42/5.64 = ( ( C = zero_zero_int )
% 5.42/5.64 | ( B = one_one_int ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_cancel_left1
% 5.42/5.64 thf(fact_1984_sum__squares__eq__zero__iff,axiom,
% 5.42/5.64 ! [X2: real,Y2: real] :
% 5.42/5.64 ( ( ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) )
% 5.42/5.64 = zero_zero_real )
% 5.42/5.64 = ( ( X2 = zero_zero_real )
% 5.42/5.64 & ( Y2 = zero_zero_real ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % sum_squares_eq_zero_iff
% 5.42/5.64 thf(fact_1985_sum__squares__eq__zero__iff,axiom,
% 5.42/5.64 ! [X2: rat,Y2: rat] :
% 5.42/5.64 ( ( ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 5.42/5.64 = zero_zero_rat )
% 5.42/5.64 = ( ( X2 = zero_zero_rat )
% 5.42/5.64 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % sum_squares_eq_zero_iff
% 5.42/5.64 thf(fact_1986_sum__squares__eq__zero__iff,axiom,
% 5.42/5.64 ! [X2: int,Y2: int] :
% 5.42/5.64 ( ( ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) )
% 5.42/5.64 = zero_zero_int )
% 5.42/5.64 = ( ( X2 = zero_zero_int )
% 5.42/5.64 & ( Y2 = zero_zero_int ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % sum_squares_eq_zero_iff
% 5.42/5.64 thf(fact_1987_diff__numeral__special_I9_J,axiom,
% 5.42/5.64 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % diff_numeral_special(9)
% 5.42/5.64 thf(fact_1988_diff__numeral__special_I9_J,axiom,
% 5.42/5.64 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % diff_numeral_special(9)
% 5.42/5.64 thf(fact_1989_diff__numeral__special_I9_J,axiom,
% 5.42/5.64 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % diff_numeral_special(9)
% 5.42/5.64 thf(fact_1990_diff__numeral__special_I9_J,axiom,
% 5.42/5.64 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % diff_numeral_special(9)
% 5.42/5.64 thf(fact_1991_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.42/5.64 ! [C: complex,A: complex,B: complex] :
% 5.42/5.64 ( ( C != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.42/5.64 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_right2
% 5.42/5.64 thf(fact_1992_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.42/5.64 ! [C: real,A: real,B: real] :
% 5.42/5.64 ( ( C != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.42/5.64 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_right2
% 5.42/5.64 thf(fact_1993_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.42/5.64 ! [C: rat,A: rat,B: rat] :
% 5.42/5.64 ( ( C != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.42/5.64 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_right2
% 5.42/5.64 thf(fact_1994_nonzero__mult__div__cancel__right,axiom,
% 5.42/5.64 ! [B: complex,A: complex] :
% 5.42/5.64 ( ( B != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.42/5.64 = A ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_right
% 5.42/5.64 thf(fact_1995_nonzero__mult__div__cancel__right,axiom,
% 5.42/5.64 ! [B: real,A: real] :
% 5.42/5.64 ( ( B != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.42/5.64 = A ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_right
% 5.42/5.64 thf(fact_1996_nonzero__mult__div__cancel__right,axiom,
% 5.42/5.64 ! [B: rat,A: rat] :
% 5.42/5.64 ( ( B != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.42/5.64 = A ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_right
% 5.42/5.64 thf(fact_1997_nonzero__mult__div__cancel__right,axiom,
% 5.42/5.64 ! [B: nat,A: nat] :
% 5.42/5.64 ( ( B != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.42/5.64 = A ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_right
% 5.42/5.64 thf(fact_1998_nonzero__mult__div__cancel__right,axiom,
% 5.42/5.64 ! [B: int,A: int] :
% 5.42/5.64 ( ( B != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.42/5.64 = A ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_right
% 5.42/5.64 thf(fact_1999_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.42/5.64 ! [C: complex,A: complex,B: complex] :
% 5.42/5.64 ( ( C != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.42/5.64 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_right
% 5.42/5.64 thf(fact_2000_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.42/5.64 ! [C: real,A: real,B: real] :
% 5.42/5.64 ( ( C != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.42/5.64 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_right
% 5.42/5.64 thf(fact_2001_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.42/5.64 ! [C: rat,A: rat,B: rat] :
% 5.42/5.64 ( ( C != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.42/5.64 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_right
% 5.42/5.64 thf(fact_2002_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.42/5.64 ! [C: complex,A: complex,B: complex] :
% 5.42/5.64 ( ( C != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.42/5.64 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_left2
% 5.42/5.64 thf(fact_2003_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.42/5.64 ! [C: real,A: real,B: real] :
% 5.42/5.64 ( ( C != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.42/5.64 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_left2
% 5.42/5.64 thf(fact_2004_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.42/5.64 ! [C: rat,A: rat,B: rat] :
% 5.42/5.64 ( ( C != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.42/5.64 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_left2
% 5.42/5.64 thf(fact_2005_nonzero__mult__div__cancel__left,axiom,
% 5.42/5.64 ! [A: complex,B: complex] :
% 5.42/5.64 ( ( A != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.42/5.64 = B ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_left
% 5.42/5.64 thf(fact_2006_nonzero__mult__div__cancel__left,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( A != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.42/5.64 = B ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_left
% 5.42/5.64 thf(fact_2007_nonzero__mult__div__cancel__left,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( A != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.42/5.64 = B ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_left
% 5.42/5.64 thf(fact_2008_nonzero__mult__div__cancel__left,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( A != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.42/5.64 = B ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_left
% 5.42/5.64 thf(fact_2009_nonzero__mult__div__cancel__left,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( A != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.42/5.64 = B ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_div_cancel_left
% 5.42/5.64 thf(fact_2010_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.42/5.64 ! [C: complex,A: complex,B: complex] :
% 5.42/5.64 ( ( C != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.42/5.64 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_left
% 5.42/5.64 thf(fact_2011_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.42/5.64 ! [C: real,A: real,B: real] :
% 5.42/5.64 ( ( C != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.42/5.64 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_left
% 5.42/5.64 thf(fact_2012_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.42/5.64 ! [C: rat,A: rat,B: rat] :
% 5.42/5.64 ( ( C != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.42/5.64 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_mult_divide_mult_cancel_left
% 5.42/5.64 thf(fact_2013_mult__divide__mult__cancel__left__if,axiom,
% 5.42/5.64 ! [C: complex,A: complex,B: complex] :
% 5.42/5.64 ( ( ( C = zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.42/5.64 = zero_zero_complex ) )
% 5.42/5.64 & ( ( C != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.42/5.64 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_divide_mult_cancel_left_if
% 5.42/5.64 thf(fact_2014_mult__divide__mult__cancel__left__if,axiom,
% 5.42/5.64 ! [C: real,A: real,B: real] :
% 5.42/5.64 ( ( ( C = zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.42/5.64 = zero_zero_real ) )
% 5.42/5.64 & ( ( C != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.42/5.64 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_divide_mult_cancel_left_if
% 5.42/5.64 thf(fact_2015_mult__divide__mult__cancel__left__if,axiom,
% 5.42/5.64 ! [C: rat,A: rat,B: rat] :
% 5.42/5.64 ( ( ( C = zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.42/5.64 = zero_zero_rat ) )
% 5.42/5.64 & ( ( C != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.42/5.64 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_divide_mult_cancel_left_if
% 5.42/5.64 thf(fact_2016_div__mult__mult1__if,axiom,
% 5.42/5.64 ! [C: nat,A: nat,B: nat] :
% 5.42/5.64 ( ( ( C = zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.42/5.64 = zero_zero_nat ) )
% 5.42/5.64 & ( ( C != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.42/5.64 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_mult1_if
% 5.42/5.64 thf(fact_2017_div__mult__mult1__if,axiom,
% 5.42/5.64 ! [C: int,A: int,B: int] :
% 5.42/5.64 ( ( ( C = zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.42/5.64 = zero_zero_int ) )
% 5.42/5.64 & ( ( C != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.42/5.64 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_mult1_if
% 5.42/5.64 thf(fact_2018_div__mult__mult2,axiom,
% 5.42/5.64 ! [C: nat,A: nat,B: nat] :
% 5.42/5.64 ( ( C != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.42/5.64 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_mult2
% 5.42/5.64 thf(fact_2019_div__mult__mult2,axiom,
% 5.42/5.64 ! [C: int,A: int,B: int] :
% 5.42/5.64 ( ( C != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.42/5.64 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_mult2
% 5.42/5.64 thf(fact_2020_div__mult__mult1,axiom,
% 5.42/5.64 ! [C: nat,A: nat,B: nat] :
% 5.42/5.64 ( ( C != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.42/5.64 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_mult1
% 5.42/5.64 thf(fact_2021_div__mult__mult1,axiom,
% 5.42/5.64 ! [C: int,A: int,B: int] :
% 5.42/5.64 ( ( C != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.42/5.64 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_mult1
% 5.42/5.64 thf(fact_2022_diff__add__zero,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % diff_add_zero
% 5.42/5.64 thf(fact_2023_zero__eq__1__divide__iff,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( zero_zero_real
% 5.42/5.64 = ( divide_divide_real @ one_one_real @ A ) )
% 5.42/5.64 = ( A = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_eq_1_divide_iff
% 5.42/5.64 thf(fact_2024_zero__eq__1__divide__iff,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( zero_zero_rat
% 5.42/5.64 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.42/5.64 = ( A = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_eq_1_divide_iff
% 5.42/5.64 thf(fact_2025_one__divide__eq__0__iff,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.42/5.64 = zero_zero_real )
% 5.42/5.64 = ( A = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % one_divide_eq_0_iff
% 5.42/5.64 thf(fact_2026_one__divide__eq__0__iff,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.42/5.64 = zero_zero_rat )
% 5.42/5.64 = ( A = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % one_divide_eq_0_iff
% 5.42/5.64 thf(fact_2027_eq__divide__eq__1,axiom,
% 5.42/5.64 ! [B: real,A: real] :
% 5.42/5.64 ( ( one_one_real
% 5.42/5.64 = ( divide_divide_real @ B @ A ) )
% 5.42/5.64 = ( ( A != zero_zero_real )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % eq_divide_eq_1
% 5.42/5.64 thf(fact_2028_eq__divide__eq__1,axiom,
% 5.42/5.64 ! [B: rat,A: rat] :
% 5.42/5.64 ( ( one_one_rat
% 5.42/5.64 = ( divide_divide_rat @ B @ A ) )
% 5.42/5.64 = ( ( A != zero_zero_rat )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % eq_divide_eq_1
% 5.42/5.64 thf(fact_2029_divide__eq__eq__1,axiom,
% 5.42/5.64 ! [B: real,A: real] :
% 5.42/5.64 ( ( ( divide_divide_real @ B @ A )
% 5.42/5.64 = one_one_real )
% 5.42/5.64 = ( ( A != zero_zero_real )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_eq_1
% 5.42/5.64 thf(fact_2030_divide__eq__eq__1,axiom,
% 5.42/5.64 ! [B: rat,A: rat] :
% 5.42/5.64 ( ( ( divide_divide_rat @ B @ A )
% 5.42/5.64 = one_one_rat )
% 5.42/5.64 = ( ( A != zero_zero_rat )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_eq_1
% 5.42/5.64 thf(fact_2031_divide__self__if,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( ( A = zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.42/5.64 = zero_zero_complex ) )
% 5.42/5.64 & ( ( A != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.42/5.64 = one_one_complex ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_self_if
% 5.42/5.64 thf(fact_2032_divide__self__if,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ( A = zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ A @ A )
% 5.42/5.64 = zero_zero_real ) )
% 5.42/5.64 & ( ( A != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ A @ A )
% 5.42/5.64 = one_one_real ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_self_if
% 5.42/5.64 thf(fact_2033_divide__self__if,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ( A = zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ A @ A )
% 5.42/5.64 = zero_zero_rat ) )
% 5.42/5.64 & ( ( A != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ A @ A )
% 5.42/5.64 = one_one_rat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_self_if
% 5.42/5.64 thf(fact_2034_divide__self,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( A != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.42/5.64 = one_one_complex ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_self
% 5.42/5.64 thf(fact_2035_divide__self,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( A != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ A @ A )
% 5.42/5.64 = one_one_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_self
% 5.42/5.64 thf(fact_2036_divide__self,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( A != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ A @ A )
% 5.42/5.64 = one_one_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_self
% 5.42/5.64 thf(fact_2037_one__eq__divide__iff,axiom,
% 5.42/5.64 ! [A: complex,B: complex] :
% 5.42/5.64 ( ( one_one_complex
% 5.42/5.64 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.42/5.64 = ( ( B != zero_zero_complex )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % one_eq_divide_iff
% 5.42/5.64 thf(fact_2038_one__eq__divide__iff,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( one_one_real
% 5.42/5.64 = ( divide_divide_real @ A @ B ) )
% 5.42/5.64 = ( ( B != zero_zero_real )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % one_eq_divide_iff
% 5.42/5.64 thf(fact_2039_one__eq__divide__iff,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( one_one_rat
% 5.42/5.64 = ( divide_divide_rat @ A @ B ) )
% 5.42/5.64 = ( ( B != zero_zero_rat )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % one_eq_divide_iff
% 5.42/5.64 thf(fact_2040_div__self,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( A != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.42/5.64 = one_one_complex ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_self
% 5.42/5.64 thf(fact_2041_div__self,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( A != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ A @ A )
% 5.42/5.64 = one_one_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_self
% 5.42/5.64 thf(fact_2042_div__self,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( A != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ A @ A )
% 5.42/5.64 = one_one_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_self
% 5.42/5.64 thf(fact_2043_div__self,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( A != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ A @ A )
% 5.42/5.64 = one_one_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_self
% 5.42/5.64 thf(fact_2044_div__self,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( A != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ A @ A )
% 5.42/5.64 = one_one_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_self
% 5.42/5.64 thf(fact_2045_divide__eq__1__iff,axiom,
% 5.42/5.64 ! [A: complex,B: complex] :
% 5.42/5.64 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.42/5.64 = one_one_complex )
% 5.42/5.64 = ( ( B != zero_zero_complex )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_1_iff
% 5.42/5.64 thf(fact_2046_divide__eq__1__iff,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ( divide_divide_real @ A @ B )
% 5.42/5.64 = one_one_real )
% 5.42/5.64 = ( ( B != zero_zero_real )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_1_iff
% 5.42/5.64 thf(fact_2047_divide__eq__1__iff,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ( divide_divide_rat @ A @ B )
% 5.42/5.64 = one_one_rat )
% 5.42/5.64 = ( ( B != zero_zero_rat )
% 5.42/5.64 & ( A = B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_1_iff
% 5.42/5.64 thf(fact_2048_power__0__Suc,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % power_0_Suc
% 5.42/5.64 thf(fact_2049_power__0__Suc,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % power_0_Suc
% 5.42/5.64 thf(fact_2050_power__0__Suc,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % power_0_Suc
% 5.42/5.64 thf(fact_2051_power__0__Suc,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % power_0_Suc
% 5.42/5.64 thf(fact_2052_power__0__Suc,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % power_0_Suc
% 5.42/5.64 thf(fact_2053_power__zero__numeral,axiom,
% 5.42/5.64 ! [K: num] :
% 5.42/5.64 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.42/5.64 = zero_zero_rat ) ).
% 5.42/5.64
% 5.42/5.64 % power_zero_numeral
% 5.42/5.64 thf(fact_2054_power__zero__numeral,axiom,
% 5.42/5.64 ! [K: num] :
% 5.42/5.64 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % power_zero_numeral
% 5.42/5.64 thf(fact_2055_power__zero__numeral,axiom,
% 5.42/5.64 ! [K: num] :
% 5.42/5.64 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.42/5.64 = zero_zero_real ) ).
% 5.42/5.64
% 5.42/5.64 % power_zero_numeral
% 5.42/5.64 thf(fact_2056_power__zero__numeral,axiom,
% 5.42/5.64 ! [K: num] :
% 5.42/5.64 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.42/5.64 = zero_zero_complex ) ).
% 5.42/5.64
% 5.42/5.64 % power_zero_numeral
% 5.42/5.64 thf(fact_2057_power__zero__numeral,axiom,
% 5.42/5.64 ! [K: num] :
% 5.42/5.64 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % power_zero_numeral
% 5.42/5.64 thf(fact_2058_mod__mult__self2__is__0,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mod_mult_self2_is_0
% 5.42/5.64 thf(fact_2059_mod__mult__self2__is__0,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % mod_mult_self2_is_0
% 5.42/5.64 thf(fact_2060_mod__mult__self2__is__0,axiom,
% 5.42/5.64 ! [A: code_integer,B: code_integer] :
% 5.42/5.64 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.42/5.64 = zero_z3403309356797280102nteger ) ).
% 5.42/5.64
% 5.42/5.64 % mod_mult_self2_is_0
% 5.42/5.64 thf(fact_2061_mod__mult__self1__is__0,axiom,
% 5.42/5.64 ! [B: nat,A: nat] :
% 5.42/5.64 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mod_mult_self1_is_0
% 5.42/5.64 thf(fact_2062_mod__mult__self1__is__0,axiom,
% 5.42/5.64 ! [B: int,A: int] :
% 5.42/5.64 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % mod_mult_self1_is_0
% 5.42/5.64 thf(fact_2063_mod__mult__self1__is__0,axiom,
% 5.42/5.64 ! [B: code_integer,A: code_integer] :
% 5.42/5.64 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.42/5.64 = zero_z3403309356797280102nteger ) ).
% 5.42/5.64
% 5.42/5.64 % mod_mult_self1_is_0
% 5.42/5.64 thf(fact_2064_bits__mod__by__1,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % bits_mod_by_1
% 5.42/5.64 thf(fact_2065_bits__mod__by__1,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % bits_mod_by_1
% 5.42/5.64 thf(fact_2066_bits__mod__by__1,axiom,
% 5.42/5.64 ! [A: code_integer] :
% 5.42/5.64 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.42/5.64 = zero_z3403309356797280102nteger ) ).
% 5.42/5.64
% 5.42/5.64 % bits_mod_by_1
% 5.42/5.64 thf(fact_2067_mod__by__1,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mod_by_1
% 5.42/5.64 thf(fact_2068_mod__by__1,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % mod_by_1
% 5.42/5.64 thf(fact_2069_mod__by__1,axiom,
% 5.42/5.64 ! [A: code_integer] :
% 5.42/5.64 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.42/5.64 = zero_z3403309356797280102nteger ) ).
% 5.42/5.64
% 5.42/5.64 % mod_by_1
% 5.42/5.64 thf(fact_2070_power__Suc0__right,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % power_Suc0_right
% 5.42/5.64 thf(fact_2071_power__Suc0__right,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % power_Suc0_right
% 5.42/5.64 thf(fact_2072_power__Suc0__right,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % power_Suc0_right
% 5.42/5.64 thf(fact_2073_power__Suc0__right,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.42/5.64 = A ) ).
% 5.42/5.64
% 5.42/5.64 % power_Suc0_right
% 5.42/5.64 thf(fact_2074_bits__mod__div__trivial,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % bits_mod_div_trivial
% 5.42/5.64 thf(fact_2075_bits__mod__div__trivial,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % bits_mod_div_trivial
% 5.42/5.64 thf(fact_2076_bits__mod__div__trivial,axiom,
% 5.42/5.64 ! [A: code_integer,B: code_integer] :
% 5.42/5.64 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.42/5.64 = zero_z3403309356797280102nteger ) ).
% 5.42/5.64
% 5.42/5.64 % bits_mod_div_trivial
% 5.42/5.64 thf(fact_2077_mod__div__trivial,axiom,
% 5.42/5.64 ! [A: nat,B: nat] :
% 5.42/5.64 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mod_div_trivial
% 5.42/5.64 thf(fact_2078_mod__div__trivial,axiom,
% 5.42/5.64 ! [A: int,B: int] :
% 5.42/5.64 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % mod_div_trivial
% 5.42/5.64 thf(fact_2079_mod__div__trivial,axiom,
% 5.42/5.64 ! [A: code_integer,B: code_integer] :
% 5.42/5.64 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.42/5.64 = zero_z3403309356797280102nteger ) ).
% 5.42/5.64
% 5.42/5.64 % mod_div_trivial
% 5.42/5.64 thf(fact_2080_less__Suc0,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.42/5.64 = ( N = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_Suc0
% 5.42/5.64 thf(fact_2081_zero__less__Suc,axiom,
% 5.42/5.64 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_Suc
% 5.42/5.64 thf(fact_2082_add__gr__0,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.42/5.64 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.42/5.64 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % add_gr_0
% 5.42/5.64 thf(fact_2083_mult__eq__1__iff,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ( times_times_nat @ M @ N )
% 5.42/5.64 = ( suc @ zero_zero_nat ) )
% 5.42/5.64 = ( ( M
% 5.42/5.64 = ( suc @ zero_zero_nat ) )
% 5.42/5.64 & ( N
% 5.42/5.64 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_eq_1_iff
% 5.42/5.64 thf(fact_2084_one__eq__mult__iff,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ( suc @ zero_zero_nat )
% 5.42/5.64 = ( times_times_nat @ M @ N ) )
% 5.42/5.64 = ( ( M
% 5.42/5.64 = ( suc @ zero_zero_nat ) )
% 5.42/5.64 & ( N
% 5.42/5.64 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % one_eq_mult_iff
% 5.42/5.64 thf(fact_2085_div__by__Suc__0,axiom,
% 5.42/5.64 ! [M: nat] :
% 5.42/5.64 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.42/5.64 = M ) ).
% 5.42/5.64
% 5.42/5.64 % div_by_Suc_0
% 5.42/5.64 thf(fact_2086_less__one,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ N @ one_one_nat )
% 5.42/5.64 = ( N = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_one
% 5.42/5.64 thf(fact_2087_zero__less__diff,axiom,
% 5.42/5.64 ! [N: nat,M: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.42/5.64 = ( ord_less_nat @ M @ N ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_diff
% 5.42/5.64 thf(fact_2088_nat__0__less__mult__iff,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.42/5.64 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.42/5.64 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nat_0_less_mult_iff
% 5.42/5.64 thf(fact_2089_mult__less__cancel2,axiom,
% 5.42/5.64 ! [M: nat,K: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.42/5.64 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.42/5.64 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_less_cancel2
% 5.42/5.64 thf(fact_2090_nat__mult__less__cancel__disj,axiom,
% 5.42/5.64 ! [K: nat,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.42/5.64 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.42/5.64 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nat_mult_less_cancel_disj
% 5.42/5.64 thf(fact_2091_div__less,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ M @ N )
% 5.42/5.64 => ( ( divide_divide_nat @ M @ N )
% 5.42/5.64 = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_less
% 5.42/5.64 thf(fact_2092_diff__is__0__eq,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ( minus_minus_nat @ M @ N )
% 5.42/5.64 = zero_zero_nat )
% 5.42/5.64 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.42/5.64
% 5.42/5.64 % diff_is_0_eq
% 5.42/5.64 thf(fact_2093_diff__is__0__eq_H,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.42/5.64 => ( ( minus_minus_nat @ M @ N )
% 5.42/5.64 = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % diff_is_0_eq'
% 5.42/5.64 thf(fact_2094_nat__power__eq__Suc__0__iff,axiom,
% 5.42/5.64 ! [X2: nat,M: nat] :
% 5.42/5.64 ( ( ( power_power_nat @ X2 @ M )
% 5.42/5.64 = ( suc @ zero_zero_nat ) )
% 5.42/5.64 = ( ( M = zero_zero_nat )
% 5.42/5.64 | ( X2
% 5.42/5.64 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nat_power_eq_Suc_0_iff
% 5.42/5.64 thf(fact_2095_power__Suc__0,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.42/5.64 = ( suc @ zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_Suc_0
% 5.42/5.64 thf(fact_2096_nat__zero__less__power__iff,axiom,
% 5.42/5.64 ! [X2: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X2 @ N ) )
% 5.42/5.64 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.42/5.64 | ( N = zero_zero_nat ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nat_zero_less_power_iff
% 5.42/5.64 thf(fact_2097_nat__mult__div__cancel__disj,axiom,
% 5.42/5.64 ! [K: nat,M: nat,N: nat] :
% 5.42/5.64 ( ( ( K = zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.42/5.64 = zero_zero_nat ) )
% 5.42/5.64 & ( ( K != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.42/5.64 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nat_mult_div_cancel_disj
% 5.42/5.64 thf(fact_2098_mod__by__Suc__0,axiom,
% 5.42/5.64 ! [M: nat] :
% 5.42/5.64 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % mod_by_Suc_0
% 5.42/5.64 thf(fact_2099_dbl__inc__simps_I2_J,axiom,
% 5.42/5.64 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.42/5.64 = one_one_complex ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(2)
% 5.42/5.64 thf(fact_2100_dbl__inc__simps_I2_J,axiom,
% 5.42/5.64 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.42/5.64 = one_one_real ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(2)
% 5.42/5.64 thf(fact_2101_dbl__inc__simps_I2_J,axiom,
% 5.42/5.64 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.42/5.64 = one_one_rat ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(2)
% 5.42/5.64 thf(fact_2102_dbl__inc__simps_I2_J,axiom,
% 5.42/5.64 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.42/5.64 = one_one_int ) ).
% 5.42/5.64
% 5.42/5.64 % dbl_inc_simps(2)
% 5.42/5.64 thf(fact_2103_zero__le__divide__1__iff,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.42/5.64 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_le_divide_1_iff
% 5.42/5.64 thf(fact_2104_zero__le__divide__1__iff,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.42/5.64 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_le_divide_1_iff
% 5.42/5.64 thf(fact_2105_divide__le__0__1__iff,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.42/5.64 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_le_0_1_iff
% 5.42/5.64 thf(fact_2106_divide__le__0__1__iff,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.42/5.64 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_le_0_1_iff
% 5.42/5.64 thf(fact_2107_zero__less__divide__1__iff,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.42/5.64 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_divide_1_iff
% 5.42/5.64 thf(fact_2108_zero__less__divide__1__iff,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.42/5.64 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_divide_1_iff
% 5.42/5.64 thf(fact_2109_less__divide__eq__1__pos,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.42/5.64 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.42/5.64 = ( ord_less_real @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_divide_eq_1_pos
% 5.42/5.64 thf(fact_2110_less__divide__eq__1__pos,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.42/5.64 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.42/5.64 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_divide_eq_1_pos
% 5.42/5.64 thf(fact_2111_less__divide__eq__1__neg,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ A @ zero_zero_real )
% 5.42/5.64 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.42/5.64 = ( ord_less_real @ B @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_divide_eq_1_neg
% 5.42/5.64 thf(fact_2112_less__divide__eq__1__neg,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.42/5.64 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.42/5.64 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % less_divide_eq_1_neg
% 5.42/5.64 thf(fact_2113_divide__less__eq__1__pos,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.42/5.64 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.42/5.64 = ( ord_less_real @ B @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_less_eq_1_pos
% 5.42/5.64 thf(fact_2114_divide__less__eq__1__pos,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.42/5.64 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.42/5.64 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_less_eq_1_pos
% 5.42/5.64 thf(fact_2115_divide__less__eq__1__neg,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ A @ zero_zero_real )
% 5.42/5.64 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.42/5.64 = ( ord_less_real @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_less_eq_1_neg
% 5.42/5.64 thf(fact_2116_divide__less__eq__1__neg,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.42/5.64 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.42/5.64 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_less_eq_1_neg
% 5.42/5.64 thf(fact_2117_divide__less__0__1__iff,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.42/5.64 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_less_0_1_iff
% 5.42/5.64 thf(fact_2118_divide__less__0__1__iff,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.42/5.64 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_less_0_1_iff
% 5.42/5.64 thf(fact_2119_eq__divide__eq__numeral1_I1_J,axiom,
% 5.42/5.64 ! [A: complex,B: complex,W: num] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.42/5.64 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.42/5.64 != zero_zero_complex )
% 5.42/5.64 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.42/5.64 = B ) )
% 5.42/5.64 & ( ( ( numera6690914467698888265omplex @ W )
% 5.42/5.64 = zero_zero_complex )
% 5.42/5.64 => ( A = zero_zero_complex ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % eq_divide_eq_numeral1(1)
% 5.42/5.64 thf(fact_2120_eq__divide__eq__numeral1_I1_J,axiom,
% 5.42/5.64 ! [A: real,B: real,W: num] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.42/5.64 = ( ( ( ( numeral_numeral_real @ W )
% 5.42/5.64 != zero_zero_real )
% 5.42/5.64 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.42/5.64 = B ) )
% 5.42/5.64 & ( ( ( numeral_numeral_real @ W )
% 5.42/5.64 = zero_zero_real )
% 5.42/5.64 => ( A = zero_zero_real ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % eq_divide_eq_numeral1(1)
% 5.42/5.64 thf(fact_2121_eq__divide__eq__numeral1_I1_J,axiom,
% 5.42/5.64 ! [A: rat,B: rat,W: num] :
% 5.42/5.64 ( ( A
% 5.42/5.64 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.42/5.64 = ( ( ( ( numeral_numeral_rat @ W )
% 5.42/5.64 != zero_zero_rat )
% 5.42/5.64 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.42/5.64 = B ) )
% 5.42/5.64 & ( ( ( numeral_numeral_rat @ W )
% 5.42/5.64 = zero_zero_rat )
% 5.42/5.64 => ( A = zero_zero_rat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % eq_divide_eq_numeral1(1)
% 5.42/5.64 thf(fact_2122_divide__eq__eq__numeral1_I1_J,axiom,
% 5.42/5.64 ! [B: complex,W: num,A: complex] :
% 5.42/5.64 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.42/5.64 = A )
% 5.42/5.64 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.42/5.64 != zero_zero_complex )
% 5.42/5.64 => ( B
% 5.42/5.64 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.42/5.64 & ( ( ( numera6690914467698888265omplex @ W )
% 5.42/5.64 = zero_zero_complex )
% 5.42/5.64 => ( A = zero_zero_complex ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_eq_numeral1(1)
% 5.42/5.64 thf(fact_2123_divide__eq__eq__numeral1_I1_J,axiom,
% 5.42/5.64 ! [B: real,W: num,A: real] :
% 5.42/5.64 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.42/5.64 = A )
% 5.42/5.64 = ( ( ( ( numeral_numeral_real @ W )
% 5.42/5.64 != zero_zero_real )
% 5.42/5.64 => ( B
% 5.42/5.64 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.42/5.64 & ( ( ( numeral_numeral_real @ W )
% 5.42/5.64 = zero_zero_real )
% 5.42/5.64 => ( A = zero_zero_real ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_eq_numeral1(1)
% 5.42/5.64 thf(fact_2124_divide__eq__eq__numeral1_I1_J,axiom,
% 5.42/5.64 ! [B: rat,W: num,A: rat] :
% 5.42/5.64 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.42/5.64 = A )
% 5.42/5.64 = ( ( ( ( numeral_numeral_rat @ W )
% 5.42/5.64 != zero_zero_rat )
% 5.42/5.64 => ( B
% 5.42/5.64 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.42/5.64 & ( ( ( numeral_numeral_rat @ W )
% 5.42/5.64 = zero_zero_rat )
% 5.42/5.64 => ( A = zero_zero_rat ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_eq_eq_numeral1(1)
% 5.42/5.64 thf(fact_2125_nonzero__divide__mult__cancel__right,axiom,
% 5.42/5.64 ! [B: complex,A: complex] :
% 5.42/5.64 ( ( B != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.42/5.64 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_divide_mult_cancel_right
% 5.42/5.64 thf(fact_2126_nonzero__divide__mult__cancel__right,axiom,
% 5.42/5.64 ! [B: real,A: real] :
% 5.42/5.64 ( ( B != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.42/5.64 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_divide_mult_cancel_right
% 5.42/5.64 thf(fact_2127_nonzero__divide__mult__cancel__right,axiom,
% 5.42/5.64 ! [B: rat,A: rat] :
% 5.42/5.64 ( ( B != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.42/5.64 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_divide_mult_cancel_right
% 5.42/5.64 thf(fact_2128_nonzero__divide__mult__cancel__left,axiom,
% 5.42/5.64 ! [A: complex,B: complex] :
% 5.42/5.64 ( ( A != zero_zero_complex )
% 5.42/5.64 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.42/5.64 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_divide_mult_cancel_left
% 5.42/5.64 thf(fact_2129_nonzero__divide__mult__cancel__left,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( A != zero_zero_real )
% 5.42/5.64 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.42/5.64 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_divide_mult_cancel_left
% 5.42/5.64 thf(fact_2130_nonzero__divide__mult__cancel__left,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( A != zero_zero_rat )
% 5.42/5.64 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.42/5.64 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nonzero_divide_mult_cancel_left
% 5.42/5.64 thf(fact_2131_div__mult__self4,axiom,
% 5.42/5.64 ! [B: nat,C: nat,A: nat] :
% 5.42/5.64 ( ( B != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.42/5.64 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self4
% 5.42/5.64 thf(fact_2132_div__mult__self4,axiom,
% 5.42/5.64 ! [B: int,C: int,A: int] :
% 5.42/5.64 ( ( B != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.42/5.64 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self4
% 5.42/5.64 thf(fact_2133_div__mult__self3,axiom,
% 5.42/5.64 ! [B: nat,C: nat,A: nat] :
% 5.42/5.64 ( ( B != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.42/5.64 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self3
% 5.42/5.64 thf(fact_2134_div__mult__self3,axiom,
% 5.42/5.64 ! [B: int,C: int,A: int] :
% 5.42/5.64 ( ( B != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.42/5.64 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self3
% 5.42/5.64 thf(fact_2135_div__mult__self2,axiom,
% 5.42/5.64 ! [B: nat,A: nat,C: nat] :
% 5.42/5.64 ( ( B != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.42/5.64 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self2
% 5.42/5.64 thf(fact_2136_div__mult__self2,axiom,
% 5.42/5.64 ! [B: int,A: int,C: int] :
% 5.42/5.64 ( ( B != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.42/5.64 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self2
% 5.42/5.64 thf(fact_2137_div__mult__self1,axiom,
% 5.42/5.64 ! [B: nat,A: nat,C: nat] :
% 5.42/5.64 ( ( B != zero_zero_nat )
% 5.42/5.64 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.42/5.64 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self1
% 5.42/5.64 thf(fact_2138_div__mult__self1,axiom,
% 5.42/5.64 ! [B: int,A: int,C: int] :
% 5.42/5.64 ( ( B != zero_zero_int )
% 5.42/5.64 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.42/5.64 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self1
% 5.42/5.64 thf(fact_2139_power__eq__0__iff,axiom,
% 5.42/5.64 ! [A: rat,N: nat] :
% 5.42/5.64 ( ( ( power_power_rat @ A @ N )
% 5.42/5.64 = zero_zero_rat )
% 5.42/5.64 = ( ( A = zero_zero_rat )
% 5.42/5.64 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_eq_0_iff
% 5.42/5.64 thf(fact_2140_power__eq__0__iff,axiom,
% 5.42/5.64 ! [A: nat,N: nat] :
% 5.42/5.64 ( ( ( power_power_nat @ A @ N )
% 5.42/5.64 = zero_zero_nat )
% 5.42/5.64 = ( ( A = zero_zero_nat )
% 5.42/5.64 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_eq_0_iff
% 5.42/5.64 thf(fact_2141_power__eq__0__iff,axiom,
% 5.42/5.64 ! [A: real,N: nat] :
% 5.42/5.64 ( ( ( power_power_real @ A @ N )
% 5.42/5.64 = zero_zero_real )
% 5.42/5.64 = ( ( A = zero_zero_real )
% 5.42/5.64 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_eq_0_iff
% 5.42/5.64 thf(fact_2142_power__eq__0__iff,axiom,
% 5.42/5.64 ! [A: complex,N: nat] :
% 5.42/5.64 ( ( ( power_power_complex @ A @ N )
% 5.42/5.64 = zero_zero_complex )
% 5.42/5.64 = ( ( A = zero_zero_complex )
% 5.42/5.64 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_eq_0_iff
% 5.42/5.64 thf(fact_2143_power__eq__0__iff,axiom,
% 5.42/5.64 ! [A: int,N: nat] :
% 5.42/5.64 ( ( ( power_power_int @ A @ N )
% 5.42/5.64 = zero_zero_int )
% 5.42/5.64 = ( ( A = zero_zero_int )
% 5.42/5.64 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_eq_0_iff
% 5.42/5.64 thf(fact_2144_Suc__pred,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.64 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.42/5.64 = N ) ) ).
% 5.42/5.64
% 5.42/5.64 % Suc_pred
% 5.42/5.64 thf(fact_2145_one__le__mult__iff,axiom,
% 5.42/5.64 ! [M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.42/5.64 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.42/5.64 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % one_le_mult_iff
% 5.42/5.64 thf(fact_2146_mult__le__cancel2,axiom,
% 5.42/5.64 ! [M: nat,K: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.42/5.64 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.42/5.64 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % mult_le_cancel2
% 5.42/5.64 thf(fact_2147_nat__mult__le__cancel__disj,axiom,
% 5.42/5.64 ! [K: nat,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.42/5.64 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.42/5.64 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % nat_mult_le_cancel_disj
% 5.42/5.64 thf(fact_2148_div__mult__self1__is__m,axiom,
% 5.42/5.64 ! [N: nat,M: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.42/5.64 = M ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self1_is_m
% 5.42/5.64 thf(fact_2149_div__mult__self__is__m,axiom,
% 5.42/5.64 ! [N: nat,M: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.64 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.42/5.64 = M ) ) ).
% 5.42/5.64
% 5.42/5.64 % div_mult_self_is_m
% 5.42/5.64 thf(fact_2150_le__divide__eq__1__pos,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.42/5.64 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.42/5.64 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_divide_eq_1_pos
% 5.42/5.64 thf(fact_2151_le__divide__eq__1__pos,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.42/5.64 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.42/5.64 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_divide_eq_1_pos
% 5.42/5.64 thf(fact_2152_le__divide__eq__1__neg,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ A @ zero_zero_real )
% 5.42/5.64 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.42/5.64 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_divide_eq_1_neg
% 5.42/5.64 thf(fact_2153_le__divide__eq__1__neg,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.42/5.64 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.42/5.64 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % le_divide_eq_1_neg
% 5.42/5.64 thf(fact_2154_divide__le__eq__1__pos,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.42/5.64 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.42/5.64 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_le_eq_1_pos
% 5.42/5.64 thf(fact_2155_divide__le__eq__1__pos,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.42/5.64 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.42/5.64 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_le_eq_1_pos
% 5.42/5.64 thf(fact_2156_divide__le__eq__1__neg,axiom,
% 5.42/5.64 ! [A: real,B: real] :
% 5.42/5.64 ( ( ord_less_real @ A @ zero_zero_real )
% 5.42/5.64 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.42/5.64 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_le_eq_1_neg
% 5.42/5.64 thf(fact_2157_divide__le__eq__1__neg,axiom,
% 5.42/5.64 ! [A: rat,B: rat] :
% 5.42/5.64 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.42/5.64 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.42/5.64 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % divide_le_eq_1_neg
% 5.42/5.64 thf(fact_2158_power__strict__decreasing__iff,axiom,
% 5.42/5.64 ! [B: real,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ B )
% 5.42/5.64 => ( ( ord_less_real @ B @ one_one_real )
% 5.42/5.64 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.42/5.64 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_strict_decreasing_iff
% 5.42/5.64 thf(fact_2159_power__strict__decreasing__iff,axiom,
% 5.42/5.64 ! [B: rat,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.42/5.64 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.42/5.64 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.42/5.64 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_strict_decreasing_iff
% 5.42/5.64 thf(fact_2160_power__strict__decreasing__iff,axiom,
% 5.42/5.64 ! [B: nat,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.42/5.64 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.42/5.64 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.42/5.64 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_strict_decreasing_iff
% 5.42/5.64 thf(fact_2161_power__strict__decreasing__iff,axiom,
% 5.42/5.64 ! [B: int,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_int @ zero_zero_int @ B )
% 5.42/5.64 => ( ( ord_less_int @ B @ one_one_int )
% 5.42/5.64 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.42/5.64 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_strict_decreasing_iff
% 5.42/5.64 thf(fact_2162_zero__eq__power2,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = zero_zero_rat )
% 5.42/5.64 = ( A = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_eq_power2
% 5.42/5.64 thf(fact_2163_zero__eq__power2,axiom,
% 5.42/5.64 ! [A: nat] :
% 5.42/5.64 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = zero_zero_nat )
% 5.42/5.64 = ( A = zero_zero_nat ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_eq_power2
% 5.42/5.64 thf(fact_2164_zero__eq__power2,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = zero_zero_real )
% 5.42/5.64 = ( A = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_eq_power2
% 5.42/5.64 thf(fact_2165_zero__eq__power2,axiom,
% 5.42/5.64 ! [A: complex] :
% 5.42/5.64 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = zero_zero_complex )
% 5.42/5.64 = ( A = zero_zero_complex ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_eq_power2
% 5.42/5.64 thf(fact_2166_zero__eq__power2,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = zero_zero_int )
% 5.42/5.64 = ( A = zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_eq_power2
% 5.42/5.64 thf(fact_2167_power__mono__iff,axiom,
% 5.42/5.64 ! [A: real,B: real,N: nat] :
% 5.42/5.64 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.42/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.64 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.42/5.64 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_mono_iff
% 5.42/5.64 thf(fact_2168_power__mono__iff,axiom,
% 5.42/5.64 ! [A: rat,B: rat,N: nat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.42/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.64 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.42/5.64 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_mono_iff
% 5.42/5.64 thf(fact_2169_power__mono__iff,axiom,
% 5.42/5.64 ! [A: nat,B: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.42/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.64 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.42/5.64 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_mono_iff
% 5.42/5.64 thf(fact_2170_power__mono__iff,axiom,
% 5.42/5.64 ! [A: int,B: int,N: nat] :
% 5.42/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.42/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.64 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.42/5.64 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_mono_iff
% 5.42/5.64 thf(fact_2171_Suc__diff__1,axiom,
% 5.42/5.64 ! [N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.64 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.42/5.64 = N ) ) ).
% 5.42/5.64
% 5.42/5.64 % Suc_diff_1
% 5.42/5.64 thf(fact_2172_bits__1__div__2,axiom,
% 5.42/5.64 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % bits_1_div_2
% 5.42/5.64 thf(fact_2173_bits__1__div__2,axiom,
% 5.42/5.64 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % bits_1_div_2
% 5.42/5.64 thf(fact_2174_one__div__two__eq__zero,axiom,
% 5.42/5.64 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = zero_zero_nat ) ).
% 5.42/5.64
% 5.42/5.64 % one_div_two_eq_zero
% 5.42/5.64 thf(fact_2175_one__div__two__eq__zero,axiom,
% 5.42/5.64 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.64 = zero_zero_int ) ).
% 5.42/5.64
% 5.42/5.64 % one_div_two_eq_zero
% 5.42/5.64 thf(fact_2176_power__decreasing__iff,axiom,
% 5.42/5.64 ! [B: real,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ B )
% 5.42/5.64 => ( ( ord_less_real @ B @ one_one_real )
% 5.42/5.64 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.42/5.64 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_decreasing_iff
% 5.42/5.64 thf(fact_2177_power__decreasing__iff,axiom,
% 5.42/5.64 ! [B: rat,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.42/5.64 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.42/5.64 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.42/5.64 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_decreasing_iff
% 5.42/5.64 thf(fact_2178_power__decreasing__iff,axiom,
% 5.42/5.64 ! [B: nat,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.42/5.64 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.42/5.64 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.42/5.64 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_decreasing_iff
% 5.42/5.64 thf(fact_2179_power__decreasing__iff,axiom,
% 5.42/5.64 ! [B: int,M: nat,N: nat] :
% 5.42/5.64 ( ( ord_less_int @ zero_zero_int @ B )
% 5.42/5.64 => ( ( ord_less_int @ B @ one_one_int )
% 5.42/5.64 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.42/5.64 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power_decreasing_iff
% 5.42/5.64 thf(fact_2180_power2__eq__iff__nonneg,axiom,
% 5.42/5.64 ! [X2: real,Y2: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.42/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.42/5.64 => ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.64 = ( X2 = Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power2_eq_iff_nonneg
% 5.42/5.64 thf(fact_2181_power2__eq__iff__nonneg,axiom,
% 5.42/5.64 ! [X2: rat,Y2: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.42/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.42/5.64 => ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.64 = ( X2 = Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power2_eq_iff_nonneg
% 5.42/5.64 thf(fact_2182_power2__eq__iff__nonneg,axiom,
% 5.42/5.64 ! [X2: nat,Y2: nat] :
% 5.42/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.42/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.42/5.64 => ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.64 = ( X2 = Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power2_eq_iff_nonneg
% 5.42/5.64 thf(fact_2183_power2__eq__iff__nonneg,axiom,
% 5.42/5.64 ! [X2: int,Y2: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.42/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.42/5.64 => ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.64 = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.64 = ( X2 = Y2 ) ) ) ) ).
% 5.42/5.64
% 5.42/5.64 % power2_eq_iff_nonneg
% 5.42/5.64 thf(fact_2184_power2__less__eq__zero__iff,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.42/5.64 = ( A = zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % power2_less_eq_zero_iff
% 5.42/5.64 thf(fact_2185_power2__less__eq__zero__iff,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.42/5.64 = ( A = zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % power2_less_eq_zero_iff
% 5.42/5.64 thf(fact_2186_power2__less__eq__zero__iff,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.42/5.64 = ( A = zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % power2_less_eq_zero_iff
% 5.42/5.64 thf(fact_2187_zero__less__power2,axiom,
% 5.42/5.64 ! [A: real] :
% 5.42/5.64 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.64 = ( A != zero_zero_real ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_power2
% 5.42/5.64 thf(fact_2188_zero__less__power2,axiom,
% 5.42/5.64 ! [A: rat] :
% 5.42/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.64 = ( A != zero_zero_rat ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_power2
% 5.42/5.64 thf(fact_2189_zero__less__power2,axiom,
% 5.42/5.64 ! [A: int] :
% 5.42/5.64 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.64 = ( A != zero_zero_int ) ) ).
% 5.42/5.64
% 5.42/5.64 % zero_less_power2
% 5.42/5.64 thf(fact_2190_sum__power2__eq__zero__iff,axiom,
% 5.42/5.64 ! [X2: rat,Y2: rat] :
% 5.42/5.64 ( ( ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.65 = zero_zero_rat )
% 5.42/5.65 = ( ( X2 = zero_zero_rat )
% 5.42/5.65 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum_power2_eq_zero_iff
% 5.42/5.65 thf(fact_2191_sum__power2__eq__zero__iff,axiom,
% 5.42/5.65 ! [X2: real,Y2: real] :
% 5.42/5.65 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.65 = zero_zero_real )
% 5.42/5.65 = ( ( X2 = zero_zero_real )
% 5.42/5.65 & ( Y2 = zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum_power2_eq_zero_iff
% 5.42/5.65 thf(fact_2192_sum__power2__eq__zero__iff,axiom,
% 5.42/5.65 ! [X2: int,Y2: int] :
% 5.42/5.65 ( ( ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.65 = zero_zero_int )
% 5.42/5.65 = ( ( X2 = zero_zero_int )
% 5.42/5.65 & ( Y2 = zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum_power2_eq_zero_iff
% 5.42/5.65 thf(fact_2193_not__mod__2__eq__1__eq__0,axiom,
% 5.42/5.65 ! [A: nat] :
% 5.42/5.65 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.65 != one_one_nat )
% 5.42/5.65 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.65 = zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % not_mod_2_eq_1_eq_0
% 5.42/5.65 thf(fact_2194_not__mod__2__eq__1__eq__0,axiom,
% 5.42/5.65 ! [A: int] :
% 5.42/5.65 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.65 != one_one_int )
% 5.42/5.65 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.65 = zero_zero_int ) ) ).
% 5.42/5.65
% 5.42/5.65 % not_mod_2_eq_1_eq_0
% 5.42/5.65 thf(fact_2195_not__mod__2__eq__1__eq__0,axiom,
% 5.42/5.65 ! [A: code_integer] :
% 5.42/5.65 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.42/5.65 != one_one_Code_integer )
% 5.42/5.65 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.42/5.65 = zero_z3403309356797280102nteger ) ) ).
% 5.42/5.65
% 5.42/5.65 % not_mod_2_eq_1_eq_0
% 5.42/5.65 thf(fact_2196_not__mod__2__eq__0__eq__1,axiom,
% 5.42/5.65 ! [A: nat] :
% 5.42/5.65 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.65 != zero_zero_nat )
% 5.42/5.65 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.65 = one_one_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % not_mod_2_eq_0_eq_1
% 5.42/5.65 thf(fact_2197_not__mod__2__eq__0__eq__1,axiom,
% 5.42/5.65 ! [A: int] :
% 5.42/5.65 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.65 != zero_zero_int )
% 5.42/5.65 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.42/5.65 = one_one_int ) ) ).
% 5.42/5.65
% 5.42/5.65 % not_mod_2_eq_0_eq_1
% 5.42/5.65 thf(fact_2198_not__mod__2__eq__0__eq__1,axiom,
% 5.42/5.65 ! [A: code_integer] :
% 5.42/5.65 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.42/5.65 != zero_z3403309356797280102nteger )
% 5.42/5.65 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.42/5.65 = one_one_Code_integer ) ) ).
% 5.42/5.65
% 5.42/5.65 % not_mod_2_eq_0_eq_1
% 5.42/5.65 thf(fact_2199_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.65 != ( suc @ zero_zero_nat ) )
% 5.42/5.65 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.65 = zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % not_mod2_eq_Suc_0_eq_0
% 5.42/5.65 thf(fact_2200_add__self__mod__2,axiom,
% 5.42/5.65 ! [M: nat] :
% 5.42/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.65 = zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % add_self_mod_2
% 5.42/5.65 thf(fact_2201_mod2__gr__0,axiom,
% 5.42/5.65 ! [M: nat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.42/5.65 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.42/5.65 = one_one_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % mod2_gr_0
% 5.42/5.65 thf(fact_2202_unset__bit__0,axiom,
% 5.42/5.65 ! [A: int] :
% 5.42/5.65 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.42/5.65 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % unset_bit_0
% 5.42/5.65 thf(fact_2203_unset__bit__0,axiom,
% 5.42/5.65 ! [A: nat] :
% 5.42/5.65 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.42/5.65 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % unset_bit_0
% 5.42/5.65 thf(fact_2204_VEBT_Osize_I4_J,axiom,
% 5.42/5.65 ! [X21: $o,X222: $o] :
% 5.42/5.65 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.42/5.65 = zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % VEBT.size(4)
% 5.42/5.65 thf(fact_2205_zero__reorient,axiom,
% 5.42/5.65 ! [X2: complex] :
% 5.42/5.65 ( ( zero_zero_complex = X2 )
% 5.42/5.65 = ( X2 = zero_zero_complex ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_reorient
% 5.42/5.65 thf(fact_2206_zero__reorient,axiom,
% 5.42/5.65 ! [X2: real] :
% 5.42/5.65 ( ( zero_zero_real = X2 )
% 5.42/5.65 = ( X2 = zero_zero_real ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_reorient
% 5.42/5.65 thf(fact_2207_zero__reorient,axiom,
% 5.42/5.65 ! [X2: rat] :
% 5.42/5.65 ( ( zero_zero_rat = X2 )
% 5.42/5.65 = ( X2 = zero_zero_rat ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_reorient
% 5.42/5.65 thf(fact_2208_zero__reorient,axiom,
% 5.42/5.65 ! [X2: nat] :
% 5.42/5.65 ( ( zero_zero_nat = X2 )
% 5.42/5.65 = ( X2 = zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_reorient
% 5.42/5.65 thf(fact_2209_zero__reorient,axiom,
% 5.42/5.65 ! [X2: int] :
% 5.42/5.65 ( ( zero_zero_int = X2 )
% 5.42/5.65 = ( X2 = zero_zero_int ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_reorient
% 5.42/5.65 thf(fact_2210_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.42/5.65 ! [X2: produc9072475918466114483BT_nat] :
% 5.42/5.65 ( ! [A5: $o,B5: $o,X3: nat] :
% 5.42/5.65 ( X2
% 5.42/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X3 ) )
% 5.42/5.65 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.42/5.65 ( X2
% 5.42/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.42/5.65 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT,X3: nat] :
% 5.42/5.65 ( X2
% 5.42/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ X3 ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % VEBT_internal.naive_member.cases
% 5.42/5.65 thf(fact_2211_invar__vebt_Ointros_I1_J,axiom,
% 5.42/5.65 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % invar_vebt.intros(1)
% 5.42/5.65 thf(fact_2212_power__0__left,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ( N = zero_zero_nat )
% 5.42/5.65 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.42/5.65 = one_one_rat ) )
% 5.42/5.65 & ( ( N != zero_zero_nat )
% 5.42/5.65 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.42/5.65 = zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_0_left
% 5.42/5.65 thf(fact_2213_power__0__left,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ( N = zero_zero_nat )
% 5.42/5.65 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.42/5.65 = one_one_nat ) )
% 5.42/5.65 & ( ( N != zero_zero_nat )
% 5.42/5.65 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.42/5.65 = zero_zero_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_0_left
% 5.42/5.65 thf(fact_2214_power__0__left,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ( N = zero_zero_nat )
% 5.42/5.65 => ( ( power_power_real @ zero_zero_real @ N )
% 5.42/5.65 = one_one_real ) )
% 5.42/5.65 & ( ( N != zero_zero_nat )
% 5.42/5.65 => ( ( power_power_real @ zero_zero_real @ N )
% 5.42/5.65 = zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_0_left
% 5.42/5.65 thf(fact_2215_power__0__left,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ( N = zero_zero_nat )
% 5.42/5.65 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.42/5.65 = one_one_complex ) )
% 5.42/5.65 & ( ( N != zero_zero_nat )
% 5.42/5.65 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.42/5.65 = zero_zero_complex ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_0_left
% 5.42/5.65 thf(fact_2216_power__0__left,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ( N = zero_zero_nat )
% 5.42/5.65 => ( ( power_power_int @ zero_zero_int @ N )
% 5.42/5.65 = one_one_int ) )
% 5.42/5.65 & ( ( N != zero_zero_nat )
% 5.42/5.65 => ( ( power_power_int @ zero_zero_int @ N )
% 5.42/5.65 = zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_0_left
% 5.42/5.65 thf(fact_2217_zero__power,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.42/5.65 = zero_zero_rat ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_power
% 5.42/5.65 thf(fact_2218_zero__power,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.42/5.65 = zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_power
% 5.42/5.65 thf(fact_2219_zero__power,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ( power_power_real @ zero_zero_real @ N )
% 5.42/5.65 = zero_zero_real ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_power
% 5.42/5.65 thf(fact_2220_zero__power,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.42/5.65 = zero_zero_complex ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_power
% 5.42/5.65 thf(fact_2221_zero__power,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ( power_power_int @ zero_zero_int @ N )
% 5.42/5.65 = zero_zero_int ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_power
% 5.42/5.65 thf(fact_2222_vebt__member_Osimps_I1_J,axiom,
% 5.42/5.65 ! [A: $o,B: $o,X2: nat] :
% 5.42/5.65 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.42/5.65 = ( ( ( X2 = zero_zero_nat )
% 5.42/5.65 => A )
% 5.42/5.65 & ( ( X2 != zero_zero_nat )
% 5.42/5.65 => ( ( ( X2 = one_one_nat )
% 5.42/5.65 => B )
% 5.42/5.65 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % vebt_member.simps(1)
% 5.42/5.65 thf(fact_2223_VEBT_Oexhaust,axiom,
% 5.42/5.65 ! [Y2: vEBT_VEBT] :
% 5.42/5.65 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.42/5.65 ( Y2
% 5.42/5.65 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.42/5.65 => ~ ! [X212: $o,X223: $o] :
% 5.42/5.65 ( Y2
% 5.42/5.65 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % VEBT.exhaust
% 5.42/5.65 thf(fact_2224_VEBT_Odistinct_I1_J,axiom,
% 5.42/5.65 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.42/5.65 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.42/5.65 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.42/5.65
% 5.42/5.65 % VEBT.distinct(1)
% 5.42/5.65 thf(fact_2225_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.42/5.65 ! [X2: produc9072475918466114483BT_nat] :
% 5.42/5.65 ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 5.42/5.65 ( X2
% 5.42/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 5.42/5.65 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.42/5.65 ( X2
% 5.42/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % VEBT_internal.valid'.cases
% 5.42/5.65 thf(fact_2226_vebt__buildup_Osimps_I2_J,axiom,
% 5.42/5.65 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.42/5.65 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.42/5.65
% 5.42/5.65 % vebt_buildup.simps(2)
% 5.42/5.65 thf(fact_2227_vebt__insert_Osimps_I1_J,axiom,
% 5.42/5.65 ! [X2: nat,A: $o,B: $o] :
% 5.42/5.65 ( ( ( X2 = zero_zero_nat )
% 5.42/5.65 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.42/5.65 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.42/5.65 & ( ( X2 != zero_zero_nat )
% 5.42/5.65 => ( ( ( X2 = one_one_nat )
% 5.42/5.65 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.42/5.65 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.42/5.65 & ( ( X2 != one_one_nat )
% 5.42/5.65 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.42/5.65 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % vebt_insert.simps(1)
% 5.42/5.65 thf(fact_2228_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.42/5.65 ! [A: $o,B: $o,X2: nat] :
% 5.42/5.65 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.42/5.65 = ( ( ( X2 = zero_zero_nat )
% 5.42/5.65 => A )
% 5.42/5.65 & ( ( X2 != zero_zero_nat )
% 5.42/5.65 => ( ( ( X2 = one_one_nat )
% 5.42/5.65 => B )
% 5.42/5.65 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % VEBT_internal.naive_member.simps(1)
% 5.42/5.65 thf(fact_2229_le__numeral__extra_I3_J,axiom,
% 5.42/5.65 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.42/5.65
% 5.42/5.65 % le_numeral_extra(3)
% 5.42/5.65 thf(fact_2230_le__numeral__extra_I3_J,axiom,
% 5.42/5.65 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.42/5.65
% 5.42/5.65 % le_numeral_extra(3)
% 5.42/5.65 thf(fact_2231_le__numeral__extra_I3_J,axiom,
% 5.42/5.65 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.42/5.65
% 5.42/5.65 % le_numeral_extra(3)
% 5.42/5.65 thf(fact_2232_le__numeral__extra_I3_J,axiom,
% 5.42/5.65 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.42/5.65
% 5.42/5.65 % le_numeral_extra(3)
% 5.42/5.65 thf(fact_2233_zero__le,axiom,
% 5.42/5.65 ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le
% 5.42/5.65 thf(fact_2234_field__lbound__gt__zero,axiom,
% 5.42/5.65 ! [D1: real,D22: real] :
% 5.42/5.65 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.42/5.65 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.42/5.65 => ? [E2: real] :
% 5.42/5.65 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.42/5.65 & ( ord_less_real @ E2 @ D1 )
% 5.42/5.65 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % field_lbound_gt_zero
% 5.42/5.65 thf(fact_2235_field__lbound__gt__zero,axiom,
% 5.42/5.65 ! [D1: rat,D22: rat] :
% 5.42/5.65 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.42/5.65 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.42/5.65 => ? [E2: rat] :
% 5.42/5.65 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.42/5.65 & ( ord_less_rat @ E2 @ D1 )
% 5.42/5.65 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % field_lbound_gt_zero
% 5.42/5.65 thf(fact_2236_less__numeral__extra_I3_J,axiom,
% 5.42/5.65 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.42/5.65
% 5.42/5.65 % less_numeral_extra(3)
% 5.42/5.65 thf(fact_2237_less__numeral__extra_I3_J,axiom,
% 5.42/5.65 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.42/5.65
% 5.42/5.65 % less_numeral_extra(3)
% 5.42/5.65 thf(fact_2238_less__numeral__extra_I3_J,axiom,
% 5.42/5.65 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % less_numeral_extra(3)
% 5.42/5.65 thf(fact_2239_less__numeral__extra_I3_J,axiom,
% 5.42/5.65 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.42/5.65
% 5.42/5.65 % less_numeral_extra(3)
% 5.42/5.65 thf(fact_2240_gr__zeroI,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( N != zero_zero_nat )
% 5.42/5.65 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % gr_zeroI
% 5.42/5.65 thf(fact_2241_not__less__zero,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % not_less_zero
% 5.42/5.65 thf(fact_2242_gr__implies__not__zero,axiom,
% 5.42/5.65 ! [M: nat,N: nat] :
% 5.42/5.65 ( ( ord_less_nat @ M @ N )
% 5.42/5.65 => ( N != zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % gr_implies_not_zero
% 5.42/5.65 thf(fact_2243_zero__less__iff__neq__zero,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 = ( N != zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_less_iff_neq_zero
% 5.42/5.65 thf(fact_2244_zero__neq__numeral,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ( zero_zero_complex
% 5.42/5.65 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_numeral
% 5.42/5.65 thf(fact_2245_zero__neq__numeral,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ( zero_zero_real
% 5.42/5.65 != ( numeral_numeral_real @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_numeral
% 5.42/5.65 thf(fact_2246_zero__neq__numeral,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ( zero_zero_rat
% 5.42/5.65 != ( numeral_numeral_rat @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_numeral
% 5.42/5.65 thf(fact_2247_zero__neq__numeral,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ( zero_zero_nat
% 5.42/5.65 != ( numeral_numeral_nat @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_numeral
% 5.42/5.65 thf(fact_2248_zero__neq__numeral,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ( zero_zero_int
% 5.42/5.65 != ( numeral_numeral_int @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_numeral
% 5.42/5.65 thf(fact_2249_mult__right__cancel,axiom,
% 5.42/5.65 ! [C: complex,A: complex,B: complex] :
% 5.42/5.65 ( ( C != zero_zero_complex )
% 5.42/5.65 => ( ( ( times_times_complex @ A @ C )
% 5.42/5.65 = ( times_times_complex @ B @ C ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_cancel
% 5.42/5.65 thf(fact_2250_mult__right__cancel,axiom,
% 5.42/5.65 ! [C: real,A: real,B: real] :
% 5.42/5.65 ( ( C != zero_zero_real )
% 5.42/5.65 => ( ( ( times_times_real @ A @ C )
% 5.42/5.65 = ( times_times_real @ B @ C ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_cancel
% 5.42/5.65 thf(fact_2251_mult__right__cancel,axiom,
% 5.42/5.65 ! [C: rat,A: rat,B: rat] :
% 5.42/5.65 ( ( C != zero_zero_rat )
% 5.42/5.65 => ( ( ( times_times_rat @ A @ C )
% 5.42/5.65 = ( times_times_rat @ B @ C ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_cancel
% 5.42/5.65 thf(fact_2252_mult__right__cancel,axiom,
% 5.42/5.65 ! [C: nat,A: nat,B: nat] :
% 5.42/5.65 ( ( C != zero_zero_nat )
% 5.42/5.65 => ( ( ( times_times_nat @ A @ C )
% 5.42/5.65 = ( times_times_nat @ B @ C ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_cancel
% 5.42/5.65 thf(fact_2253_mult__right__cancel,axiom,
% 5.42/5.65 ! [C: int,A: int,B: int] :
% 5.42/5.65 ( ( C != zero_zero_int )
% 5.42/5.65 => ( ( ( times_times_int @ A @ C )
% 5.42/5.65 = ( times_times_int @ B @ C ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_cancel
% 5.42/5.65 thf(fact_2254_mult__left__cancel,axiom,
% 5.42/5.65 ! [C: complex,A: complex,B: complex] :
% 5.42/5.65 ( ( C != zero_zero_complex )
% 5.42/5.65 => ( ( ( times_times_complex @ C @ A )
% 5.42/5.65 = ( times_times_complex @ C @ B ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_cancel
% 5.42/5.65 thf(fact_2255_mult__left__cancel,axiom,
% 5.42/5.65 ! [C: real,A: real,B: real] :
% 5.42/5.65 ( ( C != zero_zero_real )
% 5.42/5.65 => ( ( ( times_times_real @ C @ A )
% 5.42/5.65 = ( times_times_real @ C @ B ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_cancel
% 5.42/5.65 thf(fact_2256_mult__left__cancel,axiom,
% 5.42/5.65 ! [C: rat,A: rat,B: rat] :
% 5.42/5.65 ( ( C != zero_zero_rat )
% 5.42/5.65 => ( ( ( times_times_rat @ C @ A )
% 5.42/5.65 = ( times_times_rat @ C @ B ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_cancel
% 5.42/5.65 thf(fact_2257_mult__left__cancel,axiom,
% 5.42/5.65 ! [C: nat,A: nat,B: nat] :
% 5.42/5.65 ( ( C != zero_zero_nat )
% 5.42/5.65 => ( ( ( times_times_nat @ C @ A )
% 5.42/5.65 = ( times_times_nat @ C @ B ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_cancel
% 5.42/5.65 thf(fact_2258_mult__left__cancel,axiom,
% 5.42/5.65 ! [C: int,A: int,B: int] :
% 5.42/5.65 ( ( C != zero_zero_int )
% 5.42/5.65 => ( ( ( times_times_int @ C @ A )
% 5.42/5.65 = ( times_times_int @ C @ B ) )
% 5.42/5.65 = ( A = B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_cancel
% 5.42/5.65 thf(fact_2259_no__zero__divisors,axiom,
% 5.42/5.65 ! [A: complex,B: complex] :
% 5.42/5.65 ( ( A != zero_zero_complex )
% 5.42/5.65 => ( ( B != zero_zero_complex )
% 5.42/5.65 => ( ( times_times_complex @ A @ B )
% 5.42/5.65 != zero_zero_complex ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % no_zero_divisors
% 5.42/5.65 thf(fact_2260_no__zero__divisors,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( A != zero_zero_real )
% 5.42/5.65 => ( ( B != zero_zero_real )
% 5.42/5.65 => ( ( times_times_real @ A @ B )
% 5.42/5.65 != zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % no_zero_divisors
% 5.42/5.65 thf(fact_2261_no__zero__divisors,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( A != zero_zero_rat )
% 5.42/5.65 => ( ( B != zero_zero_rat )
% 5.42/5.65 => ( ( times_times_rat @ A @ B )
% 5.42/5.65 != zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % no_zero_divisors
% 5.42/5.65 thf(fact_2262_no__zero__divisors,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( A != zero_zero_nat )
% 5.42/5.65 => ( ( B != zero_zero_nat )
% 5.42/5.65 => ( ( times_times_nat @ A @ B )
% 5.42/5.65 != zero_zero_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % no_zero_divisors
% 5.42/5.65 thf(fact_2263_no__zero__divisors,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( A != zero_zero_int )
% 5.42/5.65 => ( ( B != zero_zero_int )
% 5.42/5.65 => ( ( times_times_int @ A @ B )
% 5.42/5.65 != zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % no_zero_divisors
% 5.42/5.65 thf(fact_2264_divisors__zero,axiom,
% 5.42/5.65 ! [A: complex,B: complex] :
% 5.42/5.65 ( ( ( times_times_complex @ A @ B )
% 5.42/5.65 = zero_zero_complex )
% 5.42/5.65 => ( ( A = zero_zero_complex )
% 5.42/5.65 | ( B = zero_zero_complex ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % divisors_zero
% 5.42/5.65 thf(fact_2265_divisors__zero,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ( times_times_real @ A @ B )
% 5.42/5.65 = zero_zero_real )
% 5.42/5.65 => ( ( A = zero_zero_real )
% 5.42/5.65 | ( B = zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % divisors_zero
% 5.42/5.65 thf(fact_2266_divisors__zero,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ( times_times_rat @ A @ B )
% 5.42/5.65 = zero_zero_rat )
% 5.42/5.65 => ( ( A = zero_zero_rat )
% 5.42/5.65 | ( B = zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % divisors_zero
% 5.42/5.65 thf(fact_2267_divisors__zero,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( ( times_times_nat @ A @ B )
% 5.42/5.65 = zero_zero_nat )
% 5.42/5.65 => ( ( A = zero_zero_nat )
% 5.42/5.65 | ( B = zero_zero_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % divisors_zero
% 5.42/5.65 thf(fact_2268_divisors__zero,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ( times_times_int @ A @ B )
% 5.42/5.65 = zero_zero_int )
% 5.42/5.65 => ( ( A = zero_zero_int )
% 5.42/5.65 | ( B = zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % divisors_zero
% 5.42/5.65 thf(fact_2269_mult__not__zero,axiom,
% 5.42/5.65 ! [A: complex,B: complex] :
% 5.42/5.65 ( ( ( times_times_complex @ A @ B )
% 5.42/5.65 != zero_zero_complex )
% 5.42/5.65 => ( ( A != zero_zero_complex )
% 5.42/5.65 & ( B != zero_zero_complex ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_not_zero
% 5.42/5.65 thf(fact_2270_mult__not__zero,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ( times_times_real @ A @ B )
% 5.42/5.65 != zero_zero_real )
% 5.42/5.65 => ( ( A != zero_zero_real )
% 5.42/5.65 & ( B != zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_not_zero
% 5.42/5.65 thf(fact_2271_mult__not__zero,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ( times_times_rat @ A @ B )
% 5.42/5.65 != zero_zero_rat )
% 5.42/5.65 => ( ( A != zero_zero_rat )
% 5.42/5.65 & ( B != zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_not_zero
% 5.42/5.65 thf(fact_2272_mult__not__zero,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( ( times_times_nat @ A @ B )
% 5.42/5.65 != zero_zero_nat )
% 5.42/5.65 => ( ( A != zero_zero_nat )
% 5.42/5.65 & ( B != zero_zero_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_not_zero
% 5.42/5.65 thf(fact_2273_mult__not__zero,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ( times_times_int @ A @ B )
% 5.42/5.65 != zero_zero_int )
% 5.42/5.65 => ( ( A != zero_zero_int )
% 5.42/5.65 & ( B != zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_not_zero
% 5.42/5.65 thf(fact_2274_zero__neq__one,axiom,
% 5.42/5.65 zero_zero_complex != one_one_complex ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_one
% 5.42/5.65 thf(fact_2275_zero__neq__one,axiom,
% 5.42/5.65 zero_zero_real != one_one_real ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_one
% 5.42/5.65 thf(fact_2276_zero__neq__one,axiom,
% 5.42/5.65 zero_zero_rat != one_one_rat ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_one
% 5.42/5.65 thf(fact_2277_zero__neq__one,axiom,
% 5.42/5.65 zero_zero_nat != one_one_nat ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_one
% 5.42/5.65 thf(fact_2278_zero__neq__one,axiom,
% 5.42/5.65 zero_zero_int != one_one_int ).
% 5.42/5.65
% 5.42/5.65 % zero_neq_one
% 5.42/5.65 thf(fact_2279_add_Ogroup__left__neutral,axiom,
% 5.42/5.65 ! [A: complex] :
% 5.42/5.65 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % add.group_left_neutral
% 5.42/5.65 thf(fact_2280_add_Ogroup__left__neutral,axiom,
% 5.42/5.65 ! [A: real] :
% 5.42/5.65 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % add.group_left_neutral
% 5.42/5.65 thf(fact_2281_add_Ogroup__left__neutral,axiom,
% 5.42/5.65 ! [A: rat] :
% 5.42/5.65 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % add.group_left_neutral
% 5.42/5.65 thf(fact_2282_add_Ogroup__left__neutral,axiom,
% 5.42/5.65 ! [A: int] :
% 5.42/5.65 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % add.group_left_neutral
% 5.42/5.65 thf(fact_2283_add_Ocomm__neutral,axiom,
% 5.42/5.65 ! [A: complex] :
% 5.42/5.65 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % add.comm_neutral
% 5.42/5.65 thf(fact_2284_add_Ocomm__neutral,axiom,
% 5.42/5.65 ! [A: real] :
% 5.42/5.65 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % add.comm_neutral
% 5.42/5.65 thf(fact_2285_add_Ocomm__neutral,axiom,
% 5.42/5.65 ! [A: rat] :
% 5.42/5.65 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % add.comm_neutral
% 5.42/5.65 thf(fact_2286_add_Ocomm__neutral,axiom,
% 5.42/5.65 ! [A: nat] :
% 5.42/5.65 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % add.comm_neutral
% 5.42/5.65 thf(fact_2287_add_Ocomm__neutral,axiom,
% 5.42/5.65 ! [A: int] :
% 5.42/5.65 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % add.comm_neutral
% 5.42/5.65 thf(fact_2288_comm__monoid__add__class_Oadd__0,axiom,
% 5.42/5.65 ! [A: complex] :
% 5.42/5.65 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % comm_monoid_add_class.add_0
% 5.42/5.65 thf(fact_2289_comm__monoid__add__class_Oadd__0,axiom,
% 5.42/5.65 ! [A: real] :
% 5.42/5.65 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % comm_monoid_add_class.add_0
% 5.42/5.65 thf(fact_2290_comm__monoid__add__class_Oadd__0,axiom,
% 5.42/5.65 ! [A: rat] :
% 5.42/5.65 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % comm_monoid_add_class.add_0
% 5.42/5.65 thf(fact_2291_comm__monoid__add__class_Oadd__0,axiom,
% 5.42/5.65 ! [A: nat] :
% 5.42/5.65 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % comm_monoid_add_class.add_0
% 5.42/5.65 thf(fact_2292_comm__monoid__add__class_Oadd__0,axiom,
% 5.42/5.65 ! [A: int] :
% 5.42/5.65 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % comm_monoid_add_class.add_0
% 5.42/5.65 thf(fact_2293_verit__sum__simplify,axiom,
% 5.42/5.65 ! [A: complex] :
% 5.42/5.65 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % verit_sum_simplify
% 5.42/5.65 thf(fact_2294_verit__sum__simplify,axiom,
% 5.42/5.65 ! [A: real] :
% 5.42/5.65 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % verit_sum_simplify
% 5.42/5.65 thf(fact_2295_verit__sum__simplify,axiom,
% 5.42/5.65 ! [A: rat] :
% 5.42/5.65 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % verit_sum_simplify
% 5.42/5.65 thf(fact_2296_verit__sum__simplify,axiom,
% 5.42/5.65 ! [A: nat] :
% 5.42/5.65 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % verit_sum_simplify
% 5.42/5.65 thf(fact_2297_verit__sum__simplify,axiom,
% 5.42/5.65 ! [A: int] :
% 5.42/5.65 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.42/5.65 = A ) ).
% 5.42/5.65
% 5.42/5.65 % verit_sum_simplify
% 5.42/5.65 thf(fact_2298_eq__iff__diff__eq__0,axiom,
% 5.42/5.65 ( ( ^ [Y5: complex,Z5: complex] : ( Y5 = Z5 ) )
% 5.42/5.65 = ( ^ [A3: complex,B2: complex] :
% 5.42/5.65 ( ( minus_minus_complex @ A3 @ B2 )
% 5.42/5.65 = zero_zero_complex ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % eq_iff_diff_eq_0
% 5.42/5.65 thf(fact_2299_eq__iff__diff__eq__0,axiom,
% 5.42/5.65 ( ( ^ [Y5: real,Z5: real] : ( Y5 = Z5 ) )
% 5.42/5.65 = ( ^ [A3: real,B2: real] :
% 5.42/5.65 ( ( minus_minus_real @ A3 @ B2 )
% 5.42/5.65 = zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % eq_iff_diff_eq_0
% 5.42/5.65 thf(fact_2300_eq__iff__diff__eq__0,axiom,
% 5.42/5.65 ( ( ^ [Y5: rat,Z5: rat] : ( Y5 = Z5 ) )
% 5.42/5.65 = ( ^ [A3: rat,B2: rat] :
% 5.42/5.65 ( ( minus_minus_rat @ A3 @ B2 )
% 5.42/5.65 = zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % eq_iff_diff_eq_0
% 5.42/5.65 thf(fact_2301_eq__iff__diff__eq__0,axiom,
% 5.42/5.65 ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.42/5.65 = ( ^ [A3: int,B2: int] :
% 5.42/5.65 ( ( minus_minus_int @ A3 @ B2 )
% 5.42/5.65 = zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % eq_iff_diff_eq_0
% 5.42/5.65 thf(fact_2302_power__not__zero,axiom,
% 5.42/5.65 ! [A: rat,N: nat] :
% 5.42/5.65 ( ( A != zero_zero_rat )
% 5.42/5.65 => ( ( power_power_rat @ A @ N )
% 5.42/5.65 != zero_zero_rat ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_not_zero
% 5.42/5.65 thf(fact_2303_power__not__zero,axiom,
% 5.42/5.65 ! [A: nat,N: nat] :
% 5.42/5.65 ( ( A != zero_zero_nat )
% 5.42/5.65 => ( ( power_power_nat @ A @ N )
% 5.42/5.65 != zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_not_zero
% 5.42/5.65 thf(fact_2304_power__not__zero,axiom,
% 5.42/5.65 ! [A: real,N: nat] :
% 5.42/5.65 ( ( A != zero_zero_real )
% 5.42/5.65 => ( ( power_power_real @ A @ N )
% 5.42/5.65 != zero_zero_real ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_not_zero
% 5.42/5.65 thf(fact_2305_power__not__zero,axiom,
% 5.42/5.65 ! [A: complex,N: nat] :
% 5.42/5.65 ( ( A != zero_zero_complex )
% 5.42/5.65 => ( ( power_power_complex @ A @ N )
% 5.42/5.65 != zero_zero_complex ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_not_zero
% 5.42/5.65 thf(fact_2306_power__not__zero,axiom,
% 5.42/5.65 ! [A: int,N: nat] :
% 5.42/5.65 ( ( A != zero_zero_int )
% 5.42/5.65 => ( ( power_power_int @ A @ N )
% 5.42/5.65 != zero_zero_int ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_not_zero
% 5.42/5.65 thf(fact_2307_num_Osize_I4_J,axiom,
% 5.42/5.65 ( ( size_size_num @ one )
% 5.42/5.65 = zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % num.size(4)
% 5.42/5.65 thf(fact_2308_not0__implies__Suc,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( N != zero_zero_nat )
% 5.42/5.65 => ? [M4: nat] :
% 5.42/5.65 ( N
% 5.42/5.65 = ( suc @ M4 ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % not0_implies_Suc
% 5.42/5.65 thf(fact_2309_Zero__not__Suc,axiom,
% 5.42/5.65 ! [M: nat] :
% 5.42/5.65 ( zero_zero_nat
% 5.42/5.65 != ( suc @ M ) ) ).
% 5.42/5.65
% 5.42/5.65 % Zero_not_Suc
% 5.42/5.65 thf(fact_2310_Zero__neq__Suc,axiom,
% 5.42/5.65 ! [M: nat] :
% 5.42/5.65 ( zero_zero_nat
% 5.42/5.65 != ( suc @ M ) ) ).
% 5.42/5.65
% 5.42/5.65 % Zero_neq_Suc
% 5.42/5.65 thf(fact_2311_Suc__neq__Zero,axiom,
% 5.42/5.65 ! [M: nat] :
% 5.42/5.65 ( ( suc @ M )
% 5.42/5.65 != zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % Suc_neq_Zero
% 5.42/5.65 thf(fact_2312_zero__induct,axiom,
% 5.42/5.65 ! [P: nat > $o,K: nat] :
% 5.42/5.65 ( ( P @ K )
% 5.42/5.65 => ( ! [N3: nat] :
% 5.42/5.65 ( ( P @ ( suc @ N3 ) )
% 5.42/5.65 => ( P @ N3 ) )
% 5.42/5.65 => ( P @ zero_zero_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_induct
% 5.42/5.65 thf(fact_2313_diff__induct,axiom,
% 5.42/5.65 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.42/5.65 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 5.42/5.65 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.42/5.65 => ( ! [X3: nat,Y3: nat] :
% 5.42/5.65 ( ( P @ X3 @ Y3 )
% 5.42/5.65 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 5.42/5.65 => ( P @ M @ N ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % diff_induct
% 5.42/5.65 thf(fact_2314_nat__induct,axiom,
% 5.42/5.65 ! [P: nat > $o,N: nat] :
% 5.42/5.65 ( ( P @ zero_zero_nat )
% 5.42/5.65 => ( ! [N3: nat] :
% 5.42/5.65 ( ( P @ N3 )
% 5.42/5.65 => ( P @ ( suc @ N3 ) ) )
% 5.42/5.65 => ( P @ N ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % nat_induct
% 5.42/5.65 thf(fact_2315_old_Onat_Oexhaust,axiom,
% 5.42/5.65 ! [Y2: nat] :
% 5.42/5.65 ( ( Y2 != zero_zero_nat )
% 5.42/5.65 => ~ ! [Nat3: nat] :
% 5.42/5.65 ( Y2
% 5.42/5.65 != ( suc @ Nat3 ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % old.nat.exhaust
% 5.42/5.65 thf(fact_2316_nat_OdiscI,axiom,
% 5.42/5.65 ! [Nat: nat,X23: nat] :
% 5.42/5.65 ( ( Nat
% 5.42/5.65 = ( suc @ X23 ) )
% 5.42/5.65 => ( Nat != zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % nat.discI
% 5.42/5.65 thf(fact_2317_old_Onat_Odistinct_I1_J,axiom,
% 5.42/5.65 ! [Nat2: nat] :
% 5.42/5.65 ( zero_zero_nat
% 5.42/5.65 != ( suc @ Nat2 ) ) ).
% 5.42/5.65
% 5.42/5.65 % old.nat.distinct(1)
% 5.42/5.65 thf(fact_2318_old_Onat_Odistinct_I2_J,axiom,
% 5.42/5.65 ! [Nat2: nat] :
% 5.42/5.65 ( ( suc @ Nat2 )
% 5.42/5.65 != zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % old.nat.distinct(2)
% 5.42/5.65 thf(fact_2319_nat_Odistinct_I1_J,axiom,
% 5.42/5.65 ! [X23: nat] :
% 5.42/5.65 ( zero_zero_nat
% 5.42/5.65 != ( suc @ X23 ) ) ).
% 5.42/5.65
% 5.42/5.65 % nat.distinct(1)
% 5.42/5.65 thf(fact_2320_vebt__buildup_Ocases,axiom,
% 5.42/5.65 ! [X2: nat] :
% 5.42/5.65 ( ( X2 != zero_zero_nat )
% 5.42/5.65 => ( ( X2
% 5.42/5.65 != ( suc @ zero_zero_nat ) )
% 5.42/5.65 => ~ ! [Va3: nat] :
% 5.42/5.65 ( X2
% 5.42/5.65 != ( suc @ ( suc @ Va3 ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % vebt_buildup.cases
% 5.42/5.65 thf(fact_2321_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.42/5.65 ! [Uu: $o] :
% 5.42/5.65 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.42/5.65
% 5.42/5.65 % VEBT_internal.minNull.simps(3)
% 5.42/5.65 thf(fact_2322_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.42/5.65 ! [Uv: $o] :
% 5.42/5.65 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.42/5.65
% 5.42/5.65 % VEBT_internal.minNull.simps(2)
% 5.42/5.65 thf(fact_2323_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.42/5.65 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.42/5.65
% 5.42/5.65 % VEBT_internal.minNull.simps(1)
% 5.42/5.65 thf(fact_2324_bot__nat__0_Oextremum__strict,axiom,
% 5.42/5.65 ! [A: nat] :
% 5.42/5.65 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % bot_nat_0.extremum_strict
% 5.42/5.65 thf(fact_2325_gr0I,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( N != zero_zero_nat )
% 5.42/5.65 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % gr0I
% 5.42/5.65 thf(fact_2326_not__gr0,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.42/5.65 = ( N = zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % not_gr0
% 5.42/5.65 thf(fact_2327_not__less0,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % not_less0
% 5.42/5.65 thf(fact_2328_less__zeroE,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % less_zeroE
% 5.42/5.65 thf(fact_2329_gr__implies__not0,axiom,
% 5.42/5.65 ! [M: nat,N: nat] :
% 5.42/5.65 ( ( ord_less_nat @ M @ N )
% 5.42/5.65 => ( N != zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % gr_implies_not0
% 5.42/5.65 thf(fact_2330_infinite__descent0,axiom,
% 5.42/5.65 ! [P: nat > $o,N: nat] :
% 5.42/5.65 ( ( P @ zero_zero_nat )
% 5.42/5.65 => ( ! [N3: nat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.42/5.65 => ( ~ ( P @ N3 )
% 5.42/5.65 => ? [M2: nat] :
% 5.42/5.65 ( ( ord_less_nat @ M2 @ N3 )
% 5.42/5.65 & ~ ( P @ M2 ) ) ) )
% 5.42/5.65 => ( P @ N ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % infinite_descent0
% 5.42/5.65 thf(fact_2331_le__0__eq,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.42/5.65 = ( N = zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % le_0_eq
% 5.42/5.65 thf(fact_2332_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.42/5.65 ! [A: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.42/5.65 => ( A = zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % bot_nat_0.extremum_uniqueI
% 5.42/5.65 thf(fact_2333_bot__nat__0_Oextremum__unique,axiom,
% 5.42/5.65 ! [A: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.42/5.65 = ( A = zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % bot_nat_0.extremum_unique
% 5.42/5.65 thf(fact_2334_less__eq__nat_Osimps_I1_J,axiom,
% 5.42/5.65 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.42/5.65
% 5.42/5.65 % less_eq_nat.simps(1)
% 5.42/5.65 thf(fact_2335_add__eq__self__zero,axiom,
% 5.42/5.65 ! [M: nat,N: nat] :
% 5.42/5.65 ( ( ( plus_plus_nat @ M @ N )
% 5.42/5.65 = M )
% 5.42/5.65 => ( N = zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_eq_self_zero
% 5.42/5.65 thf(fact_2336_plus__nat_Oadd__0,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.42/5.65 = N ) ).
% 5.42/5.65
% 5.42/5.65 % plus_nat.add_0
% 5.42/5.65 thf(fact_2337_diffs0__imp__equal,axiom,
% 5.42/5.65 ! [M: nat,N: nat] :
% 5.42/5.65 ( ( ( minus_minus_nat @ M @ N )
% 5.42/5.65 = zero_zero_nat )
% 5.42/5.65 => ( ( ( minus_minus_nat @ N @ M )
% 5.42/5.65 = zero_zero_nat )
% 5.42/5.65 => ( M = N ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % diffs0_imp_equal
% 5.42/5.65 thf(fact_2338_minus__nat_Odiff__0,axiom,
% 5.42/5.65 ! [M: nat] :
% 5.42/5.65 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.42/5.65 = M ) ).
% 5.42/5.65
% 5.42/5.65 % minus_nat.diff_0
% 5.42/5.65 thf(fact_2339_mult__0,axiom,
% 5.42/5.65 ! [N: nat] :
% 5.42/5.65 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.42/5.65 = zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % mult_0
% 5.42/5.65 thf(fact_2340_nat__mult__eq__cancel__disj,axiom,
% 5.42/5.65 ! [K: nat,M: nat,N: nat] :
% 5.42/5.65 ( ( ( times_times_nat @ K @ M )
% 5.42/5.65 = ( times_times_nat @ K @ N ) )
% 5.42/5.65 = ( ( K = zero_zero_nat )
% 5.42/5.65 | ( M = N ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % nat_mult_eq_cancel_disj
% 5.42/5.65 thf(fact_2341_power__eq__iff__eq__base,axiom,
% 5.42/5.65 ! [N: nat,A: real,B: real] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.42/5.65 => ( ( ( power_power_real @ A @ N )
% 5.42/5.65 = ( power_power_real @ B @ N ) )
% 5.42/5.65 = ( A = B ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_eq_iff_eq_base
% 5.42/5.65 thf(fact_2342_power__eq__iff__eq__base,axiom,
% 5.42/5.65 ! [N: nat,A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.42/5.65 => ( ( ( power_power_rat @ A @ N )
% 5.42/5.65 = ( power_power_rat @ B @ N ) )
% 5.42/5.65 = ( A = B ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_eq_iff_eq_base
% 5.42/5.65 thf(fact_2343_power__eq__iff__eq__base,axiom,
% 5.42/5.65 ! [N: nat,A: nat,B: nat] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.42/5.65 => ( ( ( power_power_nat @ A @ N )
% 5.42/5.65 = ( power_power_nat @ B @ N ) )
% 5.42/5.65 = ( A = B ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_eq_iff_eq_base
% 5.42/5.65 thf(fact_2344_power__eq__iff__eq__base,axiom,
% 5.42/5.65 ! [N: nat,A: int,B: int] :
% 5.42/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.42/5.65 => ( ( ( power_power_int @ A @ N )
% 5.42/5.65 = ( power_power_int @ B @ N ) )
% 5.42/5.65 = ( A = B ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_eq_iff_eq_base
% 5.42/5.65 thf(fact_2345_power__eq__imp__eq__base,axiom,
% 5.42/5.65 ! [A: real,N: nat,B: real] :
% 5.42/5.65 ( ( ( power_power_real @ A @ N )
% 5.42/5.65 = ( power_power_real @ B @ N ) )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.42/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( A = B ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_eq_imp_eq_base
% 5.42/5.65 thf(fact_2346_power__eq__imp__eq__base,axiom,
% 5.42/5.65 ! [A: rat,N: nat,B: rat] :
% 5.42/5.65 ( ( ( power_power_rat @ A @ N )
% 5.42/5.65 = ( power_power_rat @ B @ N ) )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.42/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( A = B ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_eq_imp_eq_base
% 5.42/5.65 thf(fact_2347_power__eq__imp__eq__base,axiom,
% 5.42/5.65 ! [A: nat,N: nat,B: nat] :
% 5.42/5.65 ( ( ( power_power_nat @ A @ N )
% 5.42/5.65 = ( power_power_nat @ B @ N ) )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.42/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( A = B ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_eq_imp_eq_base
% 5.42/5.65 thf(fact_2348_power__eq__imp__eq__base,axiom,
% 5.42/5.65 ! [A: int,N: nat,B: int] :
% 5.42/5.65 ( ( ( power_power_int @ A @ N )
% 5.42/5.65 = ( power_power_int @ B @ N ) )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.42/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( A = B ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_eq_imp_eq_base
% 5.42/5.65 thf(fact_2349_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.42/5.65 ! [A: $o,B: $o,X2: nat] :
% 5.42/5.65 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.42/5.65 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(1)
% 5.42/5.65 thf(fact_2350_lambda__zero,axiom,
% 5.42/5.65 ( ( ^ [H: complex] : zero_zero_complex )
% 5.42/5.65 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.42/5.65
% 5.42/5.65 % lambda_zero
% 5.42/5.65 thf(fact_2351_lambda__zero,axiom,
% 5.42/5.65 ( ( ^ [H: real] : zero_zero_real )
% 5.42/5.65 = ( times_times_real @ zero_zero_real ) ) ).
% 5.42/5.65
% 5.42/5.65 % lambda_zero
% 5.42/5.65 thf(fact_2352_lambda__zero,axiom,
% 5.42/5.65 ( ( ^ [H: rat] : zero_zero_rat )
% 5.42/5.65 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.42/5.65
% 5.42/5.65 % lambda_zero
% 5.42/5.65 thf(fact_2353_lambda__zero,axiom,
% 5.42/5.65 ( ( ^ [H: nat] : zero_zero_nat )
% 5.42/5.65 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % lambda_zero
% 5.42/5.65 thf(fact_2354_lambda__zero,axiom,
% 5.42/5.65 ( ( ^ [H: int] : zero_zero_int )
% 5.42/5.65 = ( times_times_int @ zero_zero_int ) ) ).
% 5.42/5.65
% 5.42/5.65 % lambda_zero
% 5.42/5.65 thf(fact_2355_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_real,X2: real > complex,Y2: real > complex] :
% 5.42/5.65 ( ( finite_finite_real
% 5.42/5.65 @ ( collect_real
% 5.42/5.65 @ ^ [I4: real] :
% 5.42/5.65 ( ( member_real @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_complex ) ) ) )
% 5.42/5.65 => ( ( finite_finite_real
% 5.42/5.65 @ ( collect_real
% 5.42/5.65 @ ^ [I4: real] :
% 5.42/5.65 ( ( member_real @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_complex ) ) ) )
% 5.42/5.65 => ( finite_finite_real
% 5.42/5.65 @ ( collect_real
% 5.42/5.65 @ ^ [I4: real] :
% 5.42/5.65 ( ( member_real @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_complex ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2356_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_nat,X2: nat > complex,Y2: nat > complex] :
% 5.42/5.65 ( ( finite_finite_nat
% 5.42/5.65 @ ( collect_nat
% 5.42/5.65 @ ^ [I4: nat] :
% 5.42/5.65 ( ( member_nat @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_complex ) ) ) )
% 5.42/5.65 => ( ( finite_finite_nat
% 5.42/5.65 @ ( collect_nat
% 5.42/5.65 @ ^ [I4: nat] :
% 5.42/5.65 ( ( member_nat @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_complex ) ) ) )
% 5.42/5.65 => ( finite_finite_nat
% 5.42/5.65 @ ( collect_nat
% 5.42/5.65 @ ^ [I4: nat] :
% 5.42/5.65 ( ( member_nat @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_complex ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2357_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_int,X2: int > complex,Y2: int > complex] :
% 5.42/5.65 ( ( finite_finite_int
% 5.42/5.65 @ ( collect_int
% 5.42/5.65 @ ^ [I4: int] :
% 5.42/5.65 ( ( member_int @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_complex ) ) ) )
% 5.42/5.65 => ( ( finite_finite_int
% 5.42/5.65 @ ( collect_int
% 5.42/5.65 @ ^ [I4: int] :
% 5.42/5.65 ( ( member_int @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_complex ) ) ) )
% 5.42/5.65 => ( finite_finite_int
% 5.42/5.65 @ ( collect_int
% 5.42/5.65 @ ^ [I4: int] :
% 5.42/5.65 ( ( member_int @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_complex ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2358_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_complex,X2: complex > complex,Y2: complex > complex] :
% 5.42/5.65 ( ( finite3207457112153483333omplex
% 5.42/5.65 @ ( collect_complex
% 5.42/5.65 @ ^ [I4: complex] :
% 5.42/5.65 ( ( member_complex @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_complex ) ) ) )
% 5.42/5.65 => ( ( finite3207457112153483333omplex
% 5.42/5.65 @ ( collect_complex
% 5.42/5.65 @ ^ [I4: complex] :
% 5.42/5.65 ( ( member_complex @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_complex ) ) ) )
% 5.42/5.65 => ( finite3207457112153483333omplex
% 5.42/5.65 @ ( collect_complex
% 5.42/5.65 @ ^ [I4: complex] :
% 5.42/5.65 ( ( member_complex @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_complex ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2359_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_real,X2: real > real,Y2: real > real] :
% 5.42/5.65 ( ( finite_finite_real
% 5.42/5.65 @ ( collect_real
% 5.42/5.65 @ ^ [I4: real] :
% 5.42/5.65 ( ( member_real @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_real ) ) ) )
% 5.42/5.65 => ( ( finite_finite_real
% 5.42/5.65 @ ( collect_real
% 5.42/5.65 @ ^ [I4: real] :
% 5.42/5.65 ( ( member_real @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_real ) ) ) )
% 5.42/5.65 => ( finite_finite_real
% 5.42/5.65 @ ( collect_real
% 5.42/5.65 @ ^ [I4: real] :
% 5.42/5.65 ( ( member_real @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_real ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2360_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_nat,X2: nat > real,Y2: nat > real] :
% 5.42/5.65 ( ( finite_finite_nat
% 5.42/5.65 @ ( collect_nat
% 5.42/5.65 @ ^ [I4: nat] :
% 5.42/5.65 ( ( member_nat @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_real ) ) ) )
% 5.42/5.65 => ( ( finite_finite_nat
% 5.42/5.65 @ ( collect_nat
% 5.42/5.65 @ ^ [I4: nat] :
% 5.42/5.65 ( ( member_nat @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_real ) ) ) )
% 5.42/5.65 => ( finite_finite_nat
% 5.42/5.65 @ ( collect_nat
% 5.42/5.65 @ ^ [I4: nat] :
% 5.42/5.65 ( ( member_nat @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_real ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2361_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_int,X2: int > real,Y2: int > real] :
% 5.42/5.65 ( ( finite_finite_int
% 5.42/5.65 @ ( collect_int
% 5.42/5.65 @ ^ [I4: int] :
% 5.42/5.65 ( ( member_int @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_real ) ) ) )
% 5.42/5.65 => ( ( finite_finite_int
% 5.42/5.65 @ ( collect_int
% 5.42/5.65 @ ^ [I4: int] :
% 5.42/5.65 ( ( member_int @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_real ) ) ) )
% 5.42/5.65 => ( finite_finite_int
% 5.42/5.65 @ ( collect_int
% 5.42/5.65 @ ^ [I4: int] :
% 5.42/5.65 ( ( member_int @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_real ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2362_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_complex,X2: complex > real,Y2: complex > real] :
% 5.42/5.65 ( ( finite3207457112153483333omplex
% 5.42/5.65 @ ( collect_complex
% 5.42/5.65 @ ^ [I4: complex] :
% 5.42/5.65 ( ( member_complex @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_real ) ) ) )
% 5.42/5.65 => ( ( finite3207457112153483333omplex
% 5.42/5.65 @ ( collect_complex
% 5.42/5.65 @ ^ [I4: complex] :
% 5.42/5.65 ( ( member_complex @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_real ) ) ) )
% 5.42/5.65 => ( finite3207457112153483333omplex
% 5.42/5.65 @ ( collect_complex
% 5.42/5.65 @ ^ [I4: complex] :
% 5.42/5.65 ( ( member_complex @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_real ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2363_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_real,X2: real > rat,Y2: real > rat] :
% 5.42/5.65 ( ( finite_finite_real
% 5.42/5.65 @ ( collect_real
% 5.42/5.65 @ ^ [I4: real] :
% 5.42/5.65 ( ( member_real @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_rat ) ) ) )
% 5.42/5.65 => ( ( finite_finite_real
% 5.42/5.65 @ ( collect_real
% 5.42/5.65 @ ^ [I4: real] :
% 5.42/5.65 ( ( member_real @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_rat ) ) ) )
% 5.42/5.65 => ( finite_finite_real
% 5.42/5.65 @ ( collect_real
% 5.42/5.65 @ ^ [I4: real] :
% 5.42/5.65 ( ( member_real @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_rat @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_rat ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2364_sum_Ofinite__Collect__op,axiom,
% 5.42/5.65 ! [I5: set_nat,X2: nat > rat,Y2: nat > rat] :
% 5.42/5.65 ( ( finite_finite_nat
% 5.42/5.65 @ ( collect_nat
% 5.42/5.65 @ ^ [I4: nat] :
% 5.42/5.65 ( ( member_nat @ I4 @ I5 )
% 5.42/5.65 & ( ( X2 @ I4 )
% 5.42/5.65 != zero_zero_rat ) ) ) )
% 5.42/5.65 => ( ( finite_finite_nat
% 5.42/5.65 @ ( collect_nat
% 5.42/5.65 @ ^ [I4: nat] :
% 5.42/5.65 ( ( member_nat @ I4 @ I5 )
% 5.42/5.65 & ( ( Y2 @ I4 )
% 5.42/5.65 != zero_zero_rat ) ) ) )
% 5.42/5.65 => ( finite_finite_nat
% 5.42/5.65 @ ( collect_nat
% 5.42/5.65 @ ^ [I4: nat] :
% 5.42/5.65 ( ( member_nat @ I4 @ I5 )
% 5.42/5.65 & ( ( plus_plus_rat @ ( X2 @ I4 ) @ ( Y2 @ I4 ) )
% 5.42/5.65 != zero_zero_rat ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % sum.finite_Collect_op
% 5.42/5.65 thf(fact_2365_power__strict__mono,axiom,
% 5.42/5.65 ! [A: real,B: real,N: nat] :
% 5.42/5.65 ( ( ord_less_real @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_strict_mono
% 5.42/5.65 thf(fact_2366_power__strict__mono,axiom,
% 5.42/5.65 ! [A: rat,B: rat,N: nat] :
% 5.42/5.65 ( ( ord_less_rat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_strict_mono
% 5.42/5.65 thf(fact_2367_power__strict__mono,axiom,
% 5.42/5.65 ! [A: nat,B: nat,N: nat] :
% 5.42/5.65 ( ( ord_less_nat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_strict_mono
% 5.42/5.65 thf(fact_2368_power__strict__mono,axiom,
% 5.42/5.65 ! [A: int,B: int,N: nat] :
% 5.42/5.65 ( ( ord_less_int @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.42/5.65 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % power_strict_mono
% 5.42/5.65 thf(fact_2369_vebt__pred_Osimps_I2_J,axiom,
% 5.42/5.65 ! [A: $o,Uw: $o] :
% 5.42/5.65 ( ( A
% 5.42/5.65 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.42/5.65 = ( some_nat @ zero_zero_nat ) ) )
% 5.42/5.65 & ( ~ A
% 5.42/5.65 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.42/5.65 = none_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % vebt_pred.simps(2)
% 5.42/5.65 thf(fact_2370_vebt__mint_Osimps_I1_J,axiom,
% 5.42/5.65 ! [A: $o,B: $o] :
% 5.42/5.65 ( ( A
% 5.42/5.65 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.42/5.65 = ( some_nat @ zero_zero_nat ) ) )
% 5.42/5.65 & ( ~ A
% 5.42/5.65 => ( ( B
% 5.42/5.65 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.42/5.65 = ( some_nat @ one_one_nat ) ) )
% 5.42/5.65 & ( ~ B
% 5.42/5.65 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.42/5.65 = none_nat ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % vebt_mint.simps(1)
% 5.42/5.65 thf(fact_2371_vebt__succ_Osimps_I1_J,axiom,
% 5.42/5.65 ! [B: $o,Uu: $o] :
% 5.42/5.65 ( ( B
% 5.42/5.65 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.42/5.65 = ( some_nat @ one_one_nat ) ) )
% 5.42/5.65 & ( ~ B
% 5.42/5.65 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.42/5.65 = none_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % vebt_succ.simps(1)
% 5.42/5.65 thf(fact_2372_vebt__maxt_Osimps_I1_J,axiom,
% 5.42/5.65 ! [B: $o,A: $o] :
% 5.42/5.65 ( ( B
% 5.42/5.65 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.42/5.65 = ( some_nat @ one_one_nat ) ) )
% 5.42/5.65 & ( ~ B
% 5.42/5.65 => ( ( A
% 5.42/5.65 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.42/5.65 = ( some_nat @ zero_zero_nat ) ) )
% 5.42/5.65 & ( ~ A
% 5.42/5.65 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.42/5.65 = none_nat ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % vebt_maxt.simps(1)
% 5.42/5.65 thf(fact_2373_not__numeral__le__zero,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.42/5.65
% 5.42/5.65 % not_numeral_le_zero
% 5.42/5.65 thf(fact_2374_not__numeral__le__zero,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.42/5.65
% 5.42/5.65 % not_numeral_le_zero
% 5.42/5.65 thf(fact_2375_not__numeral__le__zero,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % not_numeral_le_zero
% 5.42/5.65 thf(fact_2376_not__numeral__le__zero,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.42/5.65
% 5.42/5.65 % not_numeral_le_zero
% 5.42/5.65 thf(fact_2377_zero__le__numeral,axiom,
% 5.42/5.65 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_numeral
% 5.42/5.65 thf(fact_2378_zero__le__numeral,axiom,
% 5.42/5.65 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_numeral
% 5.42/5.65 thf(fact_2379_zero__le__numeral,axiom,
% 5.42/5.65 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_numeral
% 5.42/5.65 thf(fact_2380_zero__le__numeral,axiom,
% 5.42/5.65 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_numeral
% 5.42/5.65 thf(fact_2381_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.42/5.65 ! [A: real,B: real,C: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.42/5.65 thf(fact_2382_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.42/5.65 ! [A: rat,B: rat,C: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.42/5.65 thf(fact_2383_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.42/5.65 ! [A: nat,B: nat,C: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.42/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.42/5.65 thf(fact_2384_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.42/5.65 ! [A: int,B: int,C: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.42/5.65 thf(fact_2385_zero__le__mult__iff,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.42/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.42/5.65 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.42/5.65 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_mult_iff
% 5.42/5.65 thf(fact_2386_zero__le__mult__iff,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.42/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.42/5.65 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.42/5.65 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_mult_iff
% 5.42/5.65 thf(fact_2387_zero__le__mult__iff,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.42/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.42/5.65 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.42/5.65 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_mult_iff
% 5.42/5.65 thf(fact_2388_mult__nonneg__nonpos2,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonpos2
% 5.42/5.65 thf(fact_2389_mult__nonneg__nonpos2,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonpos2
% 5.42/5.65 thf(fact_2390_mult__nonneg__nonpos2,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.42/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonpos2
% 5.42/5.65 thf(fact_2391_mult__nonneg__nonpos2,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonpos2
% 5.42/5.65 thf(fact_2392_mult__nonpos__nonneg,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonpos_nonneg
% 5.42/5.65 thf(fact_2393_mult__nonpos__nonneg,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonpos_nonneg
% 5.42/5.65 thf(fact_2394_mult__nonpos__nonneg,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.42/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonpos_nonneg
% 5.42/5.65 thf(fact_2395_mult__nonpos__nonneg,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonpos_nonneg
% 5.42/5.65 thf(fact_2396_mult__nonneg__nonpos,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonpos
% 5.42/5.65 thf(fact_2397_mult__nonneg__nonpos,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonpos
% 5.42/5.65 thf(fact_2398_mult__nonneg__nonpos,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.42/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonpos
% 5.42/5.65 thf(fact_2399_mult__nonneg__nonpos,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonpos
% 5.42/5.65 thf(fact_2400_mult__nonneg__nonneg,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.42/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonneg
% 5.42/5.65 thf(fact_2401_mult__nonneg__nonneg,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.42/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonneg
% 5.42/5.65 thf(fact_2402_mult__nonneg__nonneg,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.42/5.65 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonneg
% 5.42/5.65 thf(fact_2403_mult__nonneg__nonneg,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.42/5.65 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonneg_nonneg
% 5.42/5.65 thf(fact_2404_split__mult__neg__le,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.42/5.65 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.42/5.65 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.42/5.65
% 5.42/5.65 % split_mult_neg_le
% 5.42/5.65 thf(fact_2405_split__mult__neg__le,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.42/5.65 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.42/5.65 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.42/5.65
% 5.42/5.65 % split_mult_neg_le
% 5.42/5.65 thf(fact_2406_split__mult__neg__le,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.42/5.65 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.42/5.65 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.42/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.42/5.65
% 5.42/5.65 % split_mult_neg_le
% 5.42/5.65 thf(fact_2407_split__mult__neg__le,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.42/5.65 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.42/5.65 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.42/5.65
% 5.42/5.65 % split_mult_neg_le
% 5.42/5.65 thf(fact_2408_mult__le__0__iff,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.42/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.42/5.65 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.42/5.65 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_le_0_iff
% 5.42/5.65 thf(fact_2409_mult__le__0__iff,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.42/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.42/5.65 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.42/5.65 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_le_0_iff
% 5.42/5.65 thf(fact_2410_mult__le__0__iff,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.42/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.42/5.65 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.42/5.65 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_le_0_iff
% 5.42/5.65 thf(fact_2411_mult__right__mono,axiom,
% 5.42/5.65 ! [A: real,B: real,C: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_mono
% 5.42/5.65 thf(fact_2412_mult__right__mono,axiom,
% 5.42/5.65 ! [A: rat,B: rat,C: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_mono
% 5.42/5.65 thf(fact_2413_mult__right__mono,axiom,
% 5.42/5.65 ! [A: nat,B: nat,C: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.42/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_mono
% 5.42/5.65 thf(fact_2414_mult__right__mono,axiom,
% 5.42/5.65 ! [A: int,B: int,C: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_mono
% 5.42/5.65 thf(fact_2415_mult__right__mono__neg,axiom,
% 5.42/5.65 ! [B: real,A: real,C: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ B @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_mono_neg
% 5.42/5.65 thf(fact_2416_mult__right__mono__neg,axiom,
% 5.42/5.65 ! [B: rat,A: rat,C: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ B @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_mono_neg
% 5.42/5.65 thf(fact_2417_mult__right__mono__neg,axiom,
% 5.42/5.65 ! [B: int,A: int,C: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ B @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_right_mono_neg
% 5.42/5.65 thf(fact_2418_mult__left__mono,axiom,
% 5.42/5.65 ! [A: real,B: real,C: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_mono
% 5.42/5.65 thf(fact_2419_mult__left__mono,axiom,
% 5.42/5.65 ! [A: rat,B: rat,C: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_mono
% 5.42/5.65 thf(fact_2420_mult__left__mono,axiom,
% 5.42/5.65 ! [A: nat,B: nat,C: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.42/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_mono
% 5.42/5.65 thf(fact_2421_mult__left__mono,axiom,
% 5.42/5.65 ! [A: int,B: int,C: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_mono
% 5.42/5.65 thf(fact_2422_mult__nonpos__nonpos,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.42/5.65 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.42/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonpos_nonpos
% 5.42/5.65 thf(fact_2423_mult__nonpos__nonpos,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.42/5.65 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.42/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonpos_nonpos
% 5.42/5.65 thf(fact_2424_mult__nonpos__nonpos,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.42/5.65 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.42/5.65 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_nonpos_nonpos
% 5.42/5.65 thf(fact_2425_mult__left__mono__neg,axiom,
% 5.42/5.65 ! [B: real,A: real,C: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ B @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_mono_neg
% 5.42/5.65 thf(fact_2426_mult__left__mono__neg,axiom,
% 5.42/5.65 ! [B: rat,A: rat,C: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ B @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_mono_neg
% 5.42/5.65 thf(fact_2427_mult__left__mono__neg,axiom,
% 5.42/5.65 ! [B: int,A: int,C: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ B @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_left_mono_neg
% 5.42/5.65 thf(fact_2428_split__mult__pos__le,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.42/5.65 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.42/5.65 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.42/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % split_mult_pos_le
% 5.42/5.65 thf(fact_2429_split__mult__pos__le,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.42/5.65 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.42/5.65 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.42/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % split_mult_pos_le
% 5.42/5.65 thf(fact_2430_split__mult__pos__le,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.42/5.65 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.42/5.65 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.42/5.65 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % split_mult_pos_le
% 5.42/5.65 thf(fact_2431_zero__le__square,axiom,
% 5.42/5.65 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_square
% 5.42/5.65 thf(fact_2432_zero__le__square,axiom,
% 5.42/5.65 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_square
% 5.42/5.65 thf(fact_2433_zero__le__square,axiom,
% 5.42/5.65 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_le_square
% 5.42/5.65 thf(fact_2434_mult__mono_H,axiom,
% 5.42/5.65 ! [A: real,B: real,C: real,D2: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_real @ C @ D2 )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_mono'
% 5.42/5.65 thf(fact_2435_mult__mono_H,axiom,
% 5.42/5.65 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_mono'
% 5.42/5.65 thf(fact_2436_mult__mono_H,axiom,
% 5.42/5.65 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.42/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_mono'
% 5.42/5.65 thf(fact_2437_mult__mono_H,axiom,
% 5.42/5.65 ! [A: int,B: int,C: int,D2: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_int @ C @ D2 )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_mono'
% 5.42/5.65 thf(fact_2438_mult__mono,axiom,
% 5.42/5.65 ! [A: real,B: real,C: real,D2: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_real @ C @ D2 )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.42/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_mono
% 5.42/5.65 thf(fact_2439_mult__mono,axiom,
% 5.42/5.65 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.42/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_mono
% 5.42/5.65 thf(fact_2440_mult__mono,axiom,
% 5.42/5.65 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.42/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_mono
% 5.42/5.65 thf(fact_2441_mult__mono,axiom,
% 5.42/5.65 ! [A: int,B: int,C: int,D2: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.42/5.65 => ( ( ord_less_eq_int @ C @ D2 )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.42/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_mono
% 5.42/5.65 thf(fact_2442_not__numeral__less__zero,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.42/5.65
% 5.42/5.65 % not_numeral_less_zero
% 5.42/5.65 thf(fact_2443_not__numeral__less__zero,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.42/5.65
% 5.42/5.65 % not_numeral_less_zero
% 5.42/5.65 thf(fact_2444_not__numeral__less__zero,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % not_numeral_less_zero
% 5.42/5.65 thf(fact_2445_not__numeral__less__zero,axiom,
% 5.42/5.65 ! [N: num] :
% 5.42/5.65 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.42/5.65
% 5.42/5.65 % not_numeral_less_zero
% 5.42/5.65 thf(fact_2446_zero__less__numeral,axiom,
% 5.42/5.65 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_less_numeral
% 5.42/5.65 thf(fact_2447_zero__less__numeral,axiom,
% 5.42/5.65 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_less_numeral
% 5.42/5.65 thf(fact_2448_zero__less__numeral,axiom,
% 5.42/5.65 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_less_numeral
% 5.42/5.65 thf(fact_2449_zero__less__numeral,axiom,
% 5.42/5.65 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.42/5.65
% 5.42/5.65 % zero_less_numeral
% 5.42/5.65 thf(fact_2450_not__one__le__zero,axiom,
% 5.42/5.65 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.42/5.65
% 5.42/5.65 % not_one_le_zero
% 5.42/5.65 thf(fact_2451_not__one__le__zero,axiom,
% 5.42/5.65 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.42/5.65
% 5.42/5.65 % not_one_le_zero
% 5.42/5.65 thf(fact_2452_not__one__le__zero,axiom,
% 5.42/5.65 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.42/5.65
% 5.42/5.65 % not_one_le_zero
% 5.42/5.65 thf(fact_2453_not__one__le__zero,axiom,
% 5.42/5.65 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.42/5.65
% 5.42/5.65 % not_one_le_zero
% 5.42/5.65 thf(fact_2454_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.42/5.65 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.42/5.65
% 5.42/5.65 % linordered_nonzero_semiring_class.zero_le_one
% 5.42/5.65 thf(fact_2455_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.42/5.65 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.42/5.65
% 5.42/5.65 % linordered_nonzero_semiring_class.zero_le_one
% 5.42/5.65 thf(fact_2456_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.42/5.65 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.42/5.65
% 5.42/5.65 % linordered_nonzero_semiring_class.zero_le_one
% 5.42/5.65 thf(fact_2457_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.42/5.65 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.42/5.65
% 5.42/5.65 % linordered_nonzero_semiring_class.zero_le_one
% 5.42/5.65 thf(fact_2458_zero__less__one__class_Ozero__le__one,axiom,
% 5.42/5.65 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.42/5.65
% 5.42/5.65 % zero_less_one_class.zero_le_one
% 5.42/5.65 thf(fact_2459_zero__less__one__class_Ozero__le__one,axiom,
% 5.42/5.65 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.42/5.65
% 5.42/5.65 % zero_less_one_class.zero_le_one
% 5.42/5.65 thf(fact_2460_zero__less__one__class_Ozero__le__one,axiom,
% 5.42/5.65 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.42/5.65
% 5.42/5.65 % zero_less_one_class.zero_le_one
% 5.42/5.65 thf(fact_2461_zero__less__one__class_Ozero__le__one,axiom,
% 5.42/5.65 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.42/5.65
% 5.42/5.65 % zero_less_one_class.zero_le_one
% 5.42/5.65 thf(fact_2462_add__nonpos__eq__0__iff,axiom,
% 5.42/5.65 ! [X2: real,Y2: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.42/5.65 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.42/5.65 => ( ( ( plus_plus_real @ X2 @ Y2 )
% 5.42/5.65 = zero_zero_real )
% 5.42/5.65 = ( ( X2 = zero_zero_real )
% 5.42/5.65 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonpos_eq_0_iff
% 5.42/5.65 thf(fact_2463_add__nonpos__eq__0__iff,axiom,
% 5.42/5.65 ! [X2: rat,Y2: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.42/5.65 => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 5.42/5.65 => ( ( ( plus_plus_rat @ X2 @ Y2 )
% 5.42/5.65 = zero_zero_rat )
% 5.42/5.65 = ( ( X2 = zero_zero_rat )
% 5.42/5.65 & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonpos_eq_0_iff
% 5.42/5.65 thf(fact_2464_add__nonpos__eq__0__iff,axiom,
% 5.42/5.65 ! [X2: nat,Y2: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ X2 @ zero_zero_nat )
% 5.42/5.65 => ( ( ord_less_eq_nat @ Y2 @ zero_zero_nat )
% 5.42/5.65 => ( ( ( plus_plus_nat @ X2 @ Y2 )
% 5.42/5.65 = zero_zero_nat )
% 5.42/5.65 = ( ( X2 = zero_zero_nat )
% 5.42/5.65 & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonpos_eq_0_iff
% 5.42/5.65 thf(fact_2465_add__nonpos__eq__0__iff,axiom,
% 5.42/5.65 ! [X2: int,Y2: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.42/5.65 => ( ( ord_less_eq_int @ Y2 @ zero_zero_int )
% 5.42/5.65 => ( ( ( plus_plus_int @ X2 @ Y2 )
% 5.42/5.65 = zero_zero_int )
% 5.42/5.65 = ( ( X2 = zero_zero_int )
% 5.42/5.65 & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonpos_eq_0_iff
% 5.42/5.65 thf(fact_2466_add__nonneg__eq__0__iff,axiom,
% 5.42/5.65 ! [X2: real,Y2: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.42/5.65 => ( ( ( plus_plus_real @ X2 @ Y2 )
% 5.42/5.65 = zero_zero_real )
% 5.42/5.65 = ( ( X2 = zero_zero_real )
% 5.42/5.65 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonneg_eq_0_iff
% 5.42/5.65 thf(fact_2467_add__nonneg__eq__0__iff,axiom,
% 5.42/5.65 ! [X2: rat,Y2: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.42/5.65 => ( ( ( plus_plus_rat @ X2 @ Y2 )
% 5.42/5.65 = zero_zero_rat )
% 5.42/5.65 = ( ( X2 = zero_zero_rat )
% 5.42/5.65 & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonneg_eq_0_iff
% 5.42/5.65 thf(fact_2468_add__nonneg__eq__0__iff,axiom,
% 5.42/5.65 ! [X2: nat,Y2: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.42/5.65 => ( ( ( plus_plus_nat @ X2 @ Y2 )
% 5.42/5.65 = zero_zero_nat )
% 5.42/5.65 = ( ( X2 = zero_zero_nat )
% 5.42/5.65 & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonneg_eq_0_iff
% 5.42/5.65 thf(fact_2469_add__nonneg__eq__0__iff,axiom,
% 5.42/5.65 ! [X2: int,Y2: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.42/5.65 => ( ( ( plus_plus_int @ X2 @ Y2 )
% 5.42/5.65 = zero_zero_int )
% 5.42/5.65 = ( ( X2 = zero_zero_int )
% 5.42/5.65 & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonneg_eq_0_iff
% 5.42/5.65 thf(fact_2470_add__nonpos__nonpos,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.42/5.65 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.42/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonpos_nonpos
% 5.42/5.65 thf(fact_2471_add__nonpos__nonpos,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.42/5.65 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.42/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonpos_nonpos
% 5.42/5.65 thf(fact_2472_add__nonpos__nonpos,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.42/5.65 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.42/5.65 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonpos_nonpos
% 5.42/5.65 thf(fact_2473_add__nonpos__nonpos,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.42/5.65 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.42/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonpos_nonpos
% 5.42/5.65 thf(fact_2474_add__nonneg__nonneg,axiom,
% 5.42/5.65 ! [A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.42/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonneg_nonneg
% 5.42/5.65 thf(fact_2475_add__nonneg__nonneg,axiom,
% 5.42/5.65 ! [A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.42/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonneg_nonneg
% 5.42/5.65 thf(fact_2476_add__nonneg__nonneg,axiom,
% 5.42/5.65 ! [A: nat,B: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.42/5.65 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonneg_nonneg
% 5.42/5.65 thf(fact_2477_add__nonneg__nonneg,axiom,
% 5.42/5.65 ! [A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.42/5.65 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_nonneg_nonneg
% 5.42/5.65 thf(fact_2478_add__increasing2,axiom,
% 5.42/5.65 ! [C: real,B: real,A: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.42/5.65 => ( ( ord_less_eq_real @ B @ A )
% 5.42/5.65 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_increasing2
% 5.42/5.65 thf(fact_2479_add__increasing2,axiom,
% 5.42/5.65 ! [C: rat,B: rat,A: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.42/5.65 => ( ( ord_less_eq_rat @ B @ A )
% 5.42/5.65 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_increasing2
% 5.42/5.65 thf(fact_2480_add__increasing2,axiom,
% 5.42/5.65 ! [C: nat,B: nat,A: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.42/5.65 => ( ( ord_less_eq_nat @ B @ A )
% 5.42/5.65 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_increasing2
% 5.42/5.65 thf(fact_2481_add__increasing2,axiom,
% 5.42/5.65 ! [C: int,B: int,A: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.42/5.65 => ( ( ord_less_eq_int @ B @ A )
% 5.42/5.65 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_increasing2
% 5.42/5.65 thf(fact_2482_add__decreasing2,axiom,
% 5.42/5.65 ! [C: real,A: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.42/5.65 => ( ( ord_less_eq_real @ A @ B )
% 5.42/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_decreasing2
% 5.42/5.65 thf(fact_2483_add__decreasing2,axiom,
% 5.42/5.65 ! [C: rat,A: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.42/5.65 => ( ( ord_less_eq_rat @ A @ B )
% 5.42/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_decreasing2
% 5.42/5.65 thf(fact_2484_add__decreasing2,axiom,
% 5.42/5.65 ! [C: nat,A: nat,B: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.42/5.65 => ( ( ord_less_eq_nat @ A @ B )
% 5.42/5.65 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_decreasing2
% 5.42/5.65 thf(fact_2485_add__decreasing2,axiom,
% 5.42/5.65 ! [C: int,A: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.42/5.65 => ( ( ord_less_eq_int @ A @ B )
% 5.42/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_decreasing2
% 5.42/5.65 thf(fact_2486_add__increasing,axiom,
% 5.42/5.65 ! [A: real,B: real,C: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.42/5.65 => ( ( ord_less_eq_real @ B @ C )
% 5.42/5.65 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_increasing
% 5.42/5.65 thf(fact_2487_add__increasing,axiom,
% 5.42/5.65 ! [A: rat,B: rat,C: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.42/5.65 => ( ( ord_less_eq_rat @ B @ C )
% 5.42/5.65 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_increasing
% 5.42/5.65 thf(fact_2488_add__increasing,axiom,
% 5.42/5.65 ! [A: nat,B: nat,C: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.42/5.65 => ( ( ord_less_eq_nat @ B @ C )
% 5.42/5.65 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_increasing
% 5.42/5.65 thf(fact_2489_add__increasing,axiom,
% 5.42/5.65 ! [A: int,B: int,C: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.42/5.65 => ( ( ord_less_eq_int @ B @ C )
% 5.42/5.65 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_increasing
% 5.42/5.65 thf(fact_2490_add__decreasing,axiom,
% 5.42/5.65 ! [A: real,C: real,B: real] :
% 5.42/5.65 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.42/5.65 => ( ( ord_less_eq_real @ C @ B )
% 5.42/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_decreasing
% 5.42/5.65 thf(fact_2491_add__decreasing,axiom,
% 5.42/5.65 ! [A: rat,C: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.42/5.65 => ( ( ord_less_eq_rat @ C @ B )
% 5.42/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_decreasing
% 5.42/5.65 thf(fact_2492_add__decreasing,axiom,
% 5.42/5.65 ! [A: nat,C: nat,B: nat] :
% 5.42/5.65 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.42/5.65 => ( ( ord_less_eq_nat @ C @ B )
% 5.42/5.65 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_decreasing
% 5.42/5.65 thf(fact_2493_add__decreasing,axiom,
% 5.42/5.65 ! [A: int,C: int,B: int] :
% 5.42/5.65 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.42/5.65 => ( ( ord_less_eq_int @ C @ B )
% 5.42/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % add_decreasing
% 5.42/5.65 thf(fact_2494_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.42/5.65 ! [A: real,B: real,C: real] :
% 5.42/5.65 ( ( ord_less_real @ A @ B )
% 5.42/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.42/5.65 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.42/5.65 thf(fact_2495_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.42/5.65 ! [A: rat,B: rat,C: rat] :
% 5.42/5.65 ( ( ord_less_rat @ A @ B )
% 5.42/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.42/5.65 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.42/5.65 thf(fact_2496_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.42/5.65 ! [A: nat,B: nat,C: nat] :
% 5.42/5.65 ( ( ord_less_nat @ A @ B )
% 5.42/5.65 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.42/5.65 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.42/5.65 thf(fact_2497_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.42/5.65 ! [A: int,B: int,C: int] :
% 5.42/5.65 ( ( ord_less_int @ A @ B )
% 5.42/5.65 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.42/5.65 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.42/5.65 thf(fact_2498_mult__less__cancel__right__disj,axiom,
% 5.42/5.65 ! [A: real,C: real,B: real] :
% 5.42/5.65 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.42/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.42/5.65 & ( ord_less_real @ A @ B ) )
% 5.42/5.65 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.42/5.65 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.42/5.65
% 5.42/5.65 % mult_less_cancel_right_disj
% 5.42/5.65 thf(fact_2499_mult__less__cancel__right__disj,axiom,
% 5.42/5.65 ! [A: rat,C: rat,B: rat] :
% 5.42/5.65 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.42/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.42/5.65 & ( ord_less_rat @ A @ B ) )
% 5.42/5.65 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right_disj
% 5.46/5.65 thf(fact_2500_mult__less__cancel__right__disj,axiom,
% 5.46/5.65 ! [A: int,C: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 & ( ord_less_int @ A @ B ) )
% 5.46/5.65 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right_disj
% 5.46/5.65 thf(fact_2501_mult__strict__right__mono,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_right_mono
% 5.46/5.65 thf(fact_2502_mult__strict__right__mono,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_right_mono
% 5.46/5.65 thf(fact_2503_mult__strict__right__mono,axiom,
% 5.46/5.65 ! [A: nat,B: nat,C: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A @ B )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_right_mono
% 5.46/5.65 thf(fact_2504_mult__strict__right__mono,axiom,
% 5.46/5.65 ! [A: int,B: int,C: int] :
% 5.46/5.65 ( ( ord_less_int @ A @ B )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_right_mono
% 5.46/5.65 thf(fact_2505_mult__strict__right__mono__neg,axiom,
% 5.46/5.65 ! [B: real,A: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ B @ A )
% 5.46/5.65 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_right_mono_neg
% 5.46/5.65 thf(fact_2506_mult__strict__right__mono__neg,axiom,
% 5.46/5.65 ! [B: rat,A: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ B @ A )
% 5.46/5.65 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_right_mono_neg
% 5.46/5.65 thf(fact_2507_mult__strict__right__mono__neg,axiom,
% 5.46/5.65 ! [B: int,A: int,C: int] :
% 5.46/5.65 ( ( ord_less_int @ B @ A )
% 5.46/5.65 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_right_mono_neg
% 5.46/5.65 thf(fact_2508_mult__less__cancel__left__disj,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 & ( ord_less_real @ A @ B ) )
% 5.46/5.65 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left_disj
% 5.46/5.65 thf(fact_2509_mult__less__cancel__left__disj,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 & ( ord_less_rat @ A @ B ) )
% 5.46/5.65 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left_disj
% 5.46/5.65 thf(fact_2510_mult__less__cancel__left__disj,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 & ( ord_less_int @ A @ B ) )
% 5.46/5.65 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left_disj
% 5.46/5.65 thf(fact_2511_mult__strict__left__mono,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_left_mono
% 5.46/5.65 thf(fact_2512_mult__strict__left__mono,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_left_mono
% 5.46/5.65 thf(fact_2513_mult__strict__left__mono,axiom,
% 5.46/5.65 ! [A: nat,B: nat,C: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A @ B )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_left_mono
% 5.46/5.65 thf(fact_2514_mult__strict__left__mono,axiom,
% 5.46/5.65 ! [A: int,B: int,C: int] :
% 5.46/5.65 ( ( ord_less_int @ A @ B )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_left_mono
% 5.46/5.65 thf(fact_2515_mult__strict__left__mono__neg,axiom,
% 5.46/5.65 ! [B: real,A: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ B @ A )
% 5.46/5.65 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_left_mono_neg
% 5.46/5.65 thf(fact_2516_mult__strict__left__mono__neg,axiom,
% 5.46/5.65 ! [B: rat,A: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ B @ A )
% 5.46/5.65 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_left_mono_neg
% 5.46/5.65 thf(fact_2517_mult__strict__left__mono__neg,axiom,
% 5.46/5.65 ! [B: int,A: int,C: int] :
% 5.46/5.65 ( ( ord_less_int @ B @ A )
% 5.46/5.65 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_left_mono_neg
% 5.46/5.65 thf(fact_2518_mult__less__cancel__left__pos,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.65 = ( ord_less_real @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left_pos
% 5.46/5.65 thf(fact_2519_mult__less__cancel__left__pos,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left_pos
% 5.46/5.65 thf(fact_2520_mult__less__cancel__left__pos,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.65 = ( ord_less_int @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left_pos
% 5.46/5.65 thf(fact_2521_mult__less__cancel__left__neg,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.65 = ( ord_less_real @ B @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left_neg
% 5.46/5.65 thf(fact_2522_mult__less__cancel__left__neg,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left_neg
% 5.46/5.65 thf(fact_2523_mult__less__cancel__left__neg,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.65 = ( ord_less_int @ B @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left_neg
% 5.46/5.65 thf(fact_2524_zero__less__mult__pos2,axiom,
% 5.46/5.65 ! [B: real,A: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_pos2
% 5.46/5.65 thf(fact_2525_zero__less__mult__pos2,axiom,
% 5.46/5.65 ! [B: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_pos2
% 5.46/5.65 thf(fact_2526_zero__less__mult__pos2,axiom,
% 5.46/5.65 ! [B: nat,A: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_pos2
% 5.46/5.65 thf(fact_2527_zero__less__mult__pos2,axiom,
% 5.46/5.65 ! [B: int,A: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_pos2
% 5.46/5.65 thf(fact_2528_zero__less__mult__pos,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_pos
% 5.46/5.65 thf(fact_2529_zero__less__mult__pos,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_pos
% 5.46/5.65 thf(fact_2530_zero__less__mult__pos,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_pos
% 5.46/5.65 thf(fact_2531_zero__less__mult__pos,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_pos
% 5.46/5.65 thf(fact_2532_zero__less__mult__iff,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.46/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_iff
% 5.46/5.65 thf(fact_2533_zero__less__mult__iff,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.46/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_iff
% 5.46/5.65 thf(fact_2534_zero__less__mult__iff,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.46/5.65 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.65 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_mult_iff
% 5.46/5.65 thf(fact_2535_mult__pos__neg2,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_neg2
% 5.46/5.65 thf(fact_2536_mult__pos__neg2,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_neg2
% 5.46/5.65 thf(fact_2537_mult__pos__neg2,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_neg2
% 5.46/5.65 thf(fact_2538_mult__pos__neg2,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_neg2
% 5.46/5.65 thf(fact_2539_mult__pos__pos,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_pos
% 5.46/5.65 thf(fact_2540_mult__pos__pos,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_pos
% 5.46/5.65 thf(fact_2541_mult__pos__pos,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_pos
% 5.46/5.65 thf(fact_2542_mult__pos__pos,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_pos
% 5.46/5.65 thf(fact_2543_mult__pos__neg,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_neg
% 5.46/5.65 thf(fact_2544_mult__pos__neg,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_neg
% 5.46/5.65 thf(fact_2545_mult__pos__neg,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_neg
% 5.46/5.65 thf(fact_2546_mult__pos__neg,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_pos_neg
% 5.46/5.65 thf(fact_2547_mult__neg__pos,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_neg_pos
% 5.46/5.65 thf(fact_2548_mult__neg__pos,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_neg_pos
% 5.46/5.65 thf(fact_2549_mult__neg__pos,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_neg_pos
% 5.46/5.65 thf(fact_2550_mult__neg__pos,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_neg_pos
% 5.46/5.65 thf(fact_2551_mult__less__0__iff,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.46/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_0_iff
% 5.46/5.65 thf(fact_2552_mult__less__0__iff,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.46/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_0_iff
% 5.46/5.65 thf(fact_2553_mult__less__0__iff,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.46/5.65 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.65 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_0_iff
% 5.46/5.65 thf(fact_2554_not__square__less__zero,axiom,
% 5.46/5.65 ! [A: real] :
% 5.46/5.65 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.46/5.65
% 5.46/5.65 % not_square_less_zero
% 5.46/5.65 thf(fact_2555_not__square__less__zero,axiom,
% 5.46/5.65 ! [A: rat] :
% 5.46/5.65 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.46/5.65
% 5.46/5.65 % not_square_less_zero
% 5.46/5.65 thf(fact_2556_not__square__less__zero,axiom,
% 5.46/5.65 ! [A: int] :
% 5.46/5.65 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.46/5.65
% 5.46/5.65 % not_square_less_zero
% 5.46/5.65 thf(fact_2557_mult__neg__neg,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_neg_neg
% 5.46/5.65 thf(fact_2558_mult__neg__neg,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_neg_neg
% 5.46/5.65 thf(fact_2559_mult__neg__neg,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.65 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_neg_neg
% 5.46/5.65 thf(fact_2560_not__one__less__zero,axiom,
% 5.46/5.65 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.46/5.65
% 5.46/5.65 % not_one_less_zero
% 5.46/5.65 thf(fact_2561_not__one__less__zero,axiom,
% 5.46/5.65 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.46/5.65
% 5.46/5.65 % not_one_less_zero
% 5.46/5.65 thf(fact_2562_not__one__less__zero,axiom,
% 5.46/5.65 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.46/5.65
% 5.46/5.65 % not_one_less_zero
% 5.46/5.65 thf(fact_2563_not__one__less__zero,axiom,
% 5.46/5.65 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.46/5.65
% 5.46/5.65 % not_one_less_zero
% 5.46/5.65 thf(fact_2564_zero__less__one,axiom,
% 5.46/5.65 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.46/5.65
% 5.46/5.65 % zero_less_one
% 5.46/5.65 thf(fact_2565_zero__less__one,axiom,
% 5.46/5.65 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.46/5.65
% 5.46/5.65 % zero_less_one
% 5.46/5.65 thf(fact_2566_zero__less__one,axiom,
% 5.46/5.65 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.46/5.65
% 5.46/5.65 % zero_less_one
% 5.46/5.65 thf(fact_2567_zero__less__one,axiom,
% 5.46/5.65 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.46/5.65
% 5.46/5.65 % zero_less_one
% 5.46/5.65 thf(fact_2568_less__numeral__extra_I1_J,axiom,
% 5.46/5.65 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.46/5.65
% 5.46/5.65 % less_numeral_extra(1)
% 5.46/5.65 thf(fact_2569_less__numeral__extra_I1_J,axiom,
% 5.46/5.65 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.46/5.65
% 5.46/5.65 % less_numeral_extra(1)
% 5.46/5.65 thf(fact_2570_less__numeral__extra_I1_J,axiom,
% 5.46/5.65 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.46/5.65
% 5.46/5.65 % less_numeral_extra(1)
% 5.46/5.65 thf(fact_2571_less__numeral__extra_I1_J,axiom,
% 5.46/5.65 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.46/5.65
% 5.46/5.65 % less_numeral_extra(1)
% 5.46/5.65 thf(fact_2572_add__less__zeroD,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y2 ) @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.65 | ( ord_less_real @ Y2 @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_less_zeroD
% 5.46/5.65 thf(fact_2573_add__less__zeroD,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.46/5.65 | ( ord_less_rat @ Y2 @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_less_zeroD
% 5.46/5.65 thf(fact_2574_add__less__zeroD,axiom,
% 5.46/5.65 ! [X2: int,Y2: int] :
% 5.46/5.65 ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y2 ) @ zero_zero_int )
% 5.46/5.65 => ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.46/5.65 | ( ord_less_int @ Y2 @ zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_less_zeroD
% 5.46/5.65 thf(fact_2575_pos__add__strict,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ B @ C )
% 5.46/5.65 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_add_strict
% 5.46/5.65 thf(fact_2576_pos__add__strict,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ B @ C )
% 5.46/5.65 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_add_strict
% 5.46/5.65 thf(fact_2577_pos__add__strict,axiom,
% 5.46/5.65 ! [A: nat,B: nat,C: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ B @ C )
% 5.46/5.65 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_add_strict
% 5.46/5.65 thf(fact_2578_pos__add__strict,axiom,
% 5.46/5.65 ! [A: int,B: int,C: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ B @ C )
% 5.46/5.65 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_add_strict
% 5.46/5.65 thf(fact_2579_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A @ B )
% 5.46/5.65 => ~ ! [C2: nat] :
% 5.46/5.65 ( ( B
% 5.46/5.65 = ( plus_plus_nat @ A @ C2 ) )
% 5.46/5.65 => ( C2 = zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % canonically_ordered_monoid_add_class.lessE
% 5.46/5.65 thf(fact_2580_add__pos__pos,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_pos_pos
% 5.46/5.65 thf(fact_2581_add__pos__pos,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_pos_pos
% 5.46/5.65 thf(fact_2582_add__pos__pos,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_pos_pos
% 5.46/5.65 thf(fact_2583_add__pos__pos,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_pos_pos
% 5.46/5.65 thf(fact_2584_add__neg__neg,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_neg_neg
% 5.46/5.65 thf(fact_2585_add__neg__neg,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_neg_neg
% 5.46/5.65 thf(fact_2586_add__neg__neg,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.46/5.65 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.46/5.65 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_neg_neg
% 5.46/5.65 thf(fact_2587_add__neg__neg,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.65 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_neg_neg
% 5.46/5.65 thf(fact_2588_le__iff__diff__le__0,axiom,
% 5.46/5.65 ( ord_less_eq_real
% 5.46/5.65 = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % le_iff_diff_le_0
% 5.46/5.65 thf(fact_2589_le__iff__diff__le__0,axiom,
% 5.46/5.65 ( ord_less_eq_rat
% 5.46/5.65 = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % le_iff_diff_le_0
% 5.46/5.65 thf(fact_2590_le__iff__diff__le__0,axiom,
% 5.46/5.65 ( ord_less_eq_int
% 5.46/5.65 = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % le_iff_diff_le_0
% 5.46/5.65 thf(fact_2591_divide__right__mono__neg,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_right_mono_neg
% 5.46/5.65 thf(fact_2592_divide__right__mono__neg,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_right_mono_neg
% 5.46/5.65 thf(fact_2593_divide__nonpos__nonpos,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonpos_nonpos
% 5.46/5.65 thf(fact_2594_divide__nonpos__nonpos,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonpos_nonpos
% 5.46/5.65 thf(fact_2595_divide__nonpos__nonneg,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonpos_nonneg
% 5.46/5.65 thf(fact_2596_divide__nonpos__nonneg,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonpos_nonneg
% 5.46/5.65 thf(fact_2597_divide__nonneg__nonpos,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonneg_nonpos
% 5.46/5.65 thf(fact_2598_divide__nonneg__nonpos,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonneg_nonpos
% 5.46/5.65 thf(fact_2599_divide__nonneg__nonneg,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonneg_nonneg
% 5.46/5.65 thf(fact_2600_divide__nonneg__nonneg,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonneg_nonneg
% 5.46/5.65 thf(fact_2601_zero__le__divide__iff,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.46/5.65 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_le_divide_iff
% 5.46/5.65 thf(fact_2602_zero__le__divide__iff,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.46/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.46/5.65 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_le_divide_iff
% 5.46/5.65 thf(fact_2603_divide__right__mono,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_right_mono
% 5.46/5.65 thf(fact_2604_divide__right__mono,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_right_mono
% 5.46/5.65 thf(fact_2605_divide__le__0__iff,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.46/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.46/5.65 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_le_0_iff
% 5.46/5.65 thf(fact_2606_divide__le__0__iff,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.46/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.46/5.65 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_le_0_iff
% 5.46/5.65 thf(fact_2607_less__iff__diff__less__0,axiom,
% 5.46/5.65 ( ord_less_real
% 5.46/5.65 = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_iff_diff_less_0
% 5.46/5.65 thf(fact_2608_less__iff__diff__less__0,axiom,
% 5.46/5.65 ( ord_less_rat
% 5.46/5.65 = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_iff_diff_less_0
% 5.46/5.65 thf(fact_2609_less__iff__diff__less__0,axiom,
% 5.46/5.65 ( ord_less_int
% 5.46/5.65 = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_iff_diff_less_0
% 5.46/5.65 thf(fact_2610_divide__neg__neg,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_neg_neg
% 5.46/5.65 thf(fact_2611_divide__neg__neg,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_neg_neg
% 5.46/5.65 thf(fact_2612_divide__neg__pos,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_neg_pos
% 5.46/5.65 thf(fact_2613_divide__neg__pos,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_neg_pos
% 5.46/5.65 thf(fact_2614_divide__pos__neg,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_pos_neg
% 5.46/5.65 thf(fact_2615_divide__pos__neg,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_pos_neg
% 5.46/5.65 thf(fact_2616_divide__pos__pos,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_pos_pos
% 5.46/5.65 thf(fact_2617_divide__pos__pos,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_pos_pos
% 5.46/5.65 thf(fact_2618_divide__less__0__iff,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.46/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_0_iff
% 5.46/5.65 thf(fact_2619_divide__less__0__iff,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.46/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_0_iff
% 5.46/5.65 thf(fact_2620_divide__less__cancel,axiom,
% 5.46/5.65 ! [A: real,C: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ B @ A ) )
% 5.46/5.65 & ( C != zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_cancel
% 5.46/5.65 thf(fact_2621_divide__less__cancel,axiom,
% 5.46/5.65 ! [A: rat,C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ B @ A ) )
% 5.46/5.65 & ( C != zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_cancel
% 5.46/5.65 thf(fact_2622_zero__less__divide__iff,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.46/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_divide_iff
% 5.46/5.65 thf(fact_2623_zero__less__divide__iff,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.46/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_divide_iff
% 5.46/5.65 thf(fact_2624_divide__strict__right__mono,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_strict_right_mono
% 5.46/5.65 thf(fact_2625_divide__strict__right__mono,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_strict_right_mono
% 5.46/5.65 thf(fact_2626_divide__strict__right__mono__neg,axiom,
% 5.46/5.65 ! [B: real,A: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ B @ A )
% 5.46/5.65 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_strict_right_mono_neg
% 5.46/5.65 thf(fact_2627_divide__strict__right__mono__neg,axiom,
% 5.46/5.65 ! [B: rat,A: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ B @ A )
% 5.46/5.65 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_strict_right_mono_neg
% 5.46/5.65 thf(fact_2628_power__mono,axiom,
% 5.46/5.65 ! [A: real,B: real,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_mono
% 5.46/5.65 thf(fact_2629_power__mono,axiom,
% 5.46/5.65 ! [A: rat,B: rat,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_mono
% 5.46/5.65 thf(fact_2630_power__mono,axiom,
% 5.46/5.65 ! [A: nat,B: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_mono
% 5.46/5.65 thf(fact_2631_power__mono,axiom,
% 5.46/5.65 ! [A: int,B: int,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_mono
% 5.46/5.65 thf(fact_2632_zero__le__power,axiom,
% 5.46/5.65 ! [A: real,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_le_power
% 5.46/5.65 thf(fact_2633_zero__le__power,axiom,
% 5.46/5.65 ! [A: rat,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_le_power
% 5.46/5.65 thf(fact_2634_zero__le__power,axiom,
% 5.46/5.65 ! [A: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_le_power
% 5.46/5.65 thf(fact_2635_zero__le__power,axiom,
% 5.46/5.65 ! [A: int,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_le_power
% 5.46/5.65 thf(fact_2636_zero__less__power,axiom,
% 5.46/5.65 ! [A: real,N: nat] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_power
% 5.46/5.65 thf(fact_2637_zero__less__power,axiom,
% 5.46/5.65 ! [A: rat,N: nat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_power
% 5.46/5.65 thf(fact_2638_zero__less__power,axiom,
% 5.46/5.65 ! [A: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_power
% 5.46/5.65 thf(fact_2639_zero__less__power,axiom,
% 5.46/5.65 ! [A: int,N: nat] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_power
% 5.46/5.65 thf(fact_2640_nonzero__eq__divide__eq,axiom,
% 5.46/5.65 ! [C: complex,A: complex,B: complex] :
% 5.46/5.65 ( ( C != zero_zero_complex )
% 5.46/5.65 => ( ( A
% 5.46/5.65 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.46/5.65 = ( ( times_times_complex @ A @ C )
% 5.46/5.65 = B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nonzero_eq_divide_eq
% 5.46/5.65 thf(fact_2641_nonzero__eq__divide__eq,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( C != zero_zero_real )
% 5.46/5.65 => ( ( A
% 5.46/5.65 = ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ( times_times_real @ A @ C )
% 5.46/5.65 = B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nonzero_eq_divide_eq
% 5.46/5.65 thf(fact_2642_nonzero__eq__divide__eq,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( C != zero_zero_rat )
% 5.46/5.65 => ( ( A
% 5.46/5.65 = ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ( times_times_rat @ A @ C )
% 5.46/5.65 = B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nonzero_eq_divide_eq
% 5.46/5.65 thf(fact_2643_nonzero__divide__eq__eq,axiom,
% 5.46/5.65 ! [C: complex,B: complex,A: complex] :
% 5.46/5.65 ( ( C != zero_zero_complex )
% 5.46/5.65 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.46/5.65 = A )
% 5.46/5.65 = ( B
% 5.46/5.65 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nonzero_divide_eq_eq
% 5.46/5.65 thf(fact_2644_nonzero__divide__eq__eq,axiom,
% 5.46/5.65 ! [C: real,B: real,A: real] :
% 5.46/5.65 ( ( C != zero_zero_real )
% 5.46/5.65 => ( ( ( divide_divide_real @ B @ C )
% 5.46/5.65 = A )
% 5.46/5.65 = ( B
% 5.46/5.65 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nonzero_divide_eq_eq
% 5.46/5.65 thf(fact_2645_nonzero__divide__eq__eq,axiom,
% 5.46/5.65 ! [C: rat,B: rat,A: rat] :
% 5.46/5.65 ( ( C != zero_zero_rat )
% 5.46/5.65 => ( ( ( divide_divide_rat @ B @ C )
% 5.46/5.65 = A )
% 5.46/5.65 = ( B
% 5.46/5.65 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nonzero_divide_eq_eq
% 5.46/5.65 thf(fact_2646_eq__divide__imp,axiom,
% 5.46/5.65 ! [C: complex,A: complex,B: complex] :
% 5.46/5.65 ( ( C != zero_zero_complex )
% 5.46/5.65 => ( ( ( times_times_complex @ A @ C )
% 5.46/5.65 = B )
% 5.46/5.65 => ( A
% 5.46/5.65 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % eq_divide_imp
% 5.46/5.65 thf(fact_2647_eq__divide__imp,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( C != zero_zero_real )
% 5.46/5.65 => ( ( ( times_times_real @ A @ C )
% 5.46/5.65 = B )
% 5.46/5.65 => ( A
% 5.46/5.65 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % eq_divide_imp
% 5.46/5.65 thf(fact_2648_eq__divide__imp,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( C != zero_zero_rat )
% 5.46/5.65 => ( ( ( times_times_rat @ A @ C )
% 5.46/5.65 = B )
% 5.46/5.65 => ( A
% 5.46/5.65 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % eq_divide_imp
% 5.46/5.65 thf(fact_2649_divide__eq__imp,axiom,
% 5.46/5.65 ! [C: complex,B: complex,A: complex] :
% 5.46/5.65 ( ( C != zero_zero_complex )
% 5.46/5.65 => ( ( B
% 5.46/5.65 = ( times_times_complex @ A @ C ) )
% 5.46/5.65 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.46/5.65 = A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_eq_imp
% 5.46/5.65 thf(fact_2650_divide__eq__imp,axiom,
% 5.46/5.65 ! [C: real,B: real,A: real] :
% 5.46/5.65 ( ( C != zero_zero_real )
% 5.46/5.65 => ( ( B
% 5.46/5.65 = ( times_times_real @ A @ C ) )
% 5.46/5.65 => ( ( divide_divide_real @ B @ C )
% 5.46/5.65 = A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_eq_imp
% 5.46/5.65 thf(fact_2651_divide__eq__imp,axiom,
% 5.46/5.65 ! [C: rat,B: rat,A: rat] :
% 5.46/5.65 ( ( C != zero_zero_rat )
% 5.46/5.65 => ( ( B
% 5.46/5.65 = ( times_times_rat @ A @ C ) )
% 5.46/5.65 => ( ( divide_divide_rat @ B @ C )
% 5.46/5.65 = A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_eq_imp
% 5.46/5.65 thf(fact_2652_eq__divide__eq,axiom,
% 5.46/5.65 ! [A: complex,B: complex,C: complex] :
% 5.46/5.65 ( ( A
% 5.46/5.65 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.46/5.65 = ( ( ( C != zero_zero_complex )
% 5.46/5.65 => ( ( times_times_complex @ A @ C )
% 5.46/5.65 = B ) )
% 5.46/5.65 & ( ( C = zero_zero_complex )
% 5.46/5.65 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % eq_divide_eq
% 5.46/5.65 thf(fact_2653_eq__divide__eq,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( A
% 5.46/5.65 = ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ( ( C != zero_zero_real )
% 5.46/5.65 => ( ( times_times_real @ A @ C )
% 5.46/5.65 = B ) )
% 5.46/5.65 & ( ( C = zero_zero_real )
% 5.46/5.65 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % eq_divide_eq
% 5.46/5.65 thf(fact_2654_eq__divide__eq,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( A
% 5.46/5.65 = ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( C != zero_zero_rat )
% 5.46/5.65 => ( ( times_times_rat @ A @ C )
% 5.46/5.65 = B ) )
% 5.46/5.65 & ( ( C = zero_zero_rat )
% 5.46/5.65 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % eq_divide_eq
% 5.46/5.65 thf(fact_2655_divide__eq__eq,axiom,
% 5.46/5.65 ! [B: complex,C: complex,A: complex] :
% 5.46/5.65 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.46/5.65 = A )
% 5.46/5.65 = ( ( ( C != zero_zero_complex )
% 5.46/5.65 => ( B
% 5.46/5.65 = ( times_times_complex @ A @ C ) ) )
% 5.46/5.65 & ( ( C = zero_zero_complex )
% 5.46/5.65 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_eq_eq
% 5.46/5.65 thf(fact_2656_divide__eq__eq,axiom,
% 5.46/5.65 ! [B: real,C: real,A: real] :
% 5.46/5.65 ( ( ( divide_divide_real @ B @ C )
% 5.46/5.65 = A )
% 5.46/5.65 = ( ( ( C != zero_zero_real )
% 5.46/5.65 => ( B
% 5.46/5.65 = ( times_times_real @ A @ C ) ) )
% 5.46/5.65 & ( ( C = zero_zero_real )
% 5.46/5.65 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_eq_eq
% 5.46/5.65 thf(fact_2657_divide__eq__eq,axiom,
% 5.46/5.65 ! [B: rat,C: rat,A: rat] :
% 5.46/5.65 ( ( ( divide_divide_rat @ B @ C )
% 5.46/5.65 = A )
% 5.46/5.65 = ( ( ( C != zero_zero_rat )
% 5.46/5.65 => ( B
% 5.46/5.65 = ( times_times_rat @ A @ C ) ) )
% 5.46/5.65 & ( ( C = zero_zero_rat )
% 5.46/5.65 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_eq_eq
% 5.46/5.65 thf(fact_2658_frac__eq__eq,axiom,
% 5.46/5.65 ! [Y2: complex,Z: complex,X2: complex,W: complex] :
% 5.46/5.65 ( ( Y2 != zero_zero_complex )
% 5.46/5.65 => ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( ( divide1717551699836669952omplex @ X2 @ Y2 )
% 5.46/5.65 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.46/5.65 = ( ( times_times_complex @ X2 @ Z )
% 5.46/5.65 = ( times_times_complex @ W @ Y2 ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_eq_eq
% 5.46/5.65 thf(fact_2659_frac__eq__eq,axiom,
% 5.46/5.65 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.46/5.65 ( ( Y2 != zero_zero_real )
% 5.46/5.65 => ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( ( divide_divide_real @ X2 @ Y2 )
% 5.46/5.65 = ( divide_divide_real @ W @ Z ) )
% 5.46/5.65 = ( ( times_times_real @ X2 @ Z )
% 5.46/5.65 = ( times_times_real @ W @ Y2 ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_eq_eq
% 5.46/5.65 thf(fact_2660_frac__eq__eq,axiom,
% 5.46/5.65 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.46/5.65 ( ( Y2 != zero_zero_rat )
% 5.46/5.65 => ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( ( divide_divide_rat @ X2 @ Y2 )
% 5.46/5.65 = ( divide_divide_rat @ W @ Z ) )
% 5.46/5.65 = ( ( times_times_rat @ X2 @ Z )
% 5.46/5.65 = ( times_times_rat @ W @ Y2 ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_eq_eq
% 5.46/5.65 thf(fact_2661_right__inverse__eq,axiom,
% 5.46/5.65 ! [B: complex,A: complex] :
% 5.46/5.65 ( ( B != zero_zero_complex )
% 5.46/5.65 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.46/5.65 = one_one_complex )
% 5.46/5.65 = ( A = B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % right_inverse_eq
% 5.46/5.65 thf(fact_2662_right__inverse__eq,axiom,
% 5.46/5.65 ! [B: real,A: real] :
% 5.46/5.65 ( ( B != zero_zero_real )
% 5.46/5.65 => ( ( ( divide_divide_real @ A @ B )
% 5.46/5.65 = one_one_real )
% 5.46/5.65 = ( A = B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % right_inverse_eq
% 5.46/5.65 thf(fact_2663_right__inverse__eq,axiom,
% 5.46/5.65 ! [B: rat,A: rat] :
% 5.46/5.65 ( ( B != zero_zero_rat )
% 5.46/5.65 => ( ( ( divide_divide_rat @ A @ B )
% 5.46/5.65 = one_one_rat )
% 5.46/5.65 = ( A = B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % right_inverse_eq
% 5.46/5.65 thf(fact_2664_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.46/5.65 ! [A: code_integer,B: code_integer] :
% 5.46/5.65 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.65 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.46/5.65 thf(fact_2665_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.46/5.65 thf(fact_2666_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.46/5.65 thf(fact_2667_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.46/5.65 ! [B: nat,A: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.46/5.65 thf(fact_2668_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.46/5.65 ! [B: int,A: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.46/5.65 thf(fact_2669_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.46/5.65 ! [B: code_integer,A: code_integer] :
% 5.46/5.65 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.46/5.65 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.46/5.65 thf(fact_2670_power__0,axiom,
% 5.46/5.65 ! [A: rat] :
% 5.46/5.65 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.46/5.65 = one_one_rat ) ).
% 5.46/5.65
% 5.46/5.65 % power_0
% 5.46/5.65 thf(fact_2671_power__0,axiom,
% 5.46/5.65 ! [A: nat] :
% 5.46/5.65 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.46/5.65 = one_one_nat ) ).
% 5.46/5.65
% 5.46/5.65 % power_0
% 5.46/5.65 thf(fact_2672_power__0,axiom,
% 5.46/5.65 ! [A: real] :
% 5.46/5.65 ( ( power_power_real @ A @ zero_zero_nat )
% 5.46/5.65 = one_one_real ) ).
% 5.46/5.65
% 5.46/5.65 % power_0
% 5.46/5.65 thf(fact_2673_power__0,axiom,
% 5.46/5.65 ! [A: complex] :
% 5.46/5.65 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.46/5.65 = one_one_complex ) ).
% 5.46/5.65
% 5.46/5.65 % power_0
% 5.46/5.65 thf(fact_2674_power__0,axiom,
% 5.46/5.65 ! [A: int] :
% 5.46/5.65 ( ( power_power_int @ A @ zero_zero_nat )
% 5.46/5.65 = one_one_int ) ).
% 5.46/5.65
% 5.46/5.65 % power_0
% 5.46/5.65 thf(fact_2675_mod__eq__self__iff__div__eq__0,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ( modulo_modulo_nat @ A @ B )
% 5.46/5.65 = A )
% 5.46/5.65 = ( ( divide_divide_nat @ A @ B )
% 5.46/5.65 = zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % mod_eq_self_iff_div_eq_0
% 5.46/5.65 thf(fact_2676_mod__eq__self__iff__div__eq__0,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.65 = A )
% 5.46/5.65 = ( ( divide_divide_int @ A @ B )
% 5.46/5.65 = zero_zero_int ) ) ).
% 5.46/5.65
% 5.46/5.65 % mod_eq_self_iff_div_eq_0
% 5.46/5.65 thf(fact_2677_mod__eq__self__iff__div__eq__0,axiom,
% 5.46/5.65 ! [A: code_integer,B: code_integer] :
% 5.46/5.65 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.46/5.65 = A )
% 5.46/5.65 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.46/5.65 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.65
% 5.46/5.65 % mod_eq_self_iff_div_eq_0
% 5.46/5.65 thf(fact_2678_Ex__less__Suc2,axiom,
% 5.46/5.65 ! [N: nat,P: nat > $o] :
% 5.46/5.65 ( ( ? [I4: nat] :
% 5.46/5.65 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.46/5.65 & ( P @ I4 ) ) )
% 5.46/5.65 = ( ( P @ zero_zero_nat )
% 5.46/5.65 | ? [I4: nat] :
% 5.46/5.65 ( ( ord_less_nat @ I4 @ N )
% 5.46/5.65 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % Ex_less_Suc2
% 5.46/5.65 thf(fact_2679_gr0__conv__Suc,axiom,
% 5.46/5.65 ! [N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 = ( ? [M3: nat] :
% 5.46/5.65 ( N
% 5.46/5.65 = ( suc @ M3 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % gr0_conv_Suc
% 5.46/5.65 thf(fact_2680_All__less__Suc2,axiom,
% 5.46/5.65 ! [N: nat,P: nat > $o] :
% 5.46/5.65 ( ( ! [I4: nat] :
% 5.46/5.65 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.46/5.65 => ( P @ I4 ) ) )
% 5.46/5.65 = ( ( P @ zero_zero_nat )
% 5.46/5.65 & ! [I4: nat] :
% 5.46/5.65 ( ( ord_less_nat @ I4 @ N )
% 5.46/5.65 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % All_less_Suc2
% 5.46/5.65 thf(fact_2681_gr0__implies__Suc,axiom,
% 5.46/5.65 ! [N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 => ? [M4: nat] :
% 5.46/5.65 ( N
% 5.46/5.65 = ( suc @ M4 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % gr0_implies_Suc
% 5.46/5.65 thf(fact_2682_less__Suc__eq__0__disj,axiom,
% 5.46/5.65 ! [M: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.46/5.65 = ( ( M = zero_zero_nat )
% 5.46/5.65 | ? [J3: nat] :
% 5.46/5.65 ( ( M
% 5.46/5.65 = ( suc @ J3 ) )
% 5.46/5.65 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_Suc_eq_0_disj
% 5.46/5.65 thf(fact_2683_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I1_J,axiom,
% 5.46/5.65 ! [A: $o,B: $o,X2: nat] :
% 5.46/5.65 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.46/5.65 = one_one_nat ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(1)
% 5.46/5.65 thf(fact_2684_add__is__1,axiom,
% 5.46/5.65 ! [M: nat,N: nat] :
% 5.46/5.65 ( ( ( plus_plus_nat @ M @ N )
% 5.46/5.65 = ( suc @ zero_zero_nat ) )
% 5.46/5.65 = ( ( ( M
% 5.46/5.65 = ( suc @ zero_zero_nat ) )
% 5.46/5.65 & ( N = zero_zero_nat ) )
% 5.46/5.65 | ( ( M = zero_zero_nat )
% 5.46/5.65 & ( N
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_is_1
% 5.46/5.65 thf(fact_2685_one__is__add,axiom,
% 5.46/5.65 ! [M: nat,N: nat] :
% 5.46/5.65 ( ( ( suc @ zero_zero_nat )
% 5.46/5.65 = ( plus_plus_nat @ M @ N ) )
% 5.46/5.65 = ( ( ( M
% 5.46/5.65 = ( suc @ zero_zero_nat ) )
% 5.46/5.65 & ( N = zero_zero_nat ) )
% 5.46/5.65 | ( ( M = zero_zero_nat )
% 5.46/5.65 & ( N
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % one_is_add
% 5.46/5.65 thf(fact_2686_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I1_J,axiom,
% 5.46/5.65 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.65 = one_one_nat ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(1)
% 5.46/5.65 thf(fact_2687_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I2_J,axiom,
% 5.46/5.65 ! [Uv: $o] :
% 5.46/5.65 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $true @ Uv ) )
% 5.46/5.65 = one_one_nat ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(2)
% 5.46/5.65 thf(fact_2688_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J,axiom,
% 5.46/5.65 ! [Uu: $o] :
% 5.46/5.65 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ Uu @ $true ) )
% 5.46/5.65 = one_one_nat ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(3)
% 5.46/5.65 thf(fact_2689_option_Osize_I4_J,axiom,
% 5.46/5.65 ! [X23: product_prod_nat_nat] :
% 5.46/5.65 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % option.size(4)
% 5.46/5.65 thf(fact_2690_option_Osize_I4_J,axiom,
% 5.46/5.65 ! [X23: nat] :
% 5.46/5.65 ( ( size_size_option_nat @ ( some_nat @ X23 ) )
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % option.size(4)
% 5.46/5.65 thf(fact_2691_option_Osize_I4_J,axiom,
% 5.46/5.65 ! [X23: num] :
% 5.46/5.65 ( ( size_size_option_num @ ( some_num @ X23 ) )
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % option.size(4)
% 5.46/5.65 thf(fact_2692_ex__least__nat__le,axiom,
% 5.46/5.65 ! [P: nat > $o,N: nat] :
% 5.46/5.65 ( ( P @ N )
% 5.46/5.65 => ( ~ ( P @ zero_zero_nat )
% 5.46/5.65 => ? [K3: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ K3 @ N )
% 5.46/5.65 & ! [I3: nat] :
% 5.46/5.65 ( ( ord_less_nat @ I3 @ K3 )
% 5.46/5.65 => ~ ( P @ I3 ) )
% 5.46/5.65 & ( P @ K3 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % ex_least_nat_le
% 5.46/5.65 thf(fact_2693_less__imp__add__positive,axiom,
% 5.46/5.65 ! [I: nat,J: nat] :
% 5.46/5.65 ( ( ord_less_nat @ I @ J )
% 5.46/5.65 => ? [K3: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 5.46/5.65 & ( ( plus_plus_nat @ I @ K3 )
% 5.46/5.65 = J ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_imp_add_positive
% 5.46/5.65 thf(fact_2694_One__nat__def,axiom,
% 5.46/5.65 ( one_one_nat
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % One_nat_def
% 5.46/5.65 thf(fact_2695_option_Osize_I3_J,axiom,
% 5.46/5.65 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % option.size(3)
% 5.46/5.65 thf(fact_2696_option_Osize_I3_J,axiom,
% 5.46/5.65 ( ( size_size_option_nat @ none_nat )
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % option.size(3)
% 5.46/5.65 thf(fact_2697_option_Osize_I3_J,axiom,
% 5.46/5.65 ( ( size_size_option_num @ none_num )
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % option.size(3)
% 5.46/5.65 thf(fact_2698_diff__less,axiom,
% 5.46/5.65 ! [N: nat,M: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.65 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % diff_less
% 5.46/5.65 thf(fact_2699_mult__less__mono2,axiom,
% 5.46/5.65 ! [I: nat,J: nat,K: nat] :
% 5.46/5.65 ( ( ord_less_nat @ I @ J )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_mono2
% 5.46/5.65 thf(fact_2700_mult__less__mono1,axiom,
% 5.46/5.65 ! [I: nat,J: nat,K: nat] :
% 5.46/5.65 ( ( ord_less_nat @ I @ J )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_mono1
% 5.46/5.65 thf(fact_2701_nat__mult__less__cancel1,axiom,
% 5.46/5.65 ! [K: nat,M: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.65 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.65 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nat_mult_less_cancel1
% 5.46/5.65 thf(fact_2702_nat__mult__eq__cancel1,axiom,
% 5.46/5.65 ! [K: nat,M: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.65 => ( ( ( times_times_nat @ K @ M )
% 5.46/5.65 = ( times_times_nat @ K @ N ) )
% 5.46/5.65 = ( M = N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nat_mult_eq_cancel1
% 5.46/5.65 thf(fact_2703_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.46/5.65 ! [M: nat,N: nat] :
% 5.46/5.65 ( ( ( divide_divide_nat @ M @ N )
% 5.46/5.65 = zero_zero_nat )
% 5.46/5.65 = ( ( ord_less_nat @ M @ N )
% 5.46/5.65 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % Euclidean_Division.div_eq_0_iff
% 5.46/5.65 thf(fact_2704_diff__add__0,axiom,
% 5.46/5.65 ! [N: nat,M: nat] :
% 5.46/5.65 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.65 = zero_zero_nat ) ).
% 5.46/5.65
% 5.46/5.65 % diff_add_0
% 5.46/5.65 thf(fact_2705_nat__power__less__imp__less,axiom,
% 5.46/5.65 ! [I: nat,M: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.46/5.65 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.46/5.65 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nat_power_less_imp_less
% 5.46/5.65 thf(fact_2706_mult__eq__self__implies__10,axiom,
% 5.46/5.65 ! [M: nat,N: nat] :
% 5.46/5.65 ( ( M
% 5.46/5.65 = ( times_times_nat @ M @ N ) )
% 5.46/5.65 => ( ( N = one_one_nat )
% 5.46/5.65 | ( M = zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_eq_self_implies_10
% 5.46/5.65 thf(fact_2707_mod__Suc,axiom,
% 5.46/5.65 ! [M: nat,N: nat] :
% 5.46/5.65 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.65 = N )
% 5.46/5.65 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.46/5.65 = zero_zero_nat ) )
% 5.46/5.65 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.65 != N )
% 5.46/5.65 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.46/5.65 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mod_Suc
% 5.46/5.65 thf(fact_2708_mod__less__divisor,axiom,
% 5.46/5.65 ! [N: nat,M: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.46/5.65
% 5.46/5.65 % mod_less_divisor
% 5.46/5.65 thf(fact_2709_mod__eq__0D,axiom,
% 5.46/5.65 ! [M: nat,D2: nat] :
% 5.46/5.65 ( ( ( modulo_modulo_nat @ M @ D2 )
% 5.46/5.65 = zero_zero_nat )
% 5.46/5.65 => ? [Q3: nat] :
% 5.46/5.65 ( M
% 5.46/5.65 = ( times_times_nat @ D2 @ Q3 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mod_eq_0D
% 5.46/5.65 thf(fact_2710_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 5.46/5.65 ! [X2: produc9072475918466114483BT_nat] :
% 5.46/5.65 ( ! [A5: $o,B5: $o,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X3 ) )
% 5.46/5.65 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 ) )
% 5.46/5.65 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X3 ) )
% 5.46/5.65 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 5.46/5.65 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.cases
% 5.46/5.65 thf(fact_2711_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 5.46/5.65 ! [X2: produc9072475918466114483BT_nat] :
% 5.46/5.65 ( ! [A5: $o,B5: $o,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X3 ) )
% 5.46/5.65 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ X3 ) )
% 5.46/5.65 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X3 ) )
% 5.46/5.65 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 5.46/5.65 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.cases
% 5.46/5.65 thf(fact_2712_VEBT__internal_Omembermima_Ocases,axiom,
% 5.46/5.65 ! [X2: produc9072475918466114483BT_nat] :
% 5.46/5.65 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.46/5.65 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.46/5.65 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X3 ) )
% 5.46/5.65 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ X3 ) )
% 5.46/5.65 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X3 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % VEBT_internal.membermima.cases
% 5.46/5.65 thf(fact_2713_vebt__pred_Ocases,axiom,
% 5.46/5.65 ! [X2: produc9072475918466114483BT_nat] :
% 5.46/5.65 ( ! [Uu2: $o,Uv2: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 5.46/5.65 => ( ! [A5: $o,Uw2: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.46/5.65 => ( ! [A5: $o,B5: $o,Va3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va3 ) ) ) )
% 5.46/5.65 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb2: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Vb2 ) )
% 5.46/5.65 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Vf ) )
% 5.46/5.65 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 5.46/5.65 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % vebt_pred.cases
% 5.46/5.65 thf(fact_2714_vebt__succ_Ocases,axiom,
% 5.46/5.65 ! [X2: produc9072475918466114483BT_nat] :
% 5.46/5.65 ( ! [Uu2: $o,B5: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) )
% 5.46/5.65 => ( ! [Uv2: $o,Uw2: $o,N3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) )
% 5.46/5.65 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va2: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va2 ) )
% 5.46/5.65 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve ) )
% 5.46/5.65 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 5.46/5.65 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % vebt_succ.cases
% 5.46/5.65 thf(fact_2715_vebt__insert_Osimps_I2_J,axiom,
% 5.46/5.65 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.46/5.65 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X2 )
% 5.46/5.65 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) ) ).
% 5.46/5.65
% 5.46/5.65 % vebt_insert.simps(2)
% 5.46/5.65 thf(fact_2716_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.46/5.65 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.46/5.65 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.46/5.65
% 5.46/5.65 % VEBT_internal.naive_member.simps(2)
% 5.46/5.65 thf(fact_2717_vebt__pred_Osimps_I3_J,axiom,
% 5.46/5.65 ! [B: $o,A: $o,Va: nat] :
% 5.46/5.65 ( ( B
% 5.46/5.65 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.65 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.65 & ( ~ B
% 5.46/5.65 => ( ( A
% 5.46/5.65 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.65 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.65 & ( ~ A
% 5.46/5.65 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.65 = none_nat ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % vebt_pred.simps(3)
% 5.46/5.65 thf(fact_2718_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases,axiom,
% 5.46/5.65 ! [X2: vEBT_VEBT] :
% 5.46/5.65 ( ( X2
% 5.46/5.65 != ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.65 => ( ! [Uv2: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.46/5.65 => ( ! [Uu2: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.46/5.65 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.46/5.65 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.cases
% 5.46/5.65 thf(fact_2719_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 5.46/5.65 ! [A: $o,B: $o,X2: nat] :
% 5.46/5.65 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.46/5.65 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(1)
% 5.46/5.65 thf(fact_2720_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.46/5.65 ! [X2: vEBT_VEBT] :
% 5.46/5.65 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.46/5.65 => ( ! [Uv2: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.46/5.65 => ( ! [Uu2: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.46/5.65 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % VEBT_internal.minNull.elims(3)
% 5.46/5.65 thf(fact_2721_vebt__succ_Osimps_I2_J,axiom,
% 5.46/5.65 ! [Uv: $o,Uw: $o,N: nat] :
% 5.46/5.65 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 5.46/5.65 = none_nat ) ).
% 5.46/5.65
% 5.46/5.65 % vebt_succ.simps(2)
% 5.46/5.65 thf(fact_2722_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.46/5.65 ! [X2: vEBT_VEBT] :
% 5.46/5.65 ( ( vEBT_VEBT_minNull @ X2 )
% 5.46/5.65 => ( ( X2
% 5.46/5.65 != ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.65 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % VEBT_internal.minNull.elims(2)
% 5.46/5.65 thf(fact_2723_mult__less__le__imp__less,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_real @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_le_imp_less
% 5.46/5.65 thf(fact_2724_mult__less__le__imp__less,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_le_imp_less
% 5.46/5.65 thf(fact_2725_mult__less__le__imp__less,axiom,
% 5.46/5.65 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_le_imp_less
% 5.46/5.65 thf(fact_2726_mult__less__le__imp__less,axiom,
% 5.46/5.65 ! [A: int,B: int,C: int,D2: int] :
% 5.46/5.65 ( ( ord_less_int @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_int @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_le_imp_less
% 5.46/5.65 thf(fact_2727_mult__le__less__imp__less,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_real @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_less_imp_less
% 5.46/5.65 thf(fact_2728_mult__le__less__imp__less,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_rat @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_less_imp_less
% 5.46/5.65 thf(fact_2729_mult__le__less__imp__less,axiom,
% 5.46/5.65 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.46/5.65 => ( ( ord_less_nat @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_less_imp_less
% 5.46/5.65 thf(fact_2730_mult__le__less__imp__less,axiom,
% 5.46/5.65 ! [A: int,B: int,C: int,D2: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.46/5.65 => ( ( ord_less_int @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_less_imp_less
% 5.46/5.65 thf(fact_2731_mult__right__le__imp__le,axiom,
% 5.46/5.65 ! [A: real,C: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_le_imp_le
% 5.46/5.65 thf(fact_2732_mult__right__le__imp__le,axiom,
% 5.46/5.65 ! [A: rat,C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_le_imp_le
% 5.46/5.65 thf(fact_2733_mult__right__le__imp__le,axiom,
% 5.46/5.65 ! [A: nat,C: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_le_imp_le
% 5.46/5.65 thf(fact_2734_mult__right__le__imp__le,axiom,
% 5.46/5.65 ! [A: int,C: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_le_imp_le
% 5.46/5.65 thf(fact_2735_mult__left__le__imp__le,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le_imp_le
% 5.46/5.65 thf(fact_2736_mult__left__le__imp__le,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le_imp_le
% 5.46/5.65 thf(fact_2737_mult__left__le__imp__le,axiom,
% 5.46/5.65 ! [C: nat,A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le_imp_le
% 5.46/5.65 thf(fact_2738_mult__left__le__imp__le,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le_imp_le
% 5.46/5.65 thf(fact_2739_mult__le__cancel__left__pos,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.65 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left_pos
% 5.46/5.65 thf(fact_2740_mult__le__cancel__left__pos,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left_pos
% 5.46/5.65 thf(fact_2741_mult__le__cancel__left__pos,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.65 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left_pos
% 5.46/5.65 thf(fact_2742_mult__le__cancel__left__neg,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.65 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left_neg
% 5.46/5.65 thf(fact_2743_mult__le__cancel__left__neg,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left_neg
% 5.46/5.65 thf(fact_2744_mult__le__cancel__left__neg,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.65 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left_neg
% 5.46/5.65 thf(fact_2745_mult__less__cancel__right,axiom,
% 5.46/5.65 ! [A: real,C: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right
% 5.46/5.65 thf(fact_2746_mult__less__cancel__right,axiom,
% 5.46/5.65 ! [A: rat,C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right
% 5.46/5.65 thf(fact_2747_mult__less__cancel__right,axiom,
% 5.46/5.65 ! [A: int,C: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right
% 5.46/5.65 thf(fact_2748_mult__strict__mono_H,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_real @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_mono'
% 5.46/5.65 thf(fact_2749_mult__strict__mono_H,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_rat @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_mono'
% 5.46/5.65 thf(fact_2750_mult__strict__mono_H,axiom,
% 5.46/5.65 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A @ B )
% 5.46/5.65 => ( ( ord_less_nat @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_mono'
% 5.46/5.65 thf(fact_2751_mult__strict__mono_H,axiom,
% 5.46/5.65 ! [A: int,B: int,C: int,D2: int] :
% 5.46/5.65 ( ( ord_less_int @ A @ B )
% 5.46/5.65 => ( ( ord_less_int @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_mono'
% 5.46/5.65 thf(fact_2752_mult__right__less__imp__less,axiom,
% 5.46/5.65 ! [A: real,C: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_less_imp_less
% 5.46/5.65 thf(fact_2753_mult__right__less__imp__less,axiom,
% 5.46/5.65 ! [A: rat,C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_less_imp_less
% 5.46/5.65 thf(fact_2754_mult__right__less__imp__less,axiom,
% 5.46/5.65 ! [A: nat,C: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_less_imp_less
% 5.46/5.65 thf(fact_2755_mult__right__less__imp__less,axiom,
% 5.46/5.65 ! [A: int,C: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_less_imp_less
% 5.46/5.65 thf(fact_2756_mult__less__cancel__left,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left
% 5.46/5.65 thf(fact_2757_mult__less__cancel__left,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left
% 5.46/5.65 thf(fact_2758_mult__less__cancel__left,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left
% 5.46/5.65 thf(fact_2759_mult__strict__mono,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_real @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_mono
% 5.46/5.65 thf(fact_2760_mult__strict__mono,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_rat @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_mono
% 5.46/5.65 thf(fact_2761_mult__strict__mono,axiom,
% 5.46/5.65 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A @ B )
% 5.46/5.65 => ( ( ord_less_nat @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_mono
% 5.46/5.65 thf(fact_2762_mult__strict__mono,axiom,
% 5.46/5.65 ! [A: int,B: int,C: int,D2: int] :
% 5.46/5.65 ( ( ord_less_int @ A @ B )
% 5.46/5.65 => ( ( ord_less_int @ C @ D2 )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_strict_mono
% 5.46/5.65 thf(fact_2763_mult__left__less__imp__less,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_less_imp_less
% 5.46/5.65 thf(fact_2764_mult__left__less__imp__less,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_less_imp_less
% 5.46/5.65 thf(fact_2765_mult__left__less__imp__less,axiom,
% 5.46/5.65 ! [C: nat,A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_less_imp_less
% 5.46/5.65 thf(fact_2766_mult__left__less__imp__less,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_less_imp_less
% 5.46/5.65 thf(fact_2767_mult__le__cancel__right,axiom,
% 5.46/5.65 ! [A: real,C: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_right
% 5.46/5.65 thf(fact_2768_mult__le__cancel__right,axiom,
% 5.46/5.65 ! [A: rat,C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_right
% 5.46/5.65 thf(fact_2769_mult__le__cancel__right,axiom,
% 5.46/5.65 ! [A: int,C: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_eq_int @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_right
% 5.46/5.65 thf(fact_2770_mult__le__cancel__left,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left
% 5.46/5.65 thf(fact_2771_mult__le__cancel__left,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left
% 5.46/5.65 thf(fact_2772_mult__le__cancel__left,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_eq_int @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left
% 5.46/5.65 thf(fact_2773_field__le__epsilon,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ! [E2: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.46/5.65 => ( ord_less_eq_real @ X2 @ ( plus_plus_real @ Y2 @ E2 ) ) )
% 5.46/5.65 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.46/5.65
% 5.46/5.65 % field_le_epsilon
% 5.46/5.65 thf(fact_2774_field__le__epsilon,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ! [E2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.46/5.65 => ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ Y2 @ E2 ) ) )
% 5.46/5.65 => ( ord_less_eq_rat @ X2 @ Y2 ) ) ).
% 5.46/5.65
% 5.46/5.65 % field_le_epsilon
% 5.46/5.65 thf(fact_2775_add__strict__increasing2,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ B @ C )
% 5.46/5.65 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_strict_increasing2
% 5.46/5.65 thf(fact_2776_add__strict__increasing2,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ B @ C )
% 5.46/5.65 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_strict_increasing2
% 5.46/5.65 thf(fact_2777_add__strict__increasing2,axiom,
% 5.46/5.65 ! [A: nat,B: nat,C: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ B @ C )
% 5.46/5.65 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_strict_increasing2
% 5.46/5.65 thf(fact_2778_add__strict__increasing2,axiom,
% 5.46/5.65 ! [A: int,B: int,C: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ B @ C )
% 5.46/5.65 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_strict_increasing2
% 5.46/5.65 thf(fact_2779_add__strict__increasing,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ B @ C )
% 5.46/5.65 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_strict_increasing
% 5.46/5.65 thf(fact_2780_add__strict__increasing,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ B @ C )
% 5.46/5.65 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_strict_increasing
% 5.46/5.65 thf(fact_2781_add__strict__increasing,axiom,
% 5.46/5.65 ! [A: nat,B: nat,C: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_eq_nat @ B @ C )
% 5.46/5.65 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_strict_increasing
% 5.46/5.65 thf(fact_2782_add__strict__increasing,axiom,
% 5.46/5.65 ! [A: int,B: int,C: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_eq_int @ B @ C )
% 5.46/5.65 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_strict_increasing
% 5.46/5.65 thf(fact_2783_add__pos__nonneg,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_pos_nonneg
% 5.46/5.65 thf(fact_2784_add__pos__nonneg,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_pos_nonneg
% 5.46/5.65 thf(fact_2785_add__pos__nonneg,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_pos_nonneg
% 5.46/5.65 thf(fact_2786_add__pos__nonneg,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_pos_nonneg
% 5.46/5.65 thf(fact_2787_add__nonpos__neg,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_nonpos_neg
% 5.46/5.65 thf(fact_2788_add__nonpos__neg,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_nonpos_neg
% 5.46/5.65 thf(fact_2789_add__nonpos__neg,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.46/5.65 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.46/5.65 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_nonpos_neg
% 5.46/5.65 thf(fact_2790_add__nonpos__neg,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.65 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_nonpos_neg
% 5.46/5.65 thf(fact_2791_add__nonneg__pos,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_nonneg_pos
% 5.46/5.65 thf(fact_2792_add__nonneg__pos,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_nonneg_pos
% 5.46/5.65 thf(fact_2793_add__nonneg__pos,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_nonneg_pos
% 5.46/5.65 thf(fact_2794_add__nonneg__pos,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_nonneg_pos
% 5.46/5.65 thf(fact_2795_add__neg__nonpos,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_neg_nonpos
% 5.46/5.65 thf(fact_2796_add__neg__nonpos,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_neg_nonpos
% 5.46/5.65 thf(fact_2797_add__neg__nonpos,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.46/5.65 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.46/5.65 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_neg_nonpos
% 5.46/5.65 thf(fact_2798_add__neg__nonpos,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.65 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_neg_nonpos
% 5.46/5.65 thf(fact_2799_frac__le,axiom,
% 5.46/5.65 ! [Y2: real,X2: real,W: real,Z: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.46/5.65 => ( ( ord_less_eq_real @ W @ Z )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_le
% 5.46/5.65 thf(fact_2800_frac__le,axiom,
% 5.46/5.65 ! [Y2: rat,X2: rat,W: rat,Z: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.46/5.65 => ( ( ord_less_eq_rat @ W @ Z )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_le
% 5.46/5.65 thf(fact_2801_frac__less,axiom,
% 5.46/5.65 ! [X2: real,Y2: real,W: real,Z: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.46/5.65 => ( ( ord_less_eq_real @ W @ Z )
% 5.46/5.65 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_less
% 5.46/5.65 thf(fact_2802_frac__less,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat,W: rat,Z: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_rat @ X2 @ Y2 )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.46/5.65 => ( ( ord_less_eq_rat @ W @ Z )
% 5.46/5.65 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_less
% 5.46/5.65 thf(fact_2803_frac__less2,axiom,
% 5.46/5.65 ! [X2: real,Y2: real,W: real,Z: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.46/5.65 => ( ( ord_less_real @ W @ Z )
% 5.46/5.65 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_less2
% 5.46/5.65 thf(fact_2804_frac__less2,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat,W: rat,Z: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.46/5.65 => ( ( ord_less_rat @ W @ Z )
% 5.46/5.65 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_less2
% 5.46/5.65 thf(fact_2805_divide__le__cancel,axiom,
% 5.46/5.65 ! [A: real,C: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_le_cancel
% 5.46/5.65 thf(fact_2806_divide__le__cancel,axiom,
% 5.46/5.65 ! [A: rat,C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ A @ B ) )
% 5.46/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_le_cancel
% 5.46/5.65 thf(fact_2807_divide__nonneg__neg,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonneg_neg
% 5.46/5.65 thf(fact_2808_divide__nonneg__neg,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonneg_neg
% 5.46/5.65 thf(fact_2809_divide__nonneg__pos,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonneg_pos
% 5.46/5.65 thf(fact_2810_divide__nonneg__pos,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonneg_pos
% 5.46/5.65 thf(fact_2811_divide__nonpos__neg,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonpos_neg
% 5.46/5.65 thf(fact_2812_divide__nonpos__neg,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonpos_neg
% 5.46/5.65 thf(fact_2813_divide__nonpos__pos,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonpos_pos
% 5.46/5.65 thf(fact_2814_divide__nonpos__pos,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_nonpos_pos
% 5.46/5.65 thf(fact_2815_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ A @ B )
% 5.46/5.65 => ( ( divide_divide_nat @ A @ B )
% 5.46/5.65 = zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.div_less
% 5.46/5.65 thf(fact_2816_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ A @ B )
% 5.46/5.65 => ( ( divide_divide_int @ A @ B )
% 5.46/5.65 = zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.div_less
% 5.46/5.65 thf(fact_2817_div__positive,axiom,
% 5.46/5.65 ! [B: nat,A: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ( ord_less_eq_nat @ B @ A )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_positive
% 5.46/5.65 thf(fact_2818_div__positive,axiom,
% 5.46/5.65 ! [B: int,A: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ( ord_less_eq_int @ B @ A )
% 5.46/5.65 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_positive
% 5.46/5.65 thf(fact_2819_mult__left__le,axiom,
% 5.46/5.65 ! [C: real,A: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le
% 5.46/5.65 thf(fact_2820_mult__left__le,axiom,
% 5.46/5.65 ! [C: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le
% 5.46/5.65 thf(fact_2821_mult__left__le,axiom,
% 5.46/5.65 ! [C: nat,A: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le
% 5.46/5.65 thf(fact_2822_mult__left__le,axiom,
% 5.46/5.65 ! [C: int,A: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le
% 5.46/5.65 thf(fact_2823_mult__le__one,axiom,
% 5.46/5.65 ! [A: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.46/5.65 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_one
% 5.46/5.65 thf(fact_2824_mult__le__one,axiom,
% 5.46/5.65 ! [A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_one
% 5.46/5.65 thf(fact_2825_mult__le__one,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.46/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_one
% 5.46/5.65 thf(fact_2826_mult__le__one,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.46/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_one
% 5.46/5.65 thf(fact_2827_mult__right__le__one__le,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( times_times_real @ X2 @ Y2 ) @ X2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_le_one_le
% 5.46/5.65 thf(fact_2828_mult__right__le__one__le,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Y2 ) @ X2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_le_one_le
% 5.46/5.65 thf(fact_2829_mult__right__le__one__le,axiom,
% 5.46/5.65 ! [X2: int,Y2: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 5.46/5.65 => ( ord_less_eq_int @ ( times_times_int @ X2 @ Y2 ) @ X2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_right_le_one_le
% 5.46/5.65 thf(fact_2830_mult__left__le__one__le,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( times_times_real @ Y2 @ X2 ) @ X2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le_one_le
% 5.46/5.65 thf(fact_2831_mult__left__le__one__le,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ Y2 @ X2 ) @ X2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le_one_le
% 5.46/5.65 thf(fact_2832_mult__left__le__one__le,axiom,
% 5.46/5.65 ! [X2: int,Y2: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 5.46/5.65 => ( ord_less_eq_int @ ( times_times_int @ Y2 @ X2 ) @ X2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_left_le_one_le
% 5.46/5.65 thf(fact_2833_sum__squares__ge__zero,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % sum_squares_ge_zero
% 5.46/5.65 thf(fact_2834_sum__squares__ge__zero,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % sum_squares_ge_zero
% 5.46/5.65 thf(fact_2835_sum__squares__ge__zero,axiom,
% 5.46/5.65 ! [X2: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % sum_squares_ge_zero
% 5.46/5.65 thf(fact_2836_sum__squares__le__zero__iff,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real )
% 5.46/5.65 = ( ( X2 = zero_zero_real )
% 5.46/5.65 & ( Y2 = zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % sum_squares_le_zero_iff
% 5.46/5.65 thf(fact_2837_sum__squares__le__zero__iff,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat )
% 5.46/5.65 = ( ( X2 = zero_zero_rat )
% 5.46/5.65 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % sum_squares_le_zero_iff
% 5.46/5.65 thf(fact_2838_sum__squares__le__zero__iff,axiom,
% 5.46/5.65 ! [X2: int,Y2: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int )
% 5.46/5.65 = ( ( X2 = zero_zero_int )
% 5.46/5.65 & ( Y2 = zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % sum_squares_le_zero_iff
% 5.46/5.65 thf(fact_2839_not__sum__squares__lt__zero,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real ) ).
% 5.46/5.65
% 5.46/5.65 % not_sum_squares_lt_zero
% 5.46/5.65 thf(fact_2840_not__sum__squares__lt__zero,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat ) ).
% 5.46/5.65
% 5.46/5.65 % not_sum_squares_lt_zero
% 5.46/5.65 thf(fact_2841_not__sum__squares__lt__zero,axiom,
% 5.46/5.65 ! [X2: int,Y2: int] :
% 5.46/5.65 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int ) ).
% 5.46/5.65
% 5.46/5.65 % not_sum_squares_lt_zero
% 5.46/5.65 thf(fact_2842_sum__squares__gt__zero__iff,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) )
% 5.46/5.65 = ( ( X2 != zero_zero_real )
% 5.46/5.65 | ( Y2 != zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % sum_squares_gt_zero_iff
% 5.46/5.65 thf(fact_2843_sum__squares__gt__zero__iff,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y2 @ Y2 ) ) )
% 5.46/5.65 = ( ( X2 != zero_zero_rat )
% 5.46/5.65 | ( Y2 != zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % sum_squares_gt_zero_iff
% 5.46/5.65 thf(fact_2844_sum__squares__gt__zero__iff,axiom,
% 5.46/5.65 ! [X2: int,Y2: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y2 @ Y2 ) ) )
% 5.46/5.65 = ( ( X2 != zero_zero_int )
% 5.46/5.65 | ( Y2 != zero_zero_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % sum_squares_gt_zero_iff
% 5.46/5.65 thf(fact_2845_power__less__imp__less__base,axiom,
% 5.46/5.65 ! [A: real,N: nat,B: real] :
% 5.46/5.65 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.46/5.65 => ( ord_less_real @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_less_imp_less_base
% 5.46/5.65 thf(fact_2846_power__less__imp__less__base,axiom,
% 5.46/5.65 ! [A: rat,N: nat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_less_imp_less_base
% 5.46/5.65 thf(fact_2847_power__less__imp__less__base,axiom,
% 5.46/5.65 ! [A: nat,N: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_less_imp_less_base
% 5.46/5.65 thf(fact_2848_power__less__imp__less__base,axiom,
% 5.46/5.65 ! [A: int,N: nat,B: int] :
% 5.46/5.65 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ord_less_int @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_less_imp_less_base
% 5.46/5.65 thf(fact_2849_zero__less__two,axiom,
% 5.46/5.65 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_two
% 5.46/5.65 thf(fact_2850_zero__less__two,axiom,
% 5.46/5.65 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_two
% 5.46/5.65 thf(fact_2851_zero__less__two,axiom,
% 5.46/5.65 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_two
% 5.46/5.65 thf(fact_2852_zero__less__two,axiom,
% 5.46/5.65 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.46/5.65
% 5.46/5.65 % zero_less_two
% 5.46/5.65 thf(fact_2853_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.46/5.65 ! [C: nat,A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.65 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.46/5.65 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.46/5.65 thf(fact_2854_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.46/5.65 ! [C: int,A: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.46/5.65 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.46/5.65 thf(fact_2855_divide__less__eq,axiom,
% 5.46/5.65 ! [B: real,C: real,A: real] :
% 5.46/5.65 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_eq
% 5.46/5.65 thf(fact_2856_divide__less__eq,axiom,
% 5.46/5.65 ! [B: rat,C: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_eq
% 5.46/5.65 thf(fact_2857_less__divide__eq,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_divide_eq
% 5.46/5.65 thf(fact_2858_less__divide__eq,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_divide_eq
% 5.46/5.65 thf(fact_2859_neg__divide__less__eq,axiom,
% 5.46/5.65 ! [C: real,B: real,A: real] :
% 5.46/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.46/5.65 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % neg_divide_less_eq
% 5.46/5.65 thf(fact_2860_neg__divide__less__eq,axiom,
% 5.46/5.65 ! [C: rat,B: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.46/5.65 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % neg_divide_less_eq
% 5.46/5.65 thf(fact_2861_neg__less__divide__eq,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % neg_less_divide_eq
% 5.46/5.65 thf(fact_2862_neg__less__divide__eq,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % neg_less_divide_eq
% 5.46/5.65 thf(fact_2863_pos__divide__less__eq,axiom,
% 5.46/5.65 ! [C: real,B: real,A: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.46/5.65 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_divide_less_eq
% 5.46/5.65 thf(fact_2864_pos__divide__less__eq,axiom,
% 5.46/5.65 ! [C: rat,B: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.46/5.65 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_divide_less_eq
% 5.46/5.65 thf(fact_2865_pos__less__divide__eq,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_less_divide_eq
% 5.46/5.65 thf(fact_2866_pos__less__divide__eq,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_less_divide_eq
% 5.46/5.65 thf(fact_2867_mult__imp__div__pos__less,axiom,
% 5.46/5.65 ! [Y2: real,X2: real,Z: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ( ord_less_real @ X2 @ ( times_times_real @ Z @ Y2 ) )
% 5.46/5.65 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_imp_div_pos_less
% 5.46/5.65 thf(fact_2868_mult__imp__div__pos__less,axiom,
% 5.46/5.65 ! [Y2: rat,X2: rat,Z: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ( ord_less_rat @ X2 @ ( times_times_rat @ Z @ Y2 ) )
% 5.46/5.65 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_imp_div_pos_less
% 5.46/5.65 thf(fact_2869_mult__imp__less__div__pos,axiom,
% 5.46/5.65 ! [Y2: real,Z: real,X2: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ( ord_less_real @ ( times_times_real @ Z @ Y2 ) @ X2 )
% 5.46/5.65 => ( ord_less_real @ Z @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_imp_less_div_pos
% 5.46/5.65 thf(fact_2870_mult__imp__less__div__pos,axiom,
% 5.46/5.65 ! [Y2: rat,Z: rat,X2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y2 ) @ X2 )
% 5.46/5.65 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_imp_less_div_pos
% 5.46/5.65 thf(fact_2871_divide__strict__left__mono,axiom,
% 5.46/5.65 ! [B: real,A: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ B @ A )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.46/5.65 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_strict_left_mono
% 5.46/5.65 thf(fact_2872_divide__strict__left__mono,axiom,
% 5.46/5.65 ! [B: rat,A: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ B @ A )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.46/5.65 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_strict_left_mono
% 5.46/5.65 thf(fact_2873_divide__strict__left__mono__neg,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.46/5.65 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_strict_left_mono_neg
% 5.46/5.65 thf(fact_2874_divide__strict__left__mono__neg,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.46/5.65 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_strict_left_mono_neg
% 5.46/5.65 thf(fact_2875_divide__less__eq__1,axiom,
% 5.46/5.65 ! [B: real,A: real] :
% 5.46/5.65 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_real @ B @ A ) )
% 5.46/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_real @ A @ B ) )
% 5.46/5.65 | ( A = zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_eq_1
% 5.46/5.65 thf(fact_2876_divide__less__eq__1,axiom,
% 5.46/5.65 ! [B: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_rat @ B @ A ) )
% 5.46/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_rat @ A @ B ) )
% 5.46/5.65 | ( A = zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_eq_1
% 5.46/5.65 thf(fact_2877_less__divide__eq__1,axiom,
% 5.46/5.65 ! [B: real,A: real] :
% 5.46/5.65 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_real @ A @ B ) )
% 5.46/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_divide_eq_1
% 5.46/5.65 thf(fact_2878_less__divide__eq__1,axiom,
% 5.46/5.65 ! [B: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_rat @ A @ B ) )
% 5.46/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_divide_eq_1
% 5.46/5.65 thf(fact_2879_power__le__one,axiom,
% 5.46/5.65 ! [A: real,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_le_one
% 5.46/5.65 thf(fact_2880_power__le__one,axiom,
% 5.46/5.65 ! [A: rat,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_le_one
% 5.46/5.65 thf(fact_2881_power__le__one,axiom,
% 5.46/5.65 ! [A: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.46/5.65 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_le_one
% 5.46/5.65 thf(fact_2882_power__le__one,axiom,
% 5.46/5.65 ! [A: int,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.46/5.65 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_le_one
% 5.46/5.65 thf(fact_2883_eq__divide__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [W: num,B: complex,C: complex] :
% 5.46/5.65 ( ( ( numera6690914467698888265omplex @ W )
% 5.46/5.65 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.46/5.65 = ( ( ( C != zero_zero_complex )
% 5.46/5.65 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.46/5.65 = B ) )
% 5.46/5.65 & ( ( C = zero_zero_complex )
% 5.46/5.65 => ( ( numera6690914467698888265omplex @ W )
% 5.46/5.65 = zero_zero_complex ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % eq_divide_eq_numeral(1)
% 5.46/5.65 thf(fact_2884_eq__divide__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [W: num,B: real,C: real] :
% 5.46/5.65 ( ( ( numeral_numeral_real @ W )
% 5.46/5.65 = ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ( ( C != zero_zero_real )
% 5.46/5.65 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.46/5.65 = B ) )
% 5.46/5.65 & ( ( C = zero_zero_real )
% 5.46/5.65 => ( ( numeral_numeral_real @ W )
% 5.46/5.65 = zero_zero_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % eq_divide_eq_numeral(1)
% 5.46/5.65 thf(fact_2885_eq__divide__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [W: num,B: rat,C: rat] :
% 5.46/5.65 ( ( ( numeral_numeral_rat @ W )
% 5.46/5.65 = ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( C != zero_zero_rat )
% 5.46/5.65 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.46/5.65 = B ) )
% 5.46/5.65 & ( ( C = zero_zero_rat )
% 5.46/5.65 => ( ( numeral_numeral_rat @ W )
% 5.46/5.65 = zero_zero_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % eq_divide_eq_numeral(1)
% 5.46/5.65 thf(fact_2886_divide__eq__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [B: complex,C: complex,W: num] :
% 5.46/5.65 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.46/5.65 = ( numera6690914467698888265omplex @ W ) )
% 5.46/5.65 = ( ( ( C != zero_zero_complex )
% 5.46/5.65 => ( B
% 5.46/5.65 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.46/5.65 & ( ( C = zero_zero_complex )
% 5.46/5.65 => ( ( numera6690914467698888265omplex @ W )
% 5.46/5.65 = zero_zero_complex ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_eq_eq_numeral(1)
% 5.46/5.65 thf(fact_2887_divide__eq__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [B: real,C: real,W: num] :
% 5.46/5.65 ( ( ( divide_divide_real @ B @ C )
% 5.46/5.65 = ( numeral_numeral_real @ W ) )
% 5.46/5.65 = ( ( ( C != zero_zero_real )
% 5.46/5.65 => ( B
% 5.46/5.65 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.65 & ( ( C = zero_zero_real )
% 5.46/5.65 => ( ( numeral_numeral_real @ W )
% 5.46/5.65 = zero_zero_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_eq_eq_numeral(1)
% 5.46/5.65 thf(fact_2888_divide__eq__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [B: rat,C: rat,W: num] :
% 5.46/5.65 ( ( ( divide_divide_rat @ B @ C )
% 5.46/5.65 = ( numeral_numeral_rat @ W ) )
% 5.46/5.65 = ( ( ( C != zero_zero_rat )
% 5.46/5.65 => ( B
% 5.46/5.65 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.65 & ( ( C = zero_zero_rat )
% 5.46/5.65 => ( ( numeral_numeral_rat @ W )
% 5.46/5.65 = zero_zero_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_eq_eq_numeral(1)
% 5.46/5.65 thf(fact_2889_divide__add__eq__iff,axiom,
% 5.46/5.65 ! [Z: complex,X2: complex,Y2: complex] :
% 5.46/5.65 ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y2 )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_add_eq_iff
% 5.46/5.65 thf(fact_2890_divide__add__eq__iff,axiom,
% 5.46/5.65 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.65 ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Z ) @ Y2 )
% 5.46/5.65 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_add_eq_iff
% 5.46/5.65 thf(fact_2891_divide__add__eq__iff,axiom,
% 5.46/5.65 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.65 ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y2 )
% 5.46/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_add_eq_iff
% 5.46/5.65 thf(fact_2892_add__divide__eq__iff,axiom,
% 5.46/5.65 ! [Z: complex,X2: complex,Y2: complex] :
% 5.46/5.65 ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_iff
% 5.46/5.65 thf(fact_2893_add__divide__eq__iff,axiom,
% 5.46/5.65 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.65 ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( plus_plus_real @ X2 @ ( divide_divide_real @ Y2 @ Z ) )
% 5.46/5.65 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_iff
% 5.46/5.65 thf(fact_2894_add__divide__eq__iff,axiom,
% 5.46/5.65 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.65 ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( plus_plus_rat @ X2 @ ( divide_divide_rat @ Y2 @ Z ) )
% 5.46/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_iff
% 5.46/5.65 thf(fact_2895_add__num__frac,axiom,
% 5.46/5.65 ! [Y2: complex,Z: complex,X2: complex] :
% 5.46/5.65 ( ( Y2 != zero_zero_complex )
% 5.46/5.65 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X2 @ Y2 ) )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_num_frac
% 5.46/5.65 thf(fact_2896_add__num__frac,axiom,
% 5.46/5.65 ! [Y2: real,Z: real,X2: real] :
% 5.46/5.65 ( ( Y2 != zero_zero_real )
% 5.46/5.65 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.46/5.65 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_num_frac
% 5.46/5.65 thf(fact_2897_add__num__frac,axiom,
% 5.46/5.65 ! [Y2: rat,Z: rat,X2: rat] :
% 5.46/5.65 ( ( Y2 != zero_zero_rat )
% 5.46/5.65 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X2 @ Y2 ) )
% 5.46/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_num_frac
% 5.46/5.65 thf(fact_2898_add__frac__num,axiom,
% 5.46/5.65 ! [Y2: complex,X2: complex,Z: complex] :
% 5.46/5.65 ( ( Y2 != zero_zero_complex )
% 5.46/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ Z )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_frac_num
% 5.46/5.65 thf(fact_2899_add__frac__num,axiom,
% 5.46/5.65 ! [Y2: real,X2: real,Z: real] :
% 5.46/5.65 ( ( Y2 != zero_zero_real )
% 5.46/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y2 ) @ Z )
% 5.46/5.65 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_frac_num
% 5.46/5.65 thf(fact_2900_add__frac__num,axiom,
% 5.46/5.65 ! [Y2: rat,X2: rat,Z: rat] :
% 5.46/5.65 ( ( Y2 != zero_zero_rat )
% 5.46/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ Z )
% 5.46/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_frac_num
% 5.46/5.65 thf(fact_2901_add__frac__eq,axiom,
% 5.46/5.65 ! [Y2: complex,Z: complex,X2: complex,W: complex] :
% 5.46/5.65 ( ( Y2 != zero_zero_complex )
% 5.46/5.65 => ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_frac_eq
% 5.46/5.65 thf(fact_2902_add__frac__eq,axiom,
% 5.46/5.65 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.46/5.65 ( ( Y2 != zero_zero_real )
% 5.46/5.65 => ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.46/5.65 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_frac_eq
% 5.46/5.65 thf(fact_2903_add__frac__eq,axiom,
% 5.46/5.65 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.46/5.65 ( ( Y2 != zero_zero_rat )
% 5.46/5.65 => ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.46/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_frac_eq
% 5.46/5.65 thf(fact_2904_add__divide__eq__if__simps_I1_J,axiom,
% 5.46/5.65 ! [Z: complex,A: complex,B: complex] :
% 5.46/5.65 ( ( ( Z = zero_zero_complex )
% 5.46/5.65 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.46/5.65 = A ) )
% 5.46/5.65 & ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_if_simps(1)
% 5.46/5.65 thf(fact_2905_add__divide__eq__if__simps_I1_J,axiom,
% 5.46/5.65 ! [Z: real,A: real,B: real] :
% 5.46/5.65 ( ( ( Z = zero_zero_real )
% 5.46/5.65 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.46/5.65 = A ) )
% 5.46/5.65 & ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.46/5.65 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_if_simps(1)
% 5.46/5.65 thf(fact_2906_add__divide__eq__if__simps_I1_J,axiom,
% 5.46/5.65 ! [Z: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ( Z = zero_zero_rat )
% 5.46/5.65 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.46/5.65 = A ) )
% 5.46/5.65 & ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.46/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_if_simps(1)
% 5.46/5.65 thf(fact_2907_add__divide__eq__if__simps_I2_J,axiom,
% 5.46/5.65 ! [Z: complex,A: complex,B: complex] :
% 5.46/5.65 ( ( ( Z = zero_zero_complex )
% 5.46/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.46/5.65 = B ) )
% 5.46/5.65 & ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_if_simps(2)
% 5.46/5.65 thf(fact_2908_add__divide__eq__if__simps_I2_J,axiom,
% 5.46/5.65 ! [Z: real,A: real,B: real] :
% 5.46/5.65 ( ( ( Z = zero_zero_real )
% 5.46/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.46/5.65 = B ) )
% 5.46/5.65 & ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.46/5.65 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_if_simps(2)
% 5.46/5.65 thf(fact_2909_add__divide__eq__if__simps_I2_J,axiom,
% 5.46/5.65 ! [Z: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ( Z = zero_zero_rat )
% 5.46/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.46/5.65 = B ) )
% 5.46/5.65 & ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.46/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_if_simps(2)
% 5.46/5.65 thf(fact_2910_power__inject__base,axiom,
% 5.46/5.65 ! [A: real,N: nat,B: real] :
% 5.46/5.65 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.46/5.65 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.46/5.65 => ( A = B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_inject_base
% 5.46/5.65 thf(fact_2911_power__inject__base,axiom,
% 5.46/5.65 ! [A: rat,N: nat,B: rat] :
% 5.46/5.65 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.46/5.65 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( A = B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_inject_base
% 5.46/5.65 thf(fact_2912_power__inject__base,axiom,
% 5.46/5.65 ! [A: nat,N: nat,B: nat] :
% 5.46/5.65 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.46/5.65 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( A = B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_inject_base
% 5.46/5.65 thf(fact_2913_power__inject__base,axiom,
% 5.46/5.65 ! [A: int,N: nat,B: int] :
% 5.46/5.65 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.46/5.65 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.46/5.65 => ( A = B ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_inject_base
% 5.46/5.65 thf(fact_2914_power__le__imp__le__base,axiom,
% 5.46/5.65 ! [A: real,N: nat,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.46/5.65 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_le_imp_le_base
% 5.46/5.65 thf(fact_2915_power__le__imp__le__base,axiom,
% 5.46/5.65 ! [A: rat,N: nat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.46/5.65 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_le_imp_le_base
% 5.46/5.65 thf(fact_2916_power__le__imp__le__base,axiom,
% 5.46/5.65 ! [A: nat,N: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.46/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_le_imp_le_base
% 5.46/5.65 thf(fact_2917_power__le__imp__le__base,axiom,
% 5.46/5.65 ! [A: int,N: nat,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_le_imp_le_base
% 5.46/5.65 thf(fact_2918_div__add__self2,axiom,
% 5.46/5.65 ! [B: nat,A: nat] :
% 5.46/5.65 ( ( B != zero_zero_nat )
% 5.46/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.46/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_add_self2
% 5.46/5.65 thf(fact_2919_div__add__self2,axiom,
% 5.46/5.65 ! [B: int,A: int] :
% 5.46/5.65 ( ( B != zero_zero_int )
% 5.46/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.46/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_add_self2
% 5.46/5.65 thf(fact_2920_div__add__self1,axiom,
% 5.46/5.65 ! [B: nat,A: nat] :
% 5.46/5.65 ( ( B != zero_zero_nat )
% 5.46/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.46/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_add_self1
% 5.46/5.65 thf(fact_2921_div__add__self1,axiom,
% 5.46/5.65 ! [B: int,A: int] :
% 5.46/5.65 ( ( B != zero_zero_int )
% 5.46/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.46/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_add_self1
% 5.46/5.65 thf(fact_2922_add__divide__eq__if__simps_I4_J,axiom,
% 5.46/5.65 ! [Z: complex,A: complex,B: complex] :
% 5.46/5.65 ( ( ( Z = zero_zero_complex )
% 5.46/5.65 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.46/5.65 = A ) )
% 5.46/5.65 & ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_if_simps(4)
% 5.46/5.65 thf(fact_2923_add__divide__eq__if__simps_I4_J,axiom,
% 5.46/5.65 ! [Z: real,A: real,B: real] :
% 5.46/5.65 ( ( ( Z = zero_zero_real )
% 5.46/5.65 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.46/5.65 = A ) )
% 5.46/5.65 & ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.46/5.65 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_if_simps(4)
% 5.46/5.65 thf(fact_2924_add__divide__eq__if__simps_I4_J,axiom,
% 5.46/5.65 ! [Z: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ( Z = zero_zero_rat )
% 5.46/5.65 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.46/5.65 = A ) )
% 5.46/5.65 & ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.46/5.65 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % add_divide_eq_if_simps(4)
% 5.46/5.65 thf(fact_2925_diff__frac__eq,axiom,
% 5.46/5.65 ! [Y2: complex,Z: complex,X2: complex,W: complex] :
% 5.46/5.65 ( ( Y2 != zero_zero_complex )
% 5.46/5.65 => ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % diff_frac_eq
% 5.46/5.65 thf(fact_2926_diff__frac__eq,axiom,
% 5.46/5.65 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.46/5.65 ( ( Y2 != zero_zero_real )
% 5.46/5.65 => ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.46/5.65 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % diff_frac_eq
% 5.46/5.65 thf(fact_2927_diff__frac__eq,axiom,
% 5.46/5.65 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.46/5.65 ( ( Y2 != zero_zero_rat )
% 5.46/5.65 => ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.46/5.65 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % diff_frac_eq
% 5.46/5.65 thf(fact_2928_diff__divide__eq__iff,axiom,
% 5.46/5.65 ! [Z: complex,X2: complex,Y2: complex] :
% 5.46/5.65 ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( minus_minus_complex @ X2 @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % diff_divide_eq_iff
% 5.46/5.65 thf(fact_2929_diff__divide__eq__iff,axiom,
% 5.46/5.65 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.65 ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( minus_minus_real @ X2 @ ( divide_divide_real @ Y2 @ Z ) )
% 5.46/5.65 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % diff_divide_eq_iff
% 5.46/5.65 thf(fact_2930_diff__divide__eq__iff,axiom,
% 5.46/5.65 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.65 ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( minus_minus_rat @ X2 @ ( divide_divide_rat @ Y2 @ Z ) )
% 5.46/5.65 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % diff_divide_eq_iff
% 5.46/5.65 thf(fact_2931_divide__diff__eq__iff,axiom,
% 5.46/5.65 ! [Z: complex,X2: complex,Y2: complex] :
% 5.46/5.65 ( ( Z != zero_zero_complex )
% 5.46/5.65 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y2 )
% 5.46/5.65 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_diff_eq_iff
% 5.46/5.65 thf(fact_2932_divide__diff__eq__iff,axiom,
% 5.46/5.65 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.65 ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Z ) @ Y2 )
% 5.46/5.65 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_diff_eq_iff
% 5.46/5.65 thf(fact_2933_divide__diff__eq__iff,axiom,
% 5.46/5.65 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.65 ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y2 )
% 5.46/5.65 = ( divide_divide_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_diff_eq_iff
% 5.46/5.65 thf(fact_2934_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.46/5.65 ! [A: code_integer,B: code_integer] :
% 5.46/5.65 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.65 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.46/5.65 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.46/5.65 = A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.mod_less
% 5.46/5.65 thf(fact_2935_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.46/5.65 ! [A: nat,B: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ A @ B )
% 5.46/5.65 => ( ( modulo_modulo_nat @ A @ B )
% 5.46/5.65 = A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.mod_less
% 5.46/5.65 thf(fact_2936_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.46/5.65 ! [A: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ A @ B )
% 5.46/5.65 => ( ( modulo_modulo_int @ A @ B )
% 5.46/5.65 = A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.mod_less
% 5.46/5.65 thf(fact_2937_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.46/5.65 ! [B: code_integer,A: code_integer] :
% 5.46/5.65 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.46/5.65 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.46/5.65 thf(fact_2938_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.46/5.65 ! [B: nat,A: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.65 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.46/5.65 thf(fact_2939_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.46/5.65 ! [B: int,A: int] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.65 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.46/5.65 thf(fact_2940_cong__exp__iff__simps_I2_J,axiom,
% 5.46/5.65 ! [N: num,Q2: num] :
% 5.46/5.65 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.65 = zero_zero_nat )
% 5.46/5.65 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.46/5.65 = zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % cong_exp_iff_simps(2)
% 5.46/5.65 thf(fact_2941_cong__exp__iff__simps_I2_J,axiom,
% 5.46/5.65 ! [N: num,Q2: num] :
% 5.46/5.65 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.65 = zero_zero_int )
% 5.46/5.65 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.46/5.65 = zero_zero_int ) ) ).
% 5.46/5.65
% 5.46/5.65 % cong_exp_iff_simps(2)
% 5.46/5.65 thf(fact_2942_cong__exp__iff__simps_I2_J,axiom,
% 5.46/5.65 ! [N: num,Q2: num] :
% 5.46/5.65 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.65 = zero_z3403309356797280102nteger )
% 5.46/5.65 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.46/5.65 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.65
% 5.46/5.65 % cong_exp_iff_simps(2)
% 5.46/5.65 thf(fact_2943_cong__exp__iff__simps_I1_J,axiom,
% 5.46/5.65 ! [N: num] :
% 5.46/5.65 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.46/5.65 = zero_zero_nat ) ).
% 5.46/5.65
% 5.46/5.65 % cong_exp_iff_simps(1)
% 5.46/5.65 thf(fact_2944_cong__exp__iff__simps_I1_J,axiom,
% 5.46/5.65 ! [N: num] :
% 5.46/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.46/5.65 = zero_zero_int ) ).
% 5.46/5.65
% 5.46/5.65 % cong_exp_iff_simps(1)
% 5.46/5.65 thf(fact_2945_cong__exp__iff__simps_I1_J,axiom,
% 5.46/5.65 ! [N: num] :
% 5.46/5.65 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.46/5.65 = zero_z3403309356797280102nteger ) ).
% 5.46/5.65
% 5.46/5.65 % cong_exp_iff_simps(1)
% 5.46/5.65 thf(fact_2946_numeral__1__eq__Suc__0,axiom,
% 5.46/5.65 ( ( numeral_numeral_nat @ one )
% 5.46/5.65 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.65
% 5.46/5.65 % numeral_1_eq_Suc_0
% 5.46/5.65 thf(fact_2947_num_Osize_I5_J,axiom,
% 5.46/5.65 ! [X23: num] :
% 5.46/5.65 ( ( size_size_num @ ( bit0 @ X23 ) )
% 5.46/5.65 = ( plus_plus_nat @ ( size_size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % num.size(5)
% 5.46/5.65 thf(fact_2948_ex__least__nat__less,axiom,
% 5.46/5.65 ! [P: nat > $o,N: nat] :
% 5.46/5.65 ( ( P @ N )
% 5.46/5.65 => ( ~ ( P @ zero_zero_nat )
% 5.46/5.65 => ? [K3: nat] :
% 5.46/5.65 ( ( ord_less_nat @ K3 @ N )
% 5.46/5.65 & ! [I3: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ I3 @ K3 )
% 5.46/5.65 => ~ ( P @ I3 ) )
% 5.46/5.65 & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % ex_least_nat_less
% 5.46/5.65 thf(fact_2949_nat__induct__non__zero,axiom,
% 5.46/5.65 ! [N: nat,P: nat > $o] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 => ( ( P @ one_one_nat )
% 5.46/5.65 => ( ! [N3: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.46/5.65 => ( ( P @ N3 )
% 5.46/5.65 => ( P @ ( suc @ N3 ) ) ) )
% 5.46/5.65 => ( P @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nat_induct_non_zero
% 5.46/5.65 thf(fact_2950_diff__Suc__less,axiom,
% 5.46/5.65 ! [N: nat,I: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.46/5.65
% 5.46/5.65 % diff_Suc_less
% 5.46/5.65 thf(fact_2951_num_Osize_I6_J,axiom,
% 5.46/5.65 ! [X33: num] :
% 5.46/5.65 ( ( size_size_num @ ( bit1 @ X33 ) )
% 5.46/5.65 = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % num.size(6)
% 5.46/5.65 thf(fact_2952_one__less__mult,axiom,
% 5.46/5.65 ! [N: nat,M: nat] :
% 5.46/5.65 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.65 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.46/5.65 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % one_less_mult
% 5.46/5.65 thf(fact_2953_n__less__m__mult__n,axiom,
% 5.46/5.65 ! [N: nat,M: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.46/5.65 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % n_less_m_mult_n
% 5.46/5.65 thf(fact_2954_n__less__n__mult__m,axiom,
% 5.46/5.65 ! [N: nat,M: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.46/5.65 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % n_less_n_mult_m
% 5.46/5.65 thf(fact_2955_length__pos__if__in__set,axiom,
% 5.46/5.65 ! [X2: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.46/5.65 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % length_pos_if_in_set
% 5.46/5.65 thf(fact_2956_length__pos__if__in__set,axiom,
% 5.46/5.65 ! [X2: complex,Xs2: list_complex] :
% 5.46/5.65 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % length_pos_if_in_set
% 5.46/5.65 thf(fact_2957_length__pos__if__in__set,axiom,
% 5.46/5.65 ! [X2: real,Xs2: list_real] :
% 5.46/5.65 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % length_pos_if_in_set
% 5.46/5.65 thf(fact_2958_length__pos__if__in__set,axiom,
% 5.46/5.65 ! [X2: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.46/5.65 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % length_pos_if_in_set
% 5.46/5.65 thf(fact_2959_length__pos__if__in__set,axiom,
% 5.46/5.65 ! [X2: $o,Xs2: list_o] :
% 5.46/5.65 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % length_pos_if_in_set
% 5.46/5.65 thf(fact_2960_length__pos__if__in__set,axiom,
% 5.46/5.65 ! [X2: nat,Xs2: list_nat] :
% 5.46/5.65 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % length_pos_if_in_set
% 5.46/5.65 thf(fact_2961_length__pos__if__in__set,axiom,
% 5.46/5.65 ! [X2: int,Xs2: list_int] :
% 5.46/5.65 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.46/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % length_pos_if_in_set
% 5.46/5.65 thf(fact_2962_nat__mult__le__cancel1,axiom,
% 5.46/5.65 ! [K: nat,M: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.65 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.65 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nat_mult_le_cancel1
% 5.46/5.65 thf(fact_2963_nat__diff__split,axiom,
% 5.46/5.65 ! [P: nat > $o,A: nat,B: nat] :
% 5.46/5.65 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.46/5.65 = ( ( ( ord_less_nat @ A @ B )
% 5.46/5.65 => ( P @ zero_zero_nat ) )
% 5.46/5.65 & ! [D: nat] :
% 5.46/5.65 ( ( A
% 5.46/5.65 = ( plus_plus_nat @ B @ D ) )
% 5.46/5.65 => ( P @ D ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nat_diff_split
% 5.46/5.65 thf(fact_2964_nat__diff__split__asm,axiom,
% 5.46/5.65 ! [P: nat > $o,A: nat,B: nat] :
% 5.46/5.65 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.46/5.65 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.46/5.65 & ~ ( P @ zero_zero_nat ) )
% 5.46/5.65 | ? [D: nat] :
% 5.46/5.65 ( ( A
% 5.46/5.65 = ( plus_plus_nat @ B @ D ) )
% 5.46/5.65 & ~ ( P @ D ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nat_diff_split_asm
% 5.46/5.65 thf(fact_2965_power__gt__expt,axiom,
% 5.46/5.65 ! [N: nat,K: nat] :
% 5.46/5.65 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.65 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_gt_expt
% 5.46/5.65 thf(fact_2966_div__greater__zero__iff,axiom,
% 5.46/5.65 ! [M: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.65 = ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.65 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_greater_zero_iff
% 5.46/5.65 thf(fact_2967_div__le__mono2,axiom,
% 5.46/5.65 ! [M: nat,N: nat,K: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.65 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.65 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_le_mono2
% 5.46/5.65 thf(fact_2968_nat__one__le__power,axiom,
% 5.46/5.65 ! [I: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.46/5.65 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nat_one_le_power
% 5.46/5.65 thf(fact_2969_div__eq__dividend__iff,axiom,
% 5.46/5.65 ! [M: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.65 => ( ( ( divide_divide_nat @ M @ N )
% 5.46/5.65 = M )
% 5.46/5.65 = ( N = one_one_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_eq_dividend_iff
% 5.46/5.65 thf(fact_2970_div__less__dividend,axiom,
% 5.46/5.65 ! [N: nat,M: nat] :
% 5.46/5.65 ( ( ord_less_nat @ one_one_nat @ N )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.65 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_less_dividend
% 5.46/5.65 thf(fact_2971_div__less__iff__less__mult,axiom,
% 5.46/5.65 ! [Q2: nat,M: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.46/5.65 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 5.46/5.65 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_less_iff_less_mult
% 5.46/5.65 thf(fact_2972_nat__mult__div__cancel1,axiom,
% 5.46/5.65 ! [K: nat,M: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.65 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.65 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % nat_mult_div_cancel1
% 5.46/5.65 thf(fact_2973_mod__le__divisor,axiom,
% 5.46/5.65 ! [N: nat,M: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.46/5.65
% 5.46/5.65 % mod_le_divisor
% 5.46/5.65 thf(fact_2974_div__less__mono,axiom,
% 5.46/5.65 ! [A2: nat,B3: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ A2 @ B3 )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.65 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.46/5.65 = zero_zero_nat )
% 5.46/5.65 => ( ( ( modulo_modulo_nat @ B3 @ N )
% 5.46/5.65 = zero_zero_nat )
% 5.46/5.65 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B3 @ N ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % div_less_mono
% 5.46/5.65 thf(fact_2975_vebt__insert_Osimps_I3_J,axiom,
% 5.46/5.65 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.46/5.65 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X2 )
% 5.46/5.65 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) ).
% 5.46/5.65
% 5.46/5.65 % vebt_insert.simps(3)
% 5.46/5.65 thf(fact_2976_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.46/5.65 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.46/5.65 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X2 )
% 5.46/5.65 = one_one_nat ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(2)
% 5.46/5.65 thf(fact_2977_vebt__member_Osimps_I3_J,axiom,
% 5.46/5.65 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.46/5.65 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 ) ).
% 5.46/5.65
% 5.46/5.65 % vebt_member.simps(3)
% 5.46/5.65 thf(fact_2978_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.46/5.65 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.46/5.65 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.46/5.65
% 5.46/5.65 % VEBT_internal.membermima.simps(2)
% 5.46/5.65 thf(fact_2979_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 5.46/5.65 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.46/5.65 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X2 )
% 5.46/5.65 = one_one_nat ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(2)
% 5.46/5.65 thf(fact_2980_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases,axiom,
% 5.46/5.65 ! [X2: vEBT_VEBT] :
% 5.46/5.65 ( ! [A5: $o,B5: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.65 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.65 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.cases
% 5.46/5.65 thf(fact_2981_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.46/5.65 ! [X2: vEBT_VEBT,Y2: $o] :
% 5.46/5.65 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.46/5.65 = Y2 )
% 5.46/5.65 => ( ( ( X2
% 5.46/5.65 = ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.65 => ~ Y2 )
% 5.46/5.65 => ( ( ? [Uv2: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.46/5.65 => Y2 )
% 5.46/5.65 => ( ( ? [Uu2: $o] :
% 5.46/5.65 ( X2
% 5.46/5.65 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.46/5.65 => Y2 )
% 5.46/5.65 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.46/5.65 => ~ Y2 )
% 5.46/5.65 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.46/5.65 => Y2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % VEBT_internal.minNull.elims(1)
% 5.46/5.65 thf(fact_2982_field__le__mult__one__interval,axiom,
% 5.46/5.65 ! [X2: real,Y2: real] :
% 5.46/5.65 ( ! [Z3: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 5.46/5.65 => ( ( ord_less_real @ Z3 @ one_one_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X2 ) @ Y2 ) ) )
% 5.46/5.65 => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.46/5.65
% 5.46/5.65 % field_le_mult_one_interval
% 5.46/5.65 thf(fact_2983_field__le__mult__one__interval,axiom,
% 5.46/5.65 ! [X2: rat,Y2: rat] :
% 5.46/5.65 ( ! [Z3: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 5.46/5.65 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X2 ) @ Y2 ) ) )
% 5.46/5.65 => ( ord_less_eq_rat @ X2 @ Y2 ) ) ).
% 5.46/5.65
% 5.46/5.65 % field_le_mult_one_interval
% 5.46/5.65 thf(fact_2984_mult__less__cancel__right2,axiom,
% 5.46/5.65 ! [A: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.46/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ A @ one_one_real ) )
% 5.46/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right2
% 5.46/5.65 thf(fact_2985_mult__less__cancel__right2,axiom,
% 5.46/5.65 ! [A: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.46/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.46/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right2
% 5.46/5.65 thf(fact_2986_mult__less__cancel__right2,axiom,
% 5.46/5.65 ! [A: int,C: int] :
% 5.46/5.65 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.46/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ A @ one_one_int ) )
% 5.46/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right2
% 5.46/5.65 thf(fact_2987_mult__less__cancel__right1,axiom,
% 5.46/5.65 ! [C: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ one_one_real @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right1
% 5.46/5.65 thf(fact_2988_mult__less__cancel__right1,axiom,
% 5.46/5.65 ! [C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right1
% 5.46/5.65 thf(fact_2989_mult__less__cancel__right1,axiom,
% 5.46/5.65 ! [C: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ one_one_int @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_right1
% 5.46/5.65 thf(fact_2990_mult__less__cancel__left2,axiom,
% 5.46/5.65 ! [C: real,A: real] :
% 5.46/5.65 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.46/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ A @ one_one_real ) )
% 5.46/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left2
% 5.46/5.65 thf(fact_2991_mult__less__cancel__left2,axiom,
% 5.46/5.65 ! [C: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.46/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.46/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left2
% 5.46/5.65 thf(fact_2992_mult__less__cancel__left2,axiom,
% 5.46/5.65 ! [C: int,A: int] :
% 5.46/5.65 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.46/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ A @ one_one_int ) )
% 5.46/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left2
% 5.46/5.65 thf(fact_2993_mult__less__cancel__left1,axiom,
% 5.46/5.65 ! [C: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ one_one_real @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left1
% 5.46/5.65 thf(fact_2994_mult__less__cancel__left1,axiom,
% 5.46/5.65 ! [C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left1
% 5.46/5.65 thf(fact_2995_mult__less__cancel__left1,axiom,
% 5.46/5.65 ! [C: int,B: int] :
% 5.46/5.65 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_int @ one_one_int @ B ) )
% 5.46/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_less_cancel_left1
% 5.46/5.65 thf(fact_2996_mult__le__cancel__right2,axiom,
% 5.46/5.65 ! [A: real,C: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.46/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_right2
% 5.46/5.65 thf(fact_2997_mult__le__cancel__right2,axiom,
% 5.46/5.65 ! [A: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.46/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_right2
% 5.46/5.65 thf(fact_2998_mult__le__cancel__right2,axiom,
% 5.46/5.65 ! [A: int,C: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.46/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_right2
% 5.46/5.65 thf(fact_2999_mult__le__cancel__right1,axiom,
% 5.46/5.65 ! [C: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.46/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_right1
% 5.46/5.65 thf(fact_3000_mult__le__cancel__right1,axiom,
% 5.46/5.65 ! [C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.46/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_right1
% 5.46/5.65 thf(fact_3001_mult__le__cancel__right1,axiom,
% 5.46/5.65 ! [C: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.46/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_right1
% 5.46/5.65 thf(fact_3002_mult__le__cancel__left2,axiom,
% 5.46/5.65 ! [C: real,A: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.46/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left2
% 5.46/5.65 thf(fact_3003_mult__le__cancel__left2,axiom,
% 5.46/5.65 ! [C: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.46/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left2
% 5.46/5.65 thf(fact_3004_mult__le__cancel__left2,axiom,
% 5.46/5.65 ! [C: int,A: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.46/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left2
% 5.46/5.65 thf(fact_3005_mult__le__cancel__left1,axiom,
% 5.46/5.65 ! [C: real,B: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.46/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left1
% 5.46/5.65 thf(fact_3006_mult__le__cancel__left1,axiom,
% 5.46/5.65 ! [C: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.46/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left1
% 5.46/5.65 thf(fact_3007_mult__le__cancel__left1,axiom,
% 5.46/5.65 ! [C: int,B: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.46/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.65 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.46/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.65 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_le_cancel_left1
% 5.46/5.65 thf(fact_3008_divide__left__mono__neg,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_left_mono_neg
% 5.46/5.65 thf(fact_3009_divide__left__mono__neg,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.65 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_left_mono_neg
% 5.46/5.65 thf(fact_3010_mult__imp__le__div__pos,axiom,
% 5.46/5.65 ! [Y2: real,Z: real,X2: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y2 ) @ X2 )
% 5.46/5.65 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_imp_le_div_pos
% 5.46/5.65 thf(fact_3011_mult__imp__le__div__pos,axiom,
% 5.46/5.65 ! [Y2: rat,Z: rat,X2: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y2 ) @ X2 )
% 5.46/5.65 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_imp_le_div_pos
% 5.46/5.65 thf(fact_3012_mult__imp__div__pos__le,axiom,
% 5.46/5.65 ! [Y2: real,X2: real,Z: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_real @ X2 @ ( times_times_real @ Z @ Y2 ) )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_imp_div_pos_le
% 5.46/5.65 thf(fact_3013_mult__imp__div__pos__le,axiom,
% 5.46/5.65 ! [Y2: rat,X2: rat,Z: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.46/5.65 => ( ( ord_less_eq_rat @ X2 @ ( times_times_rat @ Z @ Y2 ) )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % mult_imp_div_pos_le
% 5.46/5.65 thf(fact_3014_pos__le__divide__eq,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_le_divide_eq
% 5.46/5.65 thf(fact_3015_pos__le__divide__eq,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_le_divide_eq
% 5.46/5.65 thf(fact_3016_pos__divide__le__eq,axiom,
% 5.46/5.65 ! [C: real,B: real,A: real] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.46/5.65 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_divide_le_eq
% 5.46/5.65 thf(fact_3017_pos__divide__le__eq,axiom,
% 5.46/5.65 ! [C: rat,B: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.46/5.65 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % pos_divide_le_eq
% 5.46/5.65 thf(fact_3018_neg__le__divide__eq,axiom,
% 5.46/5.65 ! [C: real,A: real,B: real] :
% 5.46/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % neg_le_divide_eq
% 5.46/5.65 thf(fact_3019_neg__le__divide__eq,axiom,
% 5.46/5.65 ! [C: rat,A: rat,B: rat] :
% 5.46/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % neg_le_divide_eq
% 5.46/5.65 thf(fact_3020_neg__divide__le__eq,axiom,
% 5.46/5.65 ! [C: real,B: real,A: real] :
% 5.46/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.46/5.65 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % neg_divide_le_eq
% 5.46/5.65 thf(fact_3021_neg__divide__le__eq,axiom,
% 5.46/5.65 ! [C: rat,B: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.46/5.65 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % neg_divide_le_eq
% 5.46/5.65 thf(fact_3022_divide__left__mono,axiom,
% 5.46/5.65 ! [B: real,A: real,C: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ B @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.46/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_left_mono
% 5.46/5.65 thf(fact_3023_divide__left__mono,axiom,
% 5.46/5.65 ! [B: rat,A: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ B @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.46/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_left_mono
% 5.46/5.65 thf(fact_3024_le__divide__eq,axiom,
% 5.46/5.65 ! [A: real,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % le_divide_eq
% 5.46/5.65 thf(fact_3025_le__divide__eq,axiom,
% 5.46/5.65 ! [A: rat,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % le_divide_eq
% 5.46/5.65 thf(fact_3026_divide__le__eq,axiom,
% 5.46/5.65 ! [B: real,C: real,A: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_le_eq
% 5.46/5.65 thf(fact_3027_divide__le__eq,axiom,
% 5.46/5.65 ! [B: rat,C: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_le_eq
% 5.46/5.65 thf(fact_3028_le__divide__eq__1,axiom,
% 5.46/5.65 ! [B: real,A: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_eq_real @ A @ B ) )
% 5.46/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % le_divide_eq_1
% 5.46/5.65 thf(fact_3029_le__divide__eq__1,axiom,
% 5.46/5.65 ! [B: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_eq_rat @ A @ B ) )
% 5.46/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % le_divide_eq_1
% 5.46/5.65 thf(fact_3030_divide__le__eq__1,axiom,
% 5.46/5.65 ! [B: real,A: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 & ( ord_less_eq_real @ B @ A ) )
% 5.46/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.65 & ( ord_less_eq_real @ A @ B ) )
% 5.46/5.65 | ( A = zero_zero_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_le_eq_1
% 5.46/5.65 thf(fact_3031_divide__le__eq__1,axiom,
% 5.46/5.65 ! [B: rat,A: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 & ( ord_less_eq_rat @ B @ A ) )
% 5.46/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.65 & ( ord_less_eq_rat @ A @ B ) )
% 5.46/5.65 | ( A = zero_zero_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_le_eq_1
% 5.46/5.65 thf(fact_3032_convex__bound__le,axiom,
% 5.46/5.65 ! [X2: real,A: real,Y2: real,U: real,V: real] :
% 5.46/5.65 ( ( ord_less_eq_real @ X2 @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ Y2 @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.46/5.65 => ( ( ( plus_plus_real @ U @ V )
% 5.46/5.65 = one_one_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % convex_bound_le
% 5.46/5.65 thf(fact_3033_convex__bound__le,axiom,
% 5.46/5.65 ! [X2: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ X2 @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ Y2 @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.46/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.46/5.65 => ( ( ( plus_plus_rat @ U @ V )
% 5.46/5.65 = one_one_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % convex_bound_le
% 5.46/5.65 thf(fact_3034_convex__bound__le,axiom,
% 5.46/5.65 ! [X2: int,A: int,Y2: int,U: int,V: int] :
% 5.46/5.65 ( ( ord_less_eq_int @ X2 @ A )
% 5.46/5.65 => ( ( ord_less_eq_int @ Y2 @ A )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.46/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.46/5.65 => ( ( ( plus_plus_int @ U @ V )
% 5.46/5.65 = one_one_int )
% 5.46/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % convex_bound_le
% 5.46/5.65 thf(fact_3035_less__divide__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [W: num,B: real,C: real] :
% 5.46/5.65 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_divide_eq_numeral(1)
% 5.46/5.65 thf(fact_3036_less__divide__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [W: num,B: rat,C: rat] :
% 5.46/5.65 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % less_divide_eq_numeral(1)
% 5.46/5.65 thf(fact_3037_divide__less__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [B: real,C: real,W: num] :
% 5.46/5.65 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.46/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.65 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_eq_numeral(1)
% 5.46/5.65 thf(fact_3038_divide__less__eq__numeral_I1_J,axiom,
% 5.46/5.65 ! [B: rat,C: rat,W: num] :
% 5.46/5.65 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.46/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.46/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.65 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % divide_less_eq_numeral(1)
% 5.46/5.65 thf(fact_3039_frac__le__eq,axiom,
% 5.46/5.65 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.46/5.65 ( ( Y2 != zero_zero_real )
% 5.46/5.65 => ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.46/5.65 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_le_eq
% 5.46/5.65 thf(fact_3040_frac__le__eq,axiom,
% 5.46/5.65 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.46/5.65 ( ( Y2 != zero_zero_rat )
% 5.46/5.65 => ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.46/5.65 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_le_eq
% 5.46/5.65 thf(fact_3041_power__Suc__less,axiom,
% 5.46/5.65 ! [A: real,N: nat] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ A @ one_one_real )
% 5.46/5.65 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_less
% 5.46/5.65 thf(fact_3042_power__Suc__less,axiom,
% 5.46/5.65 ! [A: rat,N: nat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.46/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_less
% 5.46/5.65 thf(fact_3043_power__Suc__less,axiom,
% 5.46/5.65 ! [A: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.46/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_less
% 5.46/5.65 thf(fact_3044_power__Suc__less,axiom,
% 5.46/5.65 ! [A: int,N: nat] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ A @ one_one_int )
% 5.46/5.65 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_less
% 5.46/5.65 thf(fact_3045_frac__less__eq,axiom,
% 5.46/5.65 ! [Y2: real,Z: real,X2: real,W: real] :
% 5.46/5.65 ( ( Y2 != zero_zero_real )
% 5.46/5.65 => ( ( Z != zero_zero_real )
% 5.46/5.65 => ( ( ord_less_real @ ( divide_divide_real @ X2 @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.46/5.65 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_less_eq
% 5.46/5.65 thf(fact_3046_frac__less__eq,axiom,
% 5.46/5.65 ! [Y2: rat,Z: rat,X2: rat,W: rat] :
% 5.46/5.65 ( ( Y2 != zero_zero_rat )
% 5.46/5.65 => ( ( Z != zero_zero_rat )
% 5.46/5.65 => ( ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.46/5.65 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % frac_less_eq
% 5.46/5.65 thf(fact_3047_vebt__mint_Oelims,axiom,
% 5.46/5.65 ! [X2: vEBT_VEBT,Y2: option_nat] :
% 5.46/5.65 ( ( ( vEBT_vebt_mint @ X2 )
% 5.46/5.65 = Y2 )
% 5.46/5.65 => ( ! [A5: $o,B5: $o] :
% 5.46/5.65 ( ( X2
% 5.46/5.65 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.65 => ~ ( ( A5
% 5.46/5.65 => ( Y2
% 5.46/5.65 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.65 & ( ~ A5
% 5.46/5.65 => ( ( B5
% 5.46/5.65 => ( Y2
% 5.46/5.65 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.65 & ( ~ B5
% 5.46/5.65 => ( Y2 = none_nat ) ) ) ) ) )
% 5.46/5.65 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.65 => ( Y2 != none_nat ) )
% 5.46/5.65 => ~ ! [Mi2: nat] :
% 5.46/5.65 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.46/5.65 => ( Y2
% 5.46/5.65 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % vebt_mint.elims
% 5.46/5.65 thf(fact_3048_power__Suc__le__self,axiom,
% 5.46/5.65 ! [A: real,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_le_self
% 5.46/5.65 thf(fact_3049_power__Suc__le__self,axiom,
% 5.46/5.65 ! [A: rat,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.46/5.65 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_le_self
% 5.46/5.65 thf(fact_3050_power__Suc__le__self,axiom,
% 5.46/5.65 ! [A: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.46/5.65 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_le_self
% 5.46/5.65 thf(fact_3051_power__Suc__le__self,axiom,
% 5.46/5.65 ! [A: int,N: nat] :
% 5.46/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.46/5.65 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_le_self
% 5.46/5.65 thf(fact_3052_power__Suc__less__one,axiom,
% 5.46/5.65 ! [A: real,N: nat] :
% 5.46/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ A @ one_one_real )
% 5.46/5.65 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_less_one
% 5.46/5.65 thf(fact_3053_power__Suc__less__one,axiom,
% 5.46/5.65 ! [A: rat,N: nat] :
% 5.46/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.46/5.65 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_less_one
% 5.46/5.65 thf(fact_3054_power__Suc__less__one,axiom,
% 5.46/5.65 ! [A: nat,N: nat] :
% 5.46/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.46/5.65 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_less_one
% 5.46/5.65 thf(fact_3055_power__Suc__less__one,axiom,
% 5.46/5.65 ! [A: int,N: nat] :
% 5.46/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ A @ one_one_int )
% 5.46/5.65 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_Suc_less_one
% 5.46/5.65 thf(fact_3056_vebt__maxt_Oelims,axiom,
% 5.46/5.65 ! [X2: vEBT_VEBT,Y2: option_nat] :
% 5.46/5.65 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.46/5.65 = Y2 )
% 5.46/5.65 => ( ! [A5: $o,B5: $o] :
% 5.46/5.65 ( ( X2
% 5.46/5.65 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.65 => ~ ( ( B5
% 5.46/5.65 => ( Y2
% 5.46/5.65 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.65 & ( ~ B5
% 5.46/5.65 => ( ( A5
% 5.46/5.65 => ( Y2
% 5.46/5.65 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.65 & ( ~ A5
% 5.46/5.65 => ( Y2 = none_nat ) ) ) ) ) )
% 5.46/5.65 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.65 => ( Y2 != none_nat ) )
% 5.46/5.65 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.46/5.65 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.65 ( X2
% 5.46/5.65 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.46/5.65 => ( Y2
% 5.46/5.65 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % vebt_maxt.elims
% 5.46/5.65 thf(fact_3057_power__strict__decreasing,axiom,
% 5.46/5.65 ! [N: nat,N4: nat,A: real] :
% 5.46/5.65 ( ( ord_less_nat @ N @ N4 )
% 5.46/5.65 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_real @ A @ one_one_real )
% 5.46/5.65 => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_strict_decreasing
% 5.46/5.65 thf(fact_3058_power__strict__decreasing,axiom,
% 5.46/5.65 ! [N: nat,N4: nat,A: rat] :
% 5.46/5.65 ( ( ord_less_nat @ N @ N4 )
% 5.46/5.65 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.65 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.46/5.65 => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_strict_decreasing
% 5.46/5.65 thf(fact_3059_power__strict__decreasing,axiom,
% 5.46/5.65 ! [N: nat,N4: nat,A: nat] :
% 5.46/5.65 ( ( ord_less_nat @ N @ N4 )
% 5.46/5.65 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.65 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.46/5.65 => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_strict_decreasing
% 5.46/5.65 thf(fact_3060_power__strict__decreasing,axiom,
% 5.46/5.65 ! [N: nat,N4: nat,A: int] :
% 5.46/5.65 ( ( ord_less_nat @ N @ N4 )
% 5.46/5.65 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.65 => ( ( ord_less_int @ A @ one_one_int )
% 5.46/5.65 => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_strict_decreasing
% 5.46/5.65 thf(fact_3061_power__decreasing,axiom,
% 5.46/5.65 ! [N: nat,N4: nat,A: real] :
% 5.46/5.65 ( ( ord_less_eq_nat @ N @ N4 )
% 5.46/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.65 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.46/5.65 => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.46/5.65
% 5.46/5.65 % power_decreasing
% 5.46/5.66 thf(fact_3062_power__decreasing,axiom,
% 5.46/5.66 ! [N: nat,N4: nat,A: rat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ N @ N4 )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.66 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.46/5.66 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_decreasing
% 5.46/5.66 thf(fact_3063_power__decreasing,axiom,
% 5.46/5.66 ! [N: nat,N4: nat,A: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ N @ N4 )
% 5.46/5.66 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.66 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.46/5.66 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_decreasing
% 5.46/5.66 thf(fact_3064_power__decreasing,axiom,
% 5.46/5.66 ! [N: nat,N4: nat,A: int] :
% 5.46/5.66 ( ( ord_less_eq_nat @ N @ N4 )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.66 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.46/5.66 => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_decreasing
% 5.46/5.66 thf(fact_3065_zero__power2,axiom,
% 5.46/5.66 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = zero_zero_rat ) ).
% 5.46/5.66
% 5.46/5.66 % zero_power2
% 5.46/5.66 thf(fact_3066_zero__power2,axiom,
% 5.46/5.66 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = zero_zero_nat ) ).
% 5.46/5.66
% 5.46/5.66 % zero_power2
% 5.46/5.66 thf(fact_3067_zero__power2,axiom,
% 5.46/5.66 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = zero_zero_real ) ).
% 5.46/5.66
% 5.46/5.66 % zero_power2
% 5.46/5.66 thf(fact_3068_zero__power2,axiom,
% 5.46/5.66 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = zero_zero_complex ) ).
% 5.46/5.66
% 5.46/5.66 % zero_power2
% 5.46/5.66 thf(fact_3069_zero__power2,axiom,
% 5.46/5.66 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = zero_zero_int ) ).
% 5.46/5.66
% 5.46/5.66 % zero_power2
% 5.46/5.66 thf(fact_3070_self__le__power,axiom,
% 5.46/5.66 ! [A: real,N: nat] :
% 5.46/5.66 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % self_le_power
% 5.46/5.66 thf(fact_3071_self__le__power,axiom,
% 5.46/5.66 ! [A: rat,N: nat] :
% 5.46/5.66 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % self_le_power
% 5.46/5.66 thf(fact_3072_self__le__power,axiom,
% 5.46/5.66 ! [A: nat,N: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % self_le_power
% 5.46/5.66 thf(fact_3073_self__le__power,axiom,
% 5.46/5.66 ! [A: int,N: nat] :
% 5.46/5.66 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % self_le_power
% 5.46/5.66 thf(fact_3074_cong__exp__iff__simps_I3_J,axiom,
% 5.46/5.66 ! [N: num,Q2: num] :
% 5.46/5.66 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.66 != zero_zero_nat ) ).
% 5.46/5.66
% 5.46/5.66 % cong_exp_iff_simps(3)
% 5.46/5.66 thf(fact_3075_cong__exp__iff__simps_I3_J,axiom,
% 5.46/5.66 ! [N: num,Q2: num] :
% 5.46/5.66 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.66 != zero_zero_int ) ).
% 5.46/5.66
% 5.46/5.66 % cong_exp_iff_simps(3)
% 5.46/5.66 thf(fact_3076_cong__exp__iff__simps_I3_J,axiom,
% 5.46/5.66 ! [N: num,Q2: num] :
% 5.46/5.66 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.66 != zero_z3403309356797280102nteger ) ).
% 5.46/5.66
% 5.46/5.66 % cong_exp_iff_simps(3)
% 5.46/5.66 thf(fact_3077_one__less__power,axiom,
% 5.46/5.66 ! [A: real,N: nat] :
% 5.46/5.66 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % one_less_power
% 5.46/5.66 thf(fact_3078_one__less__power,axiom,
% 5.46/5.66 ! [A: rat,N: nat] :
% 5.46/5.66 ( ( ord_less_rat @ one_one_rat @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % one_less_power
% 5.46/5.66 thf(fact_3079_one__less__power,axiom,
% 5.46/5.66 ! [A: nat,N: nat] :
% 5.46/5.66 ( ( ord_less_nat @ one_one_nat @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % one_less_power
% 5.46/5.66 thf(fact_3080_one__less__power,axiom,
% 5.46/5.66 ! [A: int,N: nat] :
% 5.46/5.66 ( ( ord_less_int @ one_one_int @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % one_less_power
% 5.46/5.66 thf(fact_3081_numeral__2__eq__2,axiom,
% 5.46/5.66 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.46/5.66 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % numeral_2_eq_2
% 5.46/5.66 thf(fact_3082_pos2,axiom,
% 5.46/5.66 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.46/5.66
% 5.46/5.66 % pos2
% 5.46/5.66 thf(fact_3083_power__diff,axiom,
% 5.46/5.66 ! [A: complex,N: nat,M: nat] :
% 5.46/5.66 ( ( A != zero_zero_complex )
% 5.46/5.66 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.66 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_diff
% 5.46/5.66 thf(fact_3084_power__diff,axiom,
% 5.46/5.66 ! [A: real,N: nat,M: nat] :
% 5.46/5.66 ( ( A != zero_zero_real )
% 5.46/5.66 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.66 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_diff
% 5.46/5.66 thf(fact_3085_power__diff,axiom,
% 5.46/5.66 ! [A: rat,N: nat,M: nat] :
% 5.46/5.66 ( ( A != zero_zero_rat )
% 5.46/5.66 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.66 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_diff
% 5.46/5.66 thf(fact_3086_power__diff,axiom,
% 5.46/5.66 ! [A: nat,N: nat,M: nat] :
% 5.46/5.66 ( ( A != zero_zero_nat )
% 5.46/5.66 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.66 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_diff
% 5.46/5.66 thf(fact_3087_power__diff,axiom,
% 5.46/5.66 ! [A: int,N: nat,M: nat] :
% 5.46/5.66 ( ( A != zero_zero_int )
% 5.46/5.66 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.66 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_diff
% 5.46/5.66 thf(fact_3088_numeral__3__eq__3,axiom,
% 5.46/5.66 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.46/5.66 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % numeral_3_eq_3
% 5.46/5.66 thf(fact_3089_Suc__pred_H,axiom,
% 5.46/5.66 ! [N: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( N
% 5.46/5.66 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Suc_pred'
% 5.46/5.66 thf(fact_3090_Suc__diff__eq__diff__pred,axiom,
% 5.46/5.66 ! [N: nat,M: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.46/5.66 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Suc_diff_eq_diff_pred
% 5.46/5.66 thf(fact_3091_div__geq,axiom,
% 5.46/5.66 ! [N: nat,M: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ~ ( ord_less_nat @ M @ N )
% 5.46/5.66 => ( ( divide_divide_nat @ M @ N )
% 5.46/5.66 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_geq
% 5.46/5.66 thf(fact_3092_div__if,axiom,
% 5.46/5.66 ( divide_divide_nat
% 5.46/5.66 = ( ^ [M3: nat,N2: nat] :
% 5.46/5.66 ( if_nat
% 5.46/5.66 @ ( ( ord_less_nat @ M3 @ N2 )
% 5.46/5.66 | ( N2 = zero_zero_nat ) )
% 5.46/5.66 @ zero_zero_nat
% 5.46/5.66 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_if
% 5.46/5.66 thf(fact_3093_add__eq__if,axiom,
% 5.46/5.66 ( plus_plus_nat
% 5.46/5.66 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % add_eq_if
% 5.46/5.66 thf(fact_3094_less__eq__div__iff__mult__less__eq,axiom,
% 5.46/5.66 ! [Q2: nat,M: nat,N: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.46/5.66 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 5.46/5.66 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % less_eq_div_iff_mult_less_eq
% 5.46/5.66 thf(fact_3095_dividend__less__times__div,axiom,
% 5.46/5.66 ! [N: nat,M: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dividend_less_times_div
% 5.46/5.66 thf(fact_3096_dividend__less__div__times,axiom,
% 5.46/5.66 ! [N: nat,M: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dividend_less_div_times
% 5.46/5.66 thf(fact_3097_split__div,axiom,
% 5.46/5.66 ! [P: nat > $o,M: nat,N: nat] :
% 5.46/5.66 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.66 = ( ( ( N = zero_zero_nat )
% 5.46/5.66 => ( P @ zero_zero_nat ) )
% 5.46/5.66 & ( ( N != zero_zero_nat )
% 5.46/5.66 => ! [I4: nat,J3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ J3 @ N )
% 5.46/5.66 => ( ( M
% 5.46/5.66 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.46/5.66 => ( P @ I4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % split_div
% 5.46/5.66 thf(fact_3098_mult__eq__if,axiom,
% 5.46/5.66 ( times_times_nat
% 5.46/5.66 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_eq_if
% 5.46/5.66 thf(fact_3099_split__mod,axiom,
% 5.46/5.66 ! [P: nat > $o,M: nat,N: nat] :
% 5.46/5.66 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.66 = ( ( ( N = zero_zero_nat )
% 5.46/5.66 => ( P @ M ) )
% 5.46/5.66 & ( ( N != zero_zero_nat )
% 5.46/5.66 => ! [I4: nat,J3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ J3 @ N )
% 5.46/5.66 => ( ( M
% 5.46/5.66 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.46/5.66 => ( P @ J3 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % split_mod
% 5.46/5.66 thf(fact_3100_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.46/5.66 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X2 )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(3)
% 5.46/5.66 thf(fact_3101_vebt__member_Osimps_I4_J,axiom,
% 5.46/5.66 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_member.simps(4)
% 5.46/5.66 thf(fact_3102_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 5.46/5.66 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X2 )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(3)
% 5.46/5.66 thf(fact_3103_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.46/5.66 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X2 )
% 5.46/5.66 = ( ( X2 = Mi )
% 5.46/5.66 | ( X2 = Ma ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.membermima.simps(3)
% 5.46/5.66 thf(fact_3104_vebt__pred_Osimps_I5_J,axiom,
% 5.46/5.66 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.46/5.66 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve2 ) @ Vf2 )
% 5.46/5.66 = none_nat ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_pred.simps(5)
% 5.46/5.66 thf(fact_3105_vebt__succ_Osimps_I4_J,axiom,
% 5.46/5.66 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve2: nat] :
% 5.46/5.66 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve2 )
% 5.46/5.66 = none_nat ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_succ.simps(4)
% 5.46/5.66 thf(fact_3106_convex__bound__lt,axiom,
% 5.46/5.66 ! [X2: real,A: real,Y2: real,U: real,V: real] :
% 5.46/5.66 ( ( ord_less_real @ X2 @ A )
% 5.46/5.66 => ( ( ord_less_real @ Y2 @ A )
% 5.46/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.46/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.46/5.66 => ( ( ( plus_plus_real @ U @ V )
% 5.46/5.66 = one_one_real )
% 5.46/5.66 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % convex_bound_lt
% 5.46/5.66 thf(fact_3107_convex__bound__lt,axiom,
% 5.46/5.66 ! [X2: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X2 @ A )
% 5.46/5.66 => ( ( ord_less_rat @ Y2 @ A )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.46/5.66 => ( ( ( plus_plus_rat @ U @ V )
% 5.46/5.66 = one_one_rat )
% 5.46/5.66 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % convex_bound_lt
% 5.46/5.66 thf(fact_3108_convex__bound__lt,axiom,
% 5.46/5.66 ! [X2: int,A: int,Y2: int,U: int,V: int] :
% 5.46/5.66 ( ( ord_less_int @ X2 @ A )
% 5.46/5.66 => ( ( ord_less_int @ Y2 @ A )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.46/5.66 => ( ( ( plus_plus_int @ U @ V )
% 5.46/5.66 = one_one_int )
% 5.46/5.66 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % convex_bound_lt
% 5.46/5.66 thf(fact_3109_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Oelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ( ( ? [Uv2: $o] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ( ( ? [Uu2: $o] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.elims
% 5.46/5.66 thf(fact_3110_le__divide__eq__numeral_I1_J,axiom,
% 5.46/5.66 ! [W: num,B: real,C: real] :
% 5.46/5.66 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.46/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.66 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.46/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.66 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.66 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % le_divide_eq_numeral(1)
% 5.46/5.66 thf(fact_3111_le__divide__eq__numeral_I1_J,axiom,
% 5.46/5.66 ! [W: num,B: rat,C: rat] :
% 5.46/5.66 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.66 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.46/5.66 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.66 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.66 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.66 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.66 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % le_divide_eq_numeral(1)
% 5.46/5.66 thf(fact_3112_divide__le__eq__numeral_I1_J,axiom,
% 5.46/5.66 ! [B: real,C: real,W: num] :
% 5.46/5.66 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.46/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.66 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.66 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.46/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.66 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divide_le_eq_numeral(1)
% 5.46/5.66 thf(fact_3113_divide__le__eq__numeral_I1_J,axiom,
% 5.46/5.66 ! [B: rat,C: rat,W: num] :
% 5.46/5.66 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.46/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.66 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.66 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.66 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.66 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.46/5.66 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.66 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divide_le_eq_numeral(1)
% 5.46/5.66 thf(fact_3114_half__gt__zero__iff,axiom,
% 5.46/5.66 ! [A: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.46/5.66
% 5.46/5.66 % half_gt_zero_iff
% 5.46/5.66 thf(fact_3115_half__gt__zero__iff,axiom,
% 5.46/5.66 ! [A: rat] :
% 5.46/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.66
% 5.46/5.66 % half_gt_zero_iff
% 5.46/5.66 thf(fact_3116_half__gt__zero,axiom,
% 5.46/5.66 ! [A: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.66 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % half_gt_zero
% 5.46/5.66 thf(fact_3117_half__gt__zero,axiom,
% 5.46/5.66 ! [A: rat] :
% 5.46/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.66 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % half_gt_zero
% 5.46/5.66 thf(fact_3118_scaling__mono,axiom,
% 5.46/5.66 ! [U: real,V: real,R: real,S: real] :
% 5.46/5.66 ( ( ord_less_eq_real @ U @ V )
% 5.46/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ R )
% 5.46/5.66 => ( ( ord_less_eq_real @ R @ S )
% 5.46/5.66 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % scaling_mono
% 5.46/5.66 thf(fact_3119_scaling__mono,axiom,
% 5.46/5.66 ! [U: rat,V: rat,R: rat,S: rat] :
% 5.46/5.66 ( ( ord_less_eq_rat @ U @ V )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 5.46/5.66 => ( ( ord_less_eq_rat @ R @ S )
% 5.46/5.66 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % scaling_mono
% 5.46/5.66 thf(fact_3120_power2__le__imp__le,axiom,
% 5.46/5.66 ! [X2: real,Y2: real] :
% 5.46/5.66 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.66 => ( ord_less_eq_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_le_imp_le
% 5.46/5.66 thf(fact_3121_power2__le__imp__le,axiom,
% 5.46/5.66 ! [X2: rat,Y2: rat] :
% 5.46/5.66 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.66 => ( ord_less_eq_rat @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_le_imp_le
% 5.46/5.66 thf(fact_3122_power2__le__imp__le,axiom,
% 5.46/5.66 ! [X2: nat,Y2: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.46/5.66 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_le_imp_le
% 5.46/5.66 thf(fact_3123_power2__le__imp__le,axiom,
% 5.46/5.66 ! [X2: int,Y2: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.66 => ( ord_less_eq_int @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_le_imp_le
% 5.46/5.66 thf(fact_3124_power2__eq__imp__eq,axiom,
% 5.46/5.66 ! [X2: real,Y2: real] :
% 5.46/5.66 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.66 => ( X2 = Y2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_eq_imp_eq
% 5.46/5.66 thf(fact_3125_power2__eq__imp__eq,axiom,
% 5.46/5.66 ! [X2: rat,Y2: rat] :
% 5.46/5.66 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.66 => ( X2 = Y2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_eq_imp_eq
% 5.46/5.66 thf(fact_3126_power2__eq__imp__eq,axiom,
% 5.46/5.66 ! [X2: nat,Y2: nat] :
% 5.46/5.66 ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.46/5.66 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.46/5.66 => ( X2 = Y2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_eq_imp_eq
% 5.46/5.66 thf(fact_3127_power2__eq__imp__eq,axiom,
% 5.46/5.66 ! [X2: int,Y2: int] :
% 5.46/5.66 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.66 => ( X2 = Y2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_eq_imp_eq
% 5.46/5.66 thf(fact_3128_zero__le__power2,axiom,
% 5.46/5.66 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zero_le_power2
% 5.46/5.66 thf(fact_3129_zero__le__power2,axiom,
% 5.46/5.66 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zero_le_power2
% 5.46/5.66 thf(fact_3130_zero__le__power2,axiom,
% 5.46/5.66 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zero_le_power2
% 5.46/5.66 thf(fact_3131_power2__less__0,axiom,
% 5.46/5.66 ! [A: real] :
% 5.46/5.66 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.46/5.66
% 5.46/5.66 % power2_less_0
% 5.46/5.66 thf(fact_3132_power2__less__0,axiom,
% 5.46/5.66 ! [A: rat] :
% 5.46/5.66 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.46/5.66
% 5.46/5.66 % power2_less_0
% 5.46/5.66 thf(fact_3133_power2__less__0,axiom,
% 5.46/5.66 ! [A: int] :
% 5.46/5.66 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.46/5.66
% 5.46/5.66 % power2_less_0
% 5.46/5.66 thf(fact_3134_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.46/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.46/5.66 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.46/5.66 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.46/5.66 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.46/5.66 thf(fact_3135_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.46/5.66 ! [C: nat,A: nat,B: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.66 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.46/5.66 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.46/5.66 thf(fact_3136_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.46/5.66 ! [C: int,A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.66 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.46/5.66 thf(fact_3137_exp__add__not__zero__imp__right,axiom,
% 5.46/5.66 ! [M: nat,N: nat] :
% 5.46/5.66 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.66 != zero_zero_nat )
% 5.46/5.66 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.66 != zero_zero_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % exp_add_not_zero_imp_right
% 5.46/5.66 thf(fact_3138_exp__add__not__zero__imp__right,axiom,
% 5.46/5.66 ! [M: nat,N: nat] :
% 5.46/5.66 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.66 != zero_zero_int )
% 5.46/5.66 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.66 != zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % exp_add_not_zero_imp_right
% 5.46/5.66 thf(fact_3139_exp__add__not__zero__imp__left,axiom,
% 5.46/5.66 ! [M: nat,N: nat] :
% 5.46/5.66 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.66 != zero_zero_nat )
% 5.46/5.66 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.46/5.66 != zero_zero_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % exp_add_not_zero_imp_left
% 5.46/5.66 thf(fact_3140_exp__add__not__zero__imp__left,axiom,
% 5.46/5.66 ! [M: nat,N: nat] :
% 5.46/5.66 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.66 != zero_zero_int )
% 5.46/5.66 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.46/5.66 != zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % exp_add_not_zero_imp_left
% 5.46/5.66 thf(fact_3141_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.46/5.66 ! [N: nat,M: nat] :
% 5.46/5.66 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.66 != zero_zero_nat )
% 5.46/5.66 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.66 != zero_zero_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % exp_not_zero_imp_exp_diff_not_zero
% 5.46/5.66 thf(fact_3142_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.46/5.66 ! [N: nat,M: nat] :
% 5.46/5.66 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.66 != zero_zero_int )
% 5.46/5.66 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.66 != zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % exp_not_zero_imp_exp_diff_not_zero
% 5.46/5.66 thf(fact_3143_cong__exp__iff__simps_I7_J,axiom,
% 5.46/5.66 ! [Q2: num,N: num] :
% 5.46/5.66 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.66 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.66 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.46/5.66 = zero_zero_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % cong_exp_iff_simps(7)
% 5.46/5.66 thf(fact_3144_cong__exp__iff__simps_I7_J,axiom,
% 5.46/5.66 ! [Q2: num,N: num] :
% 5.46/5.66 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.66 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.66 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.46/5.66 = zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % cong_exp_iff_simps(7)
% 5.46/5.66 thf(fact_3145_cong__exp__iff__simps_I7_J,axiom,
% 5.46/5.66 ! [Q2: num,N: num] :
% 5.46/5.66 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.66 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.66 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.46/5.66 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.66
% 5.46/5.66 % cong_exp_iff_simps(7)
% 5.46/5.66 thf(fact_3146_cong__exp__iff__simps_I11_J,axiom,
% 5.46/5.66 ! [M: num,Q2: num] :
% 5.46/5.66 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.66 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.66 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.46/5.66 = zero_zero_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % cong_exp_iff_simps(11)
% 5.46/5.66 thf(fact_3147_cong__exp__iff__simps_I11_J,axiom,
% 5.46/5.66 ! [M: num,Q2: num] :
% 5.46/5.66 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.66 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.66 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.46/5.66 = zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % cong_exp_iff_simps(11)
% 5.46/5.66 thf(fact_3148_cong__exp__iff__simps_I11_J,axiom,
% 5.46/5.66 ! [M: num,Q2: num] :
% 5.46/5.66 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.66 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.66 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.46/5.66 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.66
% 5.46/5.66 % cong_exp_iff_simps(11)
% 5.46/5.66 thf(fact_3149_power__diff__power__eq,axiom,
% 5.46/5.66 ! [A: nat,N: nat,M: nat] :
% 5.46/5.66 ( ( A != zero_zero_nat )
% 5.46/5.66 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.46/5.66 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.46/5.66 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.46/5.66 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_diff_power_eq
% 5.46/5.66 thf(fact_3150_power__diff__power__eq,axiom,
% 5.46/5.66 ! [A: int,N: nat,M: nat] :
% 5.46/5.66 ( ( A != zero_zero_int )
% 5.46/5.66 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.46/5.66 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.46/5.66 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.46/5.66 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_diff_power_eq
% 5.46/5.66 thf(fact_3151_less__2__cases__iff,axiom,
% 5.46/5.66 ! [N: nat] :
% 5.46/5.66 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = ( ( N = zero_zero_nat )
% 5.46/5.66 | ( N
% 5.46/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % less_2_cases_iff
% 5.46/5.66 thf(fact_3152_less__2__cases,axiom,
% 5.46/5.66 ! [N: nat] :
% 5.46/5.66 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 => ( ( N = zero_zero_nat )
% 5.46/5.66 | ( N
% 5.46/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % less_2_cases
% 5.46/5.66 thf(fact_3153_nat__induct2,axiom,
% 5.46/5.66 ! [P: nat > $o,N: nat] :
% 5.46/5.66 ( ( P @ zero_zero_nat )
% 5.46/5.66 => ( ( P @ one_one_nat )
% 5.46/5.66 => ( ! [N3: nat] :
% 5.46/5.66 ( ( P @ N3 )
% 5.46/5.66 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.66 => ( P @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % nat_induct2
% 5.46/5.66 thf(fact_3154_power__eq__if,axiom,
% 5.46/5.66 ( power_power_complex
% 5.46/5.66 = ( ^ [P5: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_eq_if
% 5.46/5.66 thf(fact_3155_power__eq__if,axiom,
% 5.46/5.66 ( power_power_real
% 5.46/5.66 = ( ^ [P5: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_eq_if
% 5.46/5.66 thf(fact_3156_power__eq__if,axiom,
% 5.46/5.66 ( power_power_rat
% 5.46/5.66 = ( ^ [P5: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_eq_if
% 5.46/5.66 thf(fact_3157_power__eq__if,axiom,
% 5.46/5.66 ( power_power_nat
% 5.46/5.66 = ( ^ [P5: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_eq_if
% 5.46/5.66 thf(fact_3158_power__eq__if,axiom,
% 5.46/5.66 ( power_power_int
% 5.46/5.66 = ( ^ [P5: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_eq_if
% 5.46/5.66 thf(fact_3159_power__minus__mult,axiom,
% 5.46/5.66 ! [N: nat,A: complex] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.66 = ( power_power_complex @ A @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_minus_mult
% 5.46/5.66 thf(fact_3160_power__minus__mult,axiom,
% 5.46/5.66 ! [N: nat,A: real] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.66 = ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_minus_mult
% 5.46/5.66 thf(fact_3161_power__minus__mult,axiom,
% 5.46/5.66 ! [N: nat,A: rat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.66 = ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_minus_mult
% 5.46/5.66 thf(fact_3162_power__minus__mult,axiom,
% 5.46/5.66 ! [N: nat,A: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.66 = ( power_power_nat @ A @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_minus_mult
% 5.46/5.66 thf(fact_3163_power__minus__mult,axiom,
% 5.46/5.66 ! [N: nat,A: int] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.66 = ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power_minus_mult
% 5.46/5.66 thf(fact_3164_le__div__geq,axiom,
% 5.46/5.66 ! [N: nat,M: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.66 => ( ( divide_divide_nat @ M @ N )
% 5.46/5.66 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % le_div_geq
% 5.46/5.66 thf(fact_3165_split__div_H,axiom,
% 5.46/5.66 ! [P: nat > $o,M: nat,N: nat] :
% 5.46/5.66 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.66 = ( ( ( N = zero_zero_nat )
% 5.46/5.66 & ( P @ zero_zero_nat ) )
% 5.46/5.66 | ? [Q4: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 5.46/5.66 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 5.46/5.66 & ( P @ Q4 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % split_div'
% 5.46/5.66 thf(fact_3166_Suc__times__mod__eq,axiom,
% 5.46/5.66 ! [M: nat,N: nat] :
% 5.46/5.66 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.46/5.66 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.46/5.66 = one_one_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % Suc_times_mod_eq
% 5.46/5.66 thf(fact_3167_vebt__pred_Osimps_I6_J,axiom,
% 5.46/5.66 ! [V: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.46/5.66 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.46/5.66 = none_nat ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_pred.simps(6)
% 5.46/5.66 thf(fact_3168_vebt__succ_Osimps_I5_J,axiom,
% 5.46/5.66 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.46/5.66 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.46/5.66 = none_nat ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_succ.simps(5)
% 5.46/5.66 thf(fact_3169_power2__less__imp__less,axiom,
% 5.46/5.66 ! [X2: real,Y2: real] :
% 5.46/5.66 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.66 => ( ord_less_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_less_imp_less
% 5.46/5.66 thf(fact_3170_power2__less__imp__less,axiom,
% 5.46/5.66 ! [X2: rat,Y2: rat] :
% 5.46/5.66 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.66 => ( ord_less_rat @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_less_imp_less
% 5.46/5.66 thf(fact_3171_power2__less__imp__less,axiom,
% 5.46/5.66 ! [X2: nat,Y2: nat] :
% 5.46/5.66 ( ( ord_less_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.46/5.66 => ( ord_less_nat @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_less_imp_less
% 5.46/5.66 thf(fact_3172_power2__less__imp__less,axiom,
% 5.46/5.66 ! [X2: int,Y2: int] :
% 5.46/5.66 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.66 => ( ord_less_int @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % power2_less_imp_less
% 5.46/5.66 thf(fact_3173_sum__power2__le__zero__iff,axiom,
% 5.46/5.66 ! [X2: real,Y2: real] :
% 5.46/5.66 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.46/5.66 = ( ( X2 = zero_zero_real )
% 5.46/5.66 & ( Y2 = zero_zero_real ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % sum_power2_le_zero_iff
% 5.46/5.66 thf(fact_3174_sum__power2__le__zero__iff,axiom,
% 5.46/5.66 ! [X2: rat,Y2: rat] :
% 5.46/5.66 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.46/5.66 = ( ( X2 = zero_zero_rat )
% 5.46/5.66 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % sum_power2_le_zero_iff
% 5.46/5.66 thf(fact_3175_sum__power2__le__zero__iff,axiom,
% 5.46/5.66 ! [X2: int,Y2: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.46/5.66 = ( ( X2 = zero_zero_int )
% 5.46/5.66 & ( Y2 = zero_zero_int ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % sum_power2_le_zero_iff
% 5.46/5.66 thf(fact_3176_sum__power2__ge__zero,axiom,
% 5.46/5.66 ! [X2: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % sum_power2_ge_zero
% 5.46/5.66 thf(fact_3177_sum__power2__ge__zero,axiom,
% 5.46/5.66 ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % sum_power2_ge_zero
% 5.46/5.66 thf(fact_3178_sum__power2__ge__zero,axiom,
% 5.46/5.66 ! [X2: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % sum_power2_ge_zero
% 5.46/5.66 thf(fact_3179_sum__power2__gt__zero__iff,axiom,
% 5.46/5.66 ! [X2: real,Y2: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.66 = ( ( X2 != zero_zero_real )
% 5.46/5.66 | ( Y2 != zero_zero_real ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % sum_power2_gt_zero_iff
% 5.46/5.66 thf(fact_3180_sum__power2__gt__zero__iff,axiom,
% 5.46/5.66 ! [X2: rat,Y2: rat] :
% 5.46/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.66 = ( ( X2 != zero_zero_rat )
% 5.46/5.66 | ( Y2 != zero_zero_rat ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % sum_power2_gt_zero_iff
% 5.46/5.66 thf(fact_3181_sum__power2__gt__zero__iff,axiom,
% 5.46/5.66 ! [X2: int,Y2: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.66 = ( ( X2 != zero_zero_int )
% 5.46/5.66 | ( Y2 != zero_zero_int ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % sum_power2_gt_zero_iff
% 5.46/5.66 thf(fact_3182_not__sum__power2__lt__zero,axiom,
% 5.46/5.66 ! [X2: real,Y2: real] :
% 5.46/5.66 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.46/5.66
% 5.46/5.66 % not_sum_power2_lt_zero
% 5.46/5.66 thf(fact_3183_not__sum__power2__lt__zero,axiom,
% 5.46/5.66 ! [X2: rat,Y2: rat] :
% 5.46/5.66 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.46/5.66
% 5.46/5.66 % not_sum_power2_lt_zero
% 5.46/5.66 thf(fact_3184_not__sum__power2__lt__zero,axiom,
% 5.46/5.66 ! [X2: int,Y2: int] :
% 5.46/5.66 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.46/5.66
% 5.46/5.66 % not_sum_power2_lt_zero
% 5.46/5.66 thf(fact_3185_divmod__digit__0_I2_J,axiom,
% 5.46/5.66 ! [B: nat,A: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.66 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.46/5.66 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.46/5.66 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_0(2)
% 5.46/5.66 thf(fact_3186_divmod__digit__0_I2_J,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.46/5.66 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.46/5.66 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_0(2)
% 5.46/5.66 thf(fact_3187_divmod__digit__0_I2_J,axiom,
% 5.46/5.66 ! [B: code_integer,A: code_integer] :
% 5.46/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.46/5.66 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.46/5.66 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.46/5.66 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_0(2)
% 5.46/5.66 thf(fact_3188_bits__stable__imp__add__self,axiom,
% 5.46/5.66 ! [A: nat] :
% 5.46/5.66 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = A )
% 5.46/5.66 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = zero_zero_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % bits_stable_imp_add_self
% 5.46/5.66 thf(fact_3189_bits__stable__imp__add__self,axiom,
% 5.46/5.66 ! [A: int] :
% 5.46/5.66 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.66 = A )
% 5.46/5.66 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % bits_stable_imp_add_self
% 5.46/5.66 thf(fact_3190_bits__stable__imp__add__self,axiom,
% 5.46/5.66 ! [A: code_integer] :
% 5.46/5.66 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.66 = A )
% 5.46/5.66 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.66
% 5.46/5.66 % bits_stable_imp_add_self
% 5.46/5.66 thf(fact_3191_zero__le__even__power_H,axiom,
% 5.46/5.66 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zero_le_even_power'
% 5.46/5.66 thf(fact_3192_zero__le__even__power_H,axiom,
% 5.46/5.66 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zero_le_even_power'
% 5.46/5.66 thf(fact_3193_zero__le__even__power_H,axiom,
% 5.46/5.66 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zero_le_even_power'
% 5.46/5.66 thf(fact_3194_nat__bit__induct,axiom,
% 5.46/5.66 ! [P: nat > $o,N: nat] :
% 5.46/5.66 ( ( P @ zero_zero_nat )
% 5.46/5.66 => ( ! [N3: nat] :
% 5.46/5.66 ( ( P @ N3 )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.46/5.66 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.46/5.66 => ( ! [N3: nat] :
% 5.46/5.66 ( ( P @ N3 )
% 5.46/5.66 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.46/5.66 => ( P @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % nat_bit_induct
% 5.46/5.66 thf(fact_3195_Suc__n__div__2__gt__zero,axiom,
% 5.46/5.66 ! [N: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Suc_n_div_2_gt_zero
% 5.46/5.66 thf(fact_3196_div__2__gt__zero,axiom,
% 5.46/5.66 ! [N: nat] :
% 5.46/5.66 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.66 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_2_gt_zero
% 5.46/5.66 thf(fact_3197_verit__le__mono__div,axiom,
% 5.46/5.66 ! [A2: nat,B3: nat,N: nat] :
% 5.46/5.66 ( ( ord_less_nat @ A2 @ B3 )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ord_less_eq_nat
% 5.46/5.66 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 5.46/5.66 @ ( if_nat
% 5.46/5.66 @ ( ( modulo_modulo_nat @ B3 @ N )
% 5.46/5.66 = zero_zero_nat )
% 5.46/5.66 @ one_one_nat
% 5.46/5.66 @ zero_zero_nat ) )
% 5.46/5.66 @ ( divide_divide_nat @ B3 @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % verit_le_mono_div
% 5.46/5.66 thf(fact_3198_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.46/5.66 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [S3: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.naive_member.elims(3)
% 5.46/5.66 thf(fact_3199_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.46/5.66 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [S3: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.46/5.66 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.naive_member.elims(2)
% 5.46/5.66 thf(fact_3200_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.46/5.66 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.46/5.66 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.46/5.66 => Y2 )
% 5.46/5.66 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [S3: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.naive_member.elims(1)
% 5.46/5.66 thf(fact_3201_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 5.46/5.66 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 )
% 5.46/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(3)
% 5.46/5.66 thf(fact_3202_divmod__digit__0_I1_J,axiom,
% 5.46/5.66 ! [B: nat,A: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.66 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.46/5.66 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.46/5.66 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_0(1)
% 5.46/5.66 thf(fact_3203_divmod__digit__0_I1_J,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.46/5.66 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.46/5.66 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_0(1)
% 5.46/5.66 thf(fact_3204_divmod__digit__0_I1_J,axiom,
% 5.46/5.66 ! [B: code_integer,A: code_integer] :
% 5.46/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.46/5.66 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.46/5.66 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.46/5.66 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_0(1)
% 5.46/5.66 thf(fact_3205_odd__0__le__power__imp__0__le,axiom,
% 5.46/5.66 ! [A: real,N: nat] :
% 5.46/5.66 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.66 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.46/5.66
% 5.46/5.66 % odd_0_le_power_imp_0_le
% 5.46/5.66 thf(fact_3206_odd__0__le__power__imp__0__le,axiom,
% 5.46/5.66 ! [A: rat,N: nat] :
% 5.46/5.66 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.66 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.66
% 5.46/5.66 % odd_0_le_power_imp_0_le
% 5.46/5.66 thf(fact_3207_odd__0__le__power__imp__0__le,axiom,
% 5.46/5.66 ! [A: int,N: nat] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.66 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.46/5.66
% 5.46/5.66 % odd_0_le_power_imp_0_le
% 5.46/5.66 thf(fact_3208_odd__power__less__zero,axiom,
% 5.46/5.66 ! [A: real,N: nat] :
% 5.46/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.66 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.66
% 5.46/5.66 % odd_power_less_zero
% 5.46/5.66 thf(fact_3209_odd__power__less__zero,axiom,
% 5.46/5.66 ! [A: rat,N: nat] :
% 5.46/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.66 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.46/5.66
% 5.46/5.66 % odd_power_less_zero
% 5.46/5.66 thf(fact_3210_odd__power__less__zero,axiom,
% 5.46/5.66 ! [A: int,N: nat] :
% 5.46/5.66 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.66 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % odd_power_less_zero
% 5.46/5.66 thf(fact_3211_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.46/5.66 ! [X2: nat,N: nat,M: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.66 => ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.exp_split_high_low(1)
% 5.46/5.66 thf(fact_3212_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.46/5.66 ! [X2: nat,N: nat,M: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.66 => ( ord_less_nat @ ( vEBT_VEBT_low @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.exp_split_high_low(2)
% 5.46/5.66 thf(fact_3213_vebt__member_Oelims_I2_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [Summary2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ~ ( ( Xa2 != Mi2 )
% 5.46/5.66 => ( ( Xa2 != Ma2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_member.elims(2)
% 5.46/5.66 thf(fact_3214_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.46/5.66 => ( ! [Uu2: $o,Uv2: $o] :
% 5.46/5.66 ( X2
% 5.46/5.66 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.66 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat] :
% 5.46/5.66 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.46/5.66 => ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 ) ) )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [Vc2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.46/5.66 => ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 )
% 5.46/5.66 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.46/5.66 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [Vd2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.membermima.elims(3)
% 5.46/5.66 thf(fact_3215_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.46/5.66 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.66 => Y2 )
% 5.46/5.66 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.46/5.66 => Y2 )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat] :
% 5.46/5.66 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( ~ ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 ) ) ) ) )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [Vc2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( ~ ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 )
% 5.46/5.66 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 5.46/5.66 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [Vd2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.membermima.elims(1)
% 5.46/5.66 thf(fact_3216_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 5.46/5.66 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 )
% 5.46/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(4)
% 5.46/5.66 thf(fact_3217_mod__double__modulus,axiom,
% 5.46/5.66 ! [M: code_integer,X2: code_integer] :
% 5.46/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.46/5.66 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.46/5.66 => ( ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.66 = ( modulo364778990260209775nteger @ X2 @ M ) )
% 5.46/5.66 | ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.66 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mod_double_modulus
% 5.46/5.66 thf(fact_3218_mod__double__modulus,axiom,
% 5.46/5.66 ! [M: nat,X2: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.66 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.46/5.66 => ( ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.66 = ( modulo_modulo_nat @ X2 @ M ) )
% 5.46/5.66 | ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.66 = ( plus_plus_nat @ ( modulo_modulo_nat @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mod_double_modulus
% 5.46/5.66 thf(fact_3219_mod__double__modulus,axiom,
% 5.46/5.66 ! [M: int,X2: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ M )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.66 => ( ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.66 = ( modulo_modulo_int @ X2 @ M ) )
% 5.46/5.66 | ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.66 = ( plus_plus_int @ ( modulo_modulo_int @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mod_double_modulus
% 5.46/5.66 thf(fact_3220_divmod__digit__1_I2_J,axiom,
% 5.46/5.66 ! [A: code_integer,B: code_integer] :
% 5.46/5.66 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.46/5.66 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.46/5.66 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.46/5.66 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_1(2)
% 5.46/5.66 thf(fact_3221_divmod__digit__1_I2_J,axiom,
% 5.46/5.66 ! [A: nat,B: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.66 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.46/5.66 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.46/5.66 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_1(2)
% 5.46/5.66 thf(fact_3222_divmod__digit__1_I2_J,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.46/5.66 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.46/5.66 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_1(2)
% 5.46/5.66 thf(fact_3223_vebt__member_Oelims_I1_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.46/5.66 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.46/5.66 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => Y2 )
% 5.46/5.66 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.46/5.66 => Y2 )
% 5.46/5.66 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.66 => Y2 )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [Summary2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( ~ ( ( Xa2 != Mi2 )
% 5.46/5.66 => ( ( Xa2 != Ma2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_member.elims(1)
% 5.46/5.66 thf(fact_3224_vebt__member_Oelims_I3_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.46/5.66 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [Summary2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( Xa2 != Mi2 )
% 5.46/5.66 => ( ( Xa2 != Ma2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_member.elims(3)
% 5.46/5.66 thf(fact_3225_arith__geo__mean,axiom,
% 5.46/5.66 ! [U: real,X2: real,Y2: real] :
% 5.46/5.66 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = ( times_times_real @ X2 @ Y2 ) )
% 5.46/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.66 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % arith_geo_mean
% 5.46/5.66 thf(fact_3226_arith__geo__mean,axiom,
% 5.46/5.66 ! [U: rat,X2: rat,Y2: rat] :
% 5.46/5.66 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 = ( times_times_rat @ X2 @ Y2 ) )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.66 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % arith_geo_mean
% 5.46/5.66 thf(fact_3227_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_m_e_m_b_e_r @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( ? [A5: $o,B5: $o] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.46/5.66 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [Summary2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.elims
% 5.46/5.66 thf(fact_3228_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( ? [A5: $o,B5: $o] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ( ( ? [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 != ( if_nat
% 5.46/5.66 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 & ~ ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 ) ) )
% 5.46/5.66 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.46/5.66 @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.elims
% 5.46/5.66 thf(fact_3229_invar__vebt_Osimps,axiom,
% 5.46/5.66 ( vEBT_invar_vebt
% 5.46/5.66 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 5.46/5.66 ( ( ? [A3: $o,B2: $o] :
% 5.46/5.66 ( A1
% 5.46/5.66 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.46/5.66 & ( A22
% 5.46/5.66 = ( suc @ zero_zero_nat ) ) )
% 5.46/5.66 | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.46/5.66 ( ( A1
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 5.46/5.66 & ! [X: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.66 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.46/5.66 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.46/5.66 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.46/5.66 & ( A22
% 5.46/5.66 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.46/5.66 & ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X5 )
% 5.46/5.66 & ! [X: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.66 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.66 | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.46/5.66 ( ( A1
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 5.46/5.66 & ! [X: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.66 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.46/5.66 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.46/5.66 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.46/5.66 & ( A22
% 5.46/5.66 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.46/5.66 & ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X5 )
% 5.46/5.66 & ! [X: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.66 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.66 | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.46/5.66 ( ( A1
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 5.46/5.66 & ! [X: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.66 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.46/5.66 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.46/5.66 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.46/5.66 & ( A22
% 5.46/5.66 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.46/5.66 & ! [I4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.46/5.66 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X5 ) )
% 5.46/5.66 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.46/5.66 & ( ( Mi3 = Ma3 )
% 5.46/5.66 => ! [X: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.66 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.66 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.66 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.46/5.66 & ( ( Mi3 != Ma3 )
% 5.46/5.66 => ! [I4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.46/5.66 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.46/5.66 = I4 )
% 5.46/5.66 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.46/5.66 & ! [X: nat] :
% 5.46/5.66 ( ( ( ( vEBT_VEBT_high @ X @ N2 )
% 5.46/5.66 = I4 )
% 5.46/5.66 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N2 ) ) )
% 5.46/5.66 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.66 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) )
% 5.46/5.66 | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.46/5.66 ( ( A1
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 5.46/5.66 & ! [X: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.66 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.46/5.66 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.46/5.66 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.46/5.66 & ( A22
% 5.46/5.66 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.46/5.66 & ! [I4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.46/5.66 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X5 ) )
% 5.46/5.66 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.46/5.66 & ( ( Mi3 = Ma3 )
% 5.46/5.66 => ! [X: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.66 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.66 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.66 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.46/5.66 & ( ( Mi3 != Ma3 )
% 5.46/5.66 => ! [I4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.46/5.66 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.46/5.66 = I4 )
% 5.46/5.66 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.46/5.66 & ! [X: nat] :
% 5.46/5.66 ( ( ( ( vEBT_VEBT_high @ X @ N2 )
% 5.46/5.66 = I4 )
% 5.46/5.66 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N2 ) ) )
% 5.46/5.66 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.66 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % invar_vebt.simps
% 5.46/5.66 thf(fact_3230_invar__vebt_Ocases,axiom,
% 5.46/5.66 ! [A12: vEBT_VEBT,A23: nat] :
% 5.46/5.66 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.46/5.66 => ( ( ? [A5: $o,B5: $o] :
% 5.46/5.66 ( A12
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( A23
% 5.46/5.66 != ( suc @ zero_zero_nat ) ) )
% 5.46/5.66 => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.46/5.66 ( ( A12
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( A23 = Deg2 )
% 5.46/5.66 => ( ! [X4: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.46/5.66 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.46/5.66 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.66 => ( ( M4 = N3 )
% 5.46/5.66 => ( ( Deg2
% 5.46/5.66 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.46/5.66 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.46/5.66 => ~ ! [X4: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.66 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.46/5.66 => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.46/5.66 ( ( A12
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( A23 = Deg2 )
% 5.46/5.66 => ( ! [X4: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.46/5.66 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.46/5.66 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.66 => ( ( M4
% 5.46/5.66 = ( suc @ N3 ) )
% 5.46/5.66 => ( ( Deg2
% 5.46/5.66 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.46/5.66 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.46/5.66 => ~ ! [X4: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.66 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.46/5.66 => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.46/5.66 ( ( A12
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( A23 = Deg2 )
% 5.46/5.66 => ( ! [X4: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.46/5.66 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.46/5.66 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.66 => ( ( M4 = N3 )
% 5.46/5.66 => ( ( Deg2
% 5.46/5.66 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.46/5.66 => ( ! [I3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.66 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X5 ) )
% 5.46/5.66 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.46/5.66 => ( ( ( Mi2 = Ma2 )
% 5.46/5.66 => ! [X4: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.66 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.46/5.66 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.46/5.66 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.66 => ~ ( ( Mi2 != Ma2 )
% 5.46/5.66 => ! [I3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.66 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.46/5.66 = I3 )
% 5.46/5.66 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.46/5.66 & ! [X4: nat] :
% 5.46/5.66 ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 5.46/5.66 = I3 )
% 5.46/5.66 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 5.46/5.66 => ( ( ord_less_nat @ Mi2 @ X4 )
% 5.46/5.66 & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.66 => ~ ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.46/5.66 ( ( A12
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( A23 = Deg2 )
% 5.46/5.66 => ( ! [X4: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.46/5.66 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.46/5.66 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.66 => ( ( M4
% 5.46/5.66 = ( suc @ N3 ) )
% 5.46/5.66 => ( ( Deg2
% 5.46/5.66 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.46/5.66 => ( ! [I3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.66 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X5 ) )
% 5.46/5.66 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.46/5.66 => ( ( ( Mi2 = Ma2 )
% 5.46/5.66 => ! [X4: vEBT_VEBT] :
% 5.46/5.66 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.66 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.46/5.66 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.46/5.66 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.66 => ~ ( ( Mi2 != Ma2 )
% 5.46/5.66 => ! [I3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.66 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.46/5.66 = I3 )
% 5.46/5.66 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.46/5.66 & ! [X4: nat] :
% 5.46/5.66 ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 5.46/5.66 = I3 )
% 5.46/5.66 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 5.46/5.66 => ( ( ord_less_nat @ Mi2 @ X4 )
% 5.46/5.66 & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % invar_vebt.cases
% 5.46/5.66 thf(fact_3231_divmod__digit__1_I1_J,axiom,
% 5.46/5.66 ! [A: code_integer,B: code_integer] :
% 5.46/5.66 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.46/5.66 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.46/5.66 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.46/5.66 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_1(1)
% 5.46/5.66 thf(fact_3232_divmod__digit__1_I1_J,axiom,
% 5.46/5.66 ! [A: nat,B: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.66 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.46/5.66 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.46/5.66 => ( ( 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 )
% 5.46/5.66 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_1(1)
% 5.46/5.66 thf(fact_3233_divmod__digit__1_I1_J,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.46/5.66 => ( ( 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 )
% 5.46/5.66 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_digit_1(1)
% 5.46/5.66 thf(fact_3234_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( ? [A5: $o,B5: $o] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT] :
% 5.46/5.66 ( ? [Summary2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 != ( plus_plus_nat @ one_one_nat
% 5.46/5.66 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat
% 5.46/5.66 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 5.46/5.66 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 5.46/5.66 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.46/5.66 @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.elims
% 5.46/5.66 thf(fact_3235_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 5.46/5.66 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.46/5.66 = ( plus_plus_nat @ one_one_nat
% 5.46/5.66 @ ( if_nat @ ( X2 = Mi ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat @ ( X2 = Ma ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat @ ( ord_less_nat @ Ma @ X2 ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat
% 5.46/5.66 @ ( ( ord_less_nat @ Mi @ X2 )
% 5.46/5.66 & ( ord_less_nat @ X2 @ Ma ) )
% 5.46/5.66 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.46/5.66 @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(5)
% 5.46/5.66 thf(fact_3236_mod__exhaust__less__4,axiom,
% 5.46/5.66 ! [M: nat] :
% 5.46/5.66 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = zero_zero_nat )
% 5.46/5.66 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = one_one_nat )
% 5.46/5.66 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mod_exhaust_less_4
% 5.46/5.66 thf(fact_3237_arcosh__1,axiom,
% 5.46/5.66 ( ( arcosh_real @ one_one_real )
% 5.46/5.66 = zero_zero_real ) ).
% 5.46/5.66
% 5.46/5.66 % arcosh_1
% 5.46/5.66 thf(fact_3238_inrange,axiom,
% 5.46/5.66 ! [T: vEBT_VEBT,N: nat] :
% 5.46/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.66 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % inrange
% 5.46/5.66 thf(fact_3239_finite__nth__roots,axiom,
% 5.46/5.66 ! [N: nat,C: complex] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( finite3207457112153483333omplex
% 5.46/5.66 @ ( collect_complex
% 5.46/5.66 @ ^ [Z4: complex] :
% 5.46/5.66 ( ( power_power_complex @ Z4 @ N )
% 5.46/5.66 = C ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % finite_nth_roots
% 5.46/5.66 thf(fact_3240_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_m_i_n_t @ X2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ! [A5: $o] :
% 5.46/5.66 ( ? [B5: $o] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.46/5.66 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.elims
% 5.46/5.66 thf(fact_3241_vebt__succ_Opelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.46/5.66 ( ( ( vEBT_vebt_succ @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [Uu2: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 5.46/5.66 => ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => ( ( ( B5
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.66 & ( ~ B5
% 5.46/5.66 => ( Y2 = none_nat ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 5.46/5.66 => ( ! [Uv2: $o,Uw2: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ! [N3: nat] :
% 5.46/5.66 ( ( Xa2
% 5.46/5.66 = ( suc @ N3 ) )
% 5.46/5.66 => ( ( Y2 = none_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 5.46/5.66 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ( ( Y2 = none_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.46/5.66 => ( ( Y2 = none_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.46/5.66 => ( ( Y2 = none_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( some_nat @ Mi2 ) ) )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 @ ( if_option_nat
% 5.46/5.66 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 != none_nat )
% 5.46/5.66 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.46/5.66 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 @ ( if_option_nat
% 5.46/5.66 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.66 = none_nat )
% 5.46/5.66 @ none_nat
% 5.46/5.66 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.66 @ none_nat ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_succ.pelims
% 5.46/5.66 thf(fact_3242_vebt__pred_Opelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.46/5.66 ( ( ( vEBT_vebt_pred @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [Uu2: $o,Uv2: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.66 => ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => ( ( Y2 = none_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.46/5.66 => ( ! [A5: $o,Uw2: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 5.46/5.66 => ( ( Xa2
% 5.46/5.66 = ( suc @ zero_zero_nat ) )
% 5.46/5.66 => ( ( ( A5
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.66 & ( ~ A5
% 5.46/5.66 => ( Y2 = none_nat ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ! [Va3: nat] :
% 5.46/5.66 ( ( Xa2
% 5.46/5.66 = ( suc @ ( suc @ Va3 ) ) )
% 5.46/5.66 => ( ( ( B5
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.66 & ( ~ B5
% 5.46/5.66 => ( ( A5
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.66 & ( ~ A5
% 5.46/5.66 => ( Y2 = none_nat ) ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) )
% 5.46/5.66 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.46/5.66 => ( ( Y2 = none_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.46/5.66 => ( ( Y2 = none_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.46/5.66 => ( ( Y2 = none_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( some_nat @ Ma2 ) ) )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 => ( Y2
% 5.46/5.66 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 @ ( if_option_nat
% 5.46/5.66 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 != none_nat )
% 5.46/5.66 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.46/5.66 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 @ ( if_option_nat
% 5.46/5.66 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.66 = none_nat )
% 5.46/5.66 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.46/5.66 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.66 @ none_nat ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_pred.pelims
% 5.46/5.66 thf(fact_3243_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_m_a_x_t @ X2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( Y2
% 5.46/5.66 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B5 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.46/5.66 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) )
% 5.46/5.66 => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ( Y2 != one_one_nat ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.elims
% 5.46/5.66 thf(fact_3244_flip__bit__nonnegative__int__iff,axiom,
% 5.46/5.66 ! [N: nat,K: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.46/5.66 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.66
% 5.46/5.66 % flip_bit_nonnegative_int_iff
% 5.46/5.66 thf(fact_3245_flip__bit__negative__int__iff,axiom,
% 5.46/5.66 ! [N: nat,K: int] :
% 5.46/5.66 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.66 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % flip_bit_negative_int_iff
% 5.46/5.66 thf(fact_3246_i0__less,axiom,
% 5.46/5.66 ! [N: extended_enat] :
% 5.46/5.66 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.46/5.66 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.46/5.66
% 5.46/5.66 % i0_less
% 5.46/5.66 thf(fact_3247_idiff__0,axiom,
% 5.46/5.66 ! [N: extended_enat] :
% 5.46/5.66 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.46/5.66 = zero_z5237406670263579293d_enat ) ).
% 5.46/5.66
% 5.46/5.66 % idiff_0
% 5.46/5.66 thf(fact_3248_idiff__0__right,axiom,
% 5.46/5.66 ! [N: extended_enat] :
% 5.46/5.66 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.46/5.66 = N ) ).
% 5.46/5.66
% 5.46/5.66 % idiff_0_right
% 5.46/5.66 thf(fact_3249_not__real__square__gt__zero,axiom,
% 5.46/5.66 ! [X2: real] :
% 5.46/5.66 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X2 @ X2 ) ) )
% 5.46/5.66 = ( X2 = zero_zero_real ) ) ).
% 5.46/5.66
% 5.46/5.66 % not_real_square_gt_zero
% 5.46/5.66 thf(fact_3250_unset__bit__nonnegative__int__iff,axiom,
% 5.46/5.66 ! [N: nat,K: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.46/5.66 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.66
% 5.46/5.66 % unset_bit_nonnegative_int_iff
% 5.46/5.66 thf(fact_3251_unset__bit__negative__int__iff,axiom,
% 5.46/5.66 ! [N: nat,K: int] :
% 5.46/5.66 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.66 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % unset_bit_negative_int_iff
% 5.46/5.66 thf(fact_3252_set__bit__nonnegative__int__iff,axiom,
% 5.46/5.66 ! [N: nat,K: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.46/5.66 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.66
% 5.46/5.66 % set_bit_nonnegative_int_iff
% 5.46/5.66 thf(fact_3253_set__bit__negative__int__iff,axiom,
% 5.46/5.66 ! [N: nat,K: int] :
% 5.46/5.66 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.66 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % set_bit_negative_int_iff
% 5.46/5.66 thf(fact_3254_div__pos__pos__trivial,axiom,
% 5.46/5.66 ! [K: int,L2: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.66 => ( ( ord_less_int @ K @ L2 )
% 5.46/5.66 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.66 = zero_zero_int ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_pos_pos_trivial
% 5.46/5.66 thf(fact_3255_div__neg__neg__trivial,axiom,
% 5.46/5.66 ! [K: int,L2: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ L2 @ K )
% 5.46/5.66 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.66 = zero_zero_int ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_neg_neg_trivial
% 5.46/5.66 thf(fact_3256_mod__pos__pos__trivial,axiom,
% 5.46/5.66 ! [K: int,L2: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.66 => ( ( ord_less_int @ K @ L2 )
% 5.46/5.66 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.66 = K ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mod_pos_pos_trivial
% 5.46/5.66 thf(fact_3257_mod__neg__neg__trivial,axiom,
% 5.46/5.66 ! [K: int,L2: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ L2 @ K )
% 5.46/5.66 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.66 = K ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mod_neg_neg_trivial
% 5.46/5.66 thf(fact_3258_half__nonnegative__int__iff,axiom,
% 5.46/5.66 ! [K: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.46/5.66 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.66
% 5.46/5.66 % half_nonnegative_int_iff
% 5.46/5.66 thf(fact_3259_half__negative__int__iff,axiom,
% 5.46/5.66 ! [K: int] :
% 5.46/5.66 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.46/5.66 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % half_negative_int_iff
% 5.46/5.66 thf(fact_3260_less__int__code_I1_J,axiom,
% 5.46/5.66 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.46/5.66
% 5.46/5.66 % less_int_code(1)
% 5.46/5.66 thf(fact_3261_minus__int__code_I1_J,axiom,
% 5.46/5.66 ! [K: int] :
% 5.46/5.66 ( ( minus_minus_int @ K @ zero_zero_int )
% 5.46/5.66 = K ) ).
% 5.46/5.66
% 5.46/5.66 % minus_int_code(1)
% 5.46/5.66 thf(fact_3262_enat__0__less__mult__iff,axiom,
% 5.46/5.66 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.66 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.46/5.66 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.46/5.66 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % enat_0_less_mult_iff
% 5.46/5.66 thf(fact_3263_not__iless0,axiom,
% 5.46/5.66 ! [N: extended_enat] :
% 5.46/5.66 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.46/5.66
% 5.46/5.66 % not_iless0
% 5.46/5.66 thf(fact_3264_iadd__is__0,axiom,
% 5.46/5.66 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.66 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.46/5.66 = zero_z5237406670263579293d_enat )
% 5.46/5.66 = ( ( M = zero_z5237406670263579293d_enat )
% 5.46/5.66 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % iadd_is_0
% 5.46/5.66 thf(fact_3265_i0__lb,axiom,
% 5.46/5.66 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.46/5.66
% 5.46/5.66 % i0_lb
% 5.46/5.66 thf(fact_3266_ile0__eq,axiom,
% 5.46/5.66 ! [N: extended_enat] :
% 5.46/5.66 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.46/5.66 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.46/5.66
% 5.46/5.66 % ile0_eq
% 5.46/5.66 thf(fact_3267_all__nat__less,axiom,
% 5.46/5.66 ! [N: nat,P: nat > $o] :
% 5.46/5.66 ( ( ! [M3: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ M3 @ N )
% 5.46/5.66 => ( P @ M3 ) ) )
% 5.46/5.66 = ( ! [X: nat] :
% 5.46/5.66 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.66 => ( P @ X ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % all_nat_less
% 5.46/5.66 thf(fact_3268_ex__nat__less,axiom,
% 5.46/5.66 ! [N: nat,P: nat > $o] :
% 5.46/5.66 ( ( ? [M3: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ M3 @ N )
% 5.46/5.66 & ( P @ M3 ) ) )
% 5.46/5.66 = ( ? [X: nat] :
% 5.46/5.66 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.66 & ( P @ X ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % ex_nat_less
% 5.46/5.66 thf(fact_3269_zmult__zless__mono2,axiom,
% 5.46/5.66 ! [I: int,J: int,K: int] :
% 5.46/5.66 ( ( ord_less_int @ I @ J )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.66 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zmult_zless_mono2
% 5.46/5.66 thf(fact_3270_pos__imp__zdiv__neg__iff,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.46/5.66 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pos_imp_zdiv_neg_iff
% 5.46/5.66 thf(fact_3271_neg__imp__zdiv__neg__iff,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.46/5.66 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % neg_imp_zdiv_neg_iff
% 5.46/5.66 thf(fact_3272_div__neg__pos__less0,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_neg_pos_less0
% 5.46/5.66 thf(fact_3273_zmod__le__nonneg__dividend,axiom,
% 5.46/5.66 ! [M: int,K: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.46/5.66 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.46/5.66
% 5.46/5.66 % zmod_le_nonneg_dividend
% 5.46/5.66 thf(fact_3274_neg__mod__bound,axiom,
% 5.46/5.66 ! [L2: int,K: int] :
% 5.46/5.66 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.66 => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % neg_mod_bound
% 5.46/5.66 thf(fact_3275_Euclidean__Division_Opos__mod__bound,axiom,
% 5.46/5.66 ! [L2: int,K: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.66 => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % Euclidean_Division.pos_mod_bound
% 5.46/5.66 thf(fact_3276_zmod__eq__0__iff,axiom,
% 5.46/5.66 ! [M: int,D2: int] :
% 5.46/5.66 ( ( ( modulo_modulo_int @ M @ D2 )
% 5.46/5.66 = zero_zero_int )
% 5.46/5.66 = ( ? [Q4: int] :
% 5.46/5.66 ( M
% 5.46/5.66 = ( times_times_int @ D2 @ Q4 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zmod_eq_0_iff
% 5.46/5.66 thf(fact_3277_zmod__eq__0D,axiom,
% 5.46/5.66 ! [M: int,D2: int] :
% 5.46/5.66 ( ( ( modulo_modulo_int @ M @ D2 )
% 5.46/5.66 = zero_zero_int )
% 5.46/5.66 => ? [Q3: int] :
% 5.46/5.66 ( M
% 5.46/5.66 = ( times_times_int @ D2 @ Q3 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zmod_eq_0D
% 5.46/5.66 thf(fact_3278_realpow__pos__nth2,axiom,
% 5.46/5.66 ! [A: real,N: nat] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.66 => ? [R3: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.66 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.46/5.66 = A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % realpow_pos_nth2
% 5.46/5.66 thf(fact_3279_real__arch__pow__inv,axiom,
% 5.46/5.66 ! [Y2: real,X2: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.66 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.66 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X2 @ N3 ) @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % real_arch_pow_inv
% 5.46/5.66 thf(fact_3280_int__one__le__iff__zero__less,axiom,
% 5.46/5.66 ! [Z: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.46/5.66 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.66
% 5.46/5.66 % int_one_le_iff_zero_less
% 5.46/5.66 thf(fact_3281_pos__zmult__eq__1__iff,axiom,
% 5.46/5.66 ! [M: int,N: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ M )
% 5.46/5.66 => ( ( ( times_times_int @ M @ N )
% 5.46/5.66 = one_one_int )
% 5.46/5.66 = ( ( M = one_one_int )
% 5.46/5.66 & ( N = one_one_int ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pos_zmult_eq_1_iff
% 5.46/5.66 thf(fact_3282_odd__less__0__iff,axiom,
% 5.46/5.66 ! [Z: int] :
% 5.46/5.66 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.46/5.66 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % odd_less_0_iff
% 5.46/5.66 thf(fact_3283_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.46/5.66 = ( ( ord_less_eq_int @ B @ A )
% 5.46/5.66 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % nonneg1_imp_zdiv_pos_iff
% 5.46/5.66 thf(fact_3284_pos__imp__zdiv__nonneg__iff,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.46/5.66 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pos_imp_zdiv_nonneg_iff
% 5.46/5.66 thf(fact_3285_neg__imp__zdiv__nonneg__iff,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.46/5.66 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % neg_imp_zdiv_nonneg_iff
% 5.46/5.66 thf(fact_3286_pos__imp__zdiv__pos__iff,axiom,
% 5.46/5.66 ! [K: int,I: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.46/5.66 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pos_imp_zdiv_pos_iff
% 5.46/5.66 thf(fact_3287_div__nonpos__pos__le0,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_nonpos_pos_le0
% 5.46/5.66 thf(fact_3288_div__nonneg__neg__le0,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.66 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_nonneg_neg_le0
% 5.46/5.66 thf(fact_3289_div__positive__int,axiom,
% 5.46/5.66 ! [L2: int,K: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ L2 @ K )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.66 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_positive_int
% 5.46/5.66 thf(fact_3290_div__int__pos__iff,axiom,
% 5.46/5.66 ! [K: int,L2: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 5.46/5.66 = ( ( K = zero_zero_int )
% 5.46/5.66 | ( L2 = zero_zero_int )
% 5.46/5.66 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.66 & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 5.46/5.66 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.66 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_int_pos_iff
% 5.46/5.66 thf(fact_3291_zdiv__mono2__neg,axiom,
% 5.46/5.66 ! [A: int,B4: int,B: int] :
% 5.46/5.66 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.46/5.66 => ( ( ord_less_eq_int @ B4 @ B )
% 5.46/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zdiv_mono2_neg
% 5.46/5.66 thf(fact_3292_zdiv__mono1__neg,axiom,
% 5.46/5.66 ! [A: int,A4: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ A @ A4 )
% 5.46/5.66 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zdiv_mono1_neg
% 5.46/5.66 thf(fact_3293_zdiv__eq__0__iff,axiom,
% 5.46/5.66 ! [I: int,K: int] :
% 5.46/5.66 ( ( ( divide_divide_int @ I @ K )
% 5.46/5.66 = zero_zero_int )
% 5.46/5.66 = ( ( K = zero_zero_int )
% 5.46/5.66 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.46/5.66 & ( ord_less_int @ I @ K ) )
% 5.46/5.66 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.46/5.66 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zdiv_eq_0_iff
% 5.46/5.66 thf(fact_3294_zdiv__mono2,axiom,
% 5.46/5.66 ! [A: int,B4: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.46/5.66 => ( ( ord_less_eq_int @ B4 @ B )
% 5.46/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zdiv_mono2
% 5.46/5.66 thf(fact_3295_zdiv__mono1,axiom,
% 5.46/5.66 ! [A: int,A4: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ A @ A4 )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zdiv_mono1
% 5.46/5.66 thf(fact_3296_int__div__less__self,axiom,
% 5.46/5.66 ! [X2: int,K: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.46/5.66 => ( ( ord_less_int @ one_one_int @ K )
% 5.46/5.66 => ( ord_less_int @ ( divide_divide_int @ X2 @ K ) @ X2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % int_div_less_self
% 5.46/5.66 thf(fact_3297_zdiv__zmult2__eq,axiom,
% 5.46/5.66 ! [C: int,A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.66 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.46/5.66 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zdiv_zmult2_eq
% 5.46/5.66 thf(fact_3298_Euclidean__Division_Opos__mod__sign,axiom,
% 5.46/5.66 ! [L2: int,K: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.66 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Euclidean_Division.pos_mod_sign
% 5.46/5.66 thf(fact_3299_neg__mod__sign,axiom,
% 5.46/5.66 ! [L2: int,K: int] :
% 5.46/5.66 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.66 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % neg_mod_sign
% 5.46/5.66 thf(fact_3300_zmod__trivial__iff,axiom,
% 5.46/5.66 ! [I: int,K: int] :
% 5.46/5.66 ( ( ( modulo_modulo_int @ I @ K )
% 5.46/5.66 = I )
% 5.46/5.66 = ( ( K = zero_zero_int )
% 5.46/5.66 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.46/5.66 & ( ord_less_int @ I @ K ) )
% 5.46/5.66 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.46/5.66 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zmod_trivial_iff
% 5.46/5.66 thf(fact_3301_pos__mod__conj,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.46/5.66 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pos_mod_conj
% 5.46/5.66 thf(fact_3302_neg__mod__conj,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ B @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.46/5.66 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % neg_mod_conj
% 5.46/5.66 thf(fact_3303_zdiv__mono__strict,axiom,
% 5.46/5.66 ! [A2: int,B3: int,N: int] :
% 5.46/5.66 ( ( ord_less_int @ A2 @ B3 )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.46/5.66 => ( ( ( modulo_modulo_int @ A2 @ N )
% 5.46/5.66 = zero_zero_int )
% 5.46/5.66 => ( ( ( modulo_modulo_int @ B3 @ N )
% 5.46/5.66 = zero_zero_int )
% 5.46/5.66 => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B3 @ N ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zdiv_mono_strict
% 5.46/5.66 thf(fact_3304_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J,axiom,
% 5.46/5.66 ! [A: $o,B: $o,X2: nat] :
% 5.46/5.66 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(1)
% 5.46/5.66 thf(fact_3305_not__exp__less__eq__0__int,axiom,
% 5.46/5.66 ! [N: nat] :
% 5.46/5.66 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.46/5.66
% 5.46/5.66 % not_exp_less_eq_0_int
% 5.46/5.66 thf(fact_3306_realpow__pos__nth__unique,axiom,
% 5.46/5.66 ! [N: nat,A: real] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.66 => ? [X3: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.46/5.66 & ( ( power_power_real @ X3 @ N )
% 5.46/5.66 = A )
% 5.46/5.66 & ! [Y4: real] :
% 5.46/5.66 ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.46/5.66 & ( ( power_power_real @ Y4 @ N )
% 5.46/5.66 = A ) )
% 5.46/5.66 => ( Y4 = X3 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % realpow_pos_nth_unique
% 5.46/5.66 thf(fact_3307_realpow__pos__nth,axiom,
% 5.46/5.66 ! [N: nat,A: real] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.66 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.66 => ? [R3: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.66 & ( ( power_power_real @ R3 @ N )
% 5.46/5.66 = A ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % realpow_pos_nth
% 5.46/5.66 thf(fact_3308_le__imp__0__less,axiom,
% 5.46/5.66 ! [Z: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.66 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % le_imp_0_less
% 5.46/5.66 thf(fact_3309_q__pos__lemma,axiom,
% 5.46/5.66 ! [B4: int,Q5: int,R4: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.46/5.66 => ( ( ord_less_int @ R4 @ B4 )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.46/5.66 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % q_pos_lemma
% 5.46/5.66 thf(fact_3310_zdiv__mono2__lemma,axiom,
% 5.46/5.66 ! [B: int,Q2: int,R: int,B4: int,Q5: int,R4: int] :
% 5.46/5.66 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.46/5.66 => ( ( ord_less_int @ R4 @ B4 )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.46/5.66 => ( ( ord_less_eq_int @ B4 @ B )
% 5.46/5.66 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zdiv_mono2_lemma
% 5.46/5.66 thf(fact_3311_zdiv__mono2__neg__lemma,axiom,
% 5.46/5.66 ! [B: int,Q2: int,R: int,B4: int,Q5: int,R4: int] :
% 5.46/5.66 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.46/5.66 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ R @ B )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.46/5.66 => ( ( ord_less_eq_int @ B4 @ B )
% 5.46/5.66 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zdiv_mono2_neg_lemma
% 5.46/5.66 thf(fact_3312_unique__quotient__lemma,axiom,
% 5.46/5.66 ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.46/5.66 => ( ( ord_less_int @ R4 @ B )
% 5.46/5.66 => ( ( ord_less_int @ R @ B )
% 5.46/5.66 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % unique_quotient_lemma
% 5.46/5.66 thf(fact_3313_unique__quotient__lemma__neg,axiom,
% 5.46/5.66 ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ B @ R )
% 5.46/5.66 => ( ( ord_less_int @ B @ R4 )
% 5.46/5.66 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % unique_quotient_lemma_neg
% 5.46/5.66 thf(fact_3314_mod__pos__neg__trivial,axiom,
% 5.46/5.66 ! [K: int,L2: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.66 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.66 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.66 = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mod_pos_neg_trivial
% 5.46/5.66 thf(fact_3315_mod__pos__geq,axiom,
% 5.46/5.66 ! [L2: int,K: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.66 => ( ( ord_less_eq_int @ L2 @ K )
% 5.46/5.66 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.66 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mod_pos_geq
% 5.46/5.66 thf(fact_3316_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J,axiom,
% 5.46/5.66 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(2)
% 5.46/5.66 thf(fact_3317_int__div__pos__eq,axiom,
% 5.46/5.66 ! [A: int,B: int,Q2: int,R: int] :
% 5.46/5.66 ( ( A
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.46/5.66 => ( ( ord_less_int @ R @ B )
% 5.46/5.66 => ( ( divide_divide_int @ A @ B )
% 5.46/5.66 = Q2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % int_div_pos_eq
% 5.46/5.66 thf(fact_3318_int__div__neg__eq,axiom,
% 5.46/5.66 ! [A: int,B: int,Q2: int,R: int] :
% 5.46/5.66 ( ( A
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ B @ R )
% 5.46/5.66 => ( ( divide_divide_int @ A @ B )
% 5.46/5.66 = Q2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % int_div_neg_eq
% 5.46/5.66 thf(fact_3319_split__zdiv,axiom,
% 5.46/5.66 ! [P: int > $o,N: int,K: int] :
% 5.46/5.66 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.46/5.66 = ( ( ( K = zero_zero_int )
% 5.46/5.66 => ( P @ zero_zero_int ) )
% 5.46/5.66 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.66 => ! [I4: int,J3: int] :
% 5.46/5.66 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.46/5.66 & ( ord_less_int @ J3 @ K )
% 5.46/5.66 & ( N
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.46/5.66 => ( P @ I4 ) ) )
% 5.46/5.66 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.66 => ! [I4: int,J3: int] :
% 5.46/5.66 ( ( ( ord_less_int @ K @ J3 )
% 5.46/5.66 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.46/5.66 & ( N
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.46/5.66 => ( P @ I4 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % split_zdiv
% 5.46/5.66 thf(fact_3320_int__mod__pos__eq,axiom,
% 5.46/5.66 ! [A: int,B: int,Q2: int,R: int] :
% 5.46/5.66 ( ( A
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.46/5.66 => ( ( ord_less_int @ R @ B )
% 5.46/5.66 => ( ( modulo_modulo_int @ A @ B )
% 5.46/5.66 = R ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % int_mod_pos_eq
% 5.46/5.66 thf(fact_3321_int__mod__neg__eq,axiom,
% 5.46/5.66 ! [A: int,B: int,Q2: int,R: int] :
% 5.46/5.66 ( ( A
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ B @ R )
% 5.46/5.66 => ( ( modulo_modulo_int @ A @ B )
% 5.46/5.66 = R ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % int_mod_neg_eq
% 5.46/5.66 thf(fact_3322_split__zmod,axiom,
% 5.46/5.66 ! [P: int > $o,N: int,K: int] :
% 5.46/5.66 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.46/5.66 = ( ( ( K = zero_zero_int )
% 5.46/5.66 => ( P @ N ) )
% 5.46/5.66 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.66 => ! [I4: int,J3: int] :
% 5.46/5.66 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.46/5.66 & ( ord_less_int @ J3 @ K )
% 5.46/5.66 & ( N
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.46/5.66 => ( P @ J3 ) ) )
% 5.46/5.66 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.66 => ! [I4: int,J3: int] :
% 5.46/5.66 ( ( ( ord_less_int @ K @ J3 )
% 5.46/5.66 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.46/5.66 & ( N
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.46/5.66 => ( P @ J3 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % split_zmod
% 5.46/5.66 thf(fact_3323_zmod__zmult2__eq,axiom,
% 5.46/5.66 ! [C: int,A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.66 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % zmod_zmult2_eq
% 5.46/5.66 thf(fact_3324_int__power__div__base,axiom,
% 5.46/5.66 ! [M: nat,K: int] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.66 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.46/5.66 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % int_power_div_base
% 5.46/5.66 thf(fact_3325_div__pos__geq,axiom,
% 5.46/5.66 ! [L2: int,K: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.66 => ( ( ord_less_eq_int @ L2 @ K )
% 5.46/5.66 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.66 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_pos_geq
% 5.46/5.66 thf(fact_3326_verit__le__mono__div__int,axiom,
% 5.46/5.66 ! [A2: int,B3: int,N: int] :
% 5.46/5.66 ( ( ord_less_int @ A2 @ B3 )
% 5.46/5.66 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.46/5.66 => ( ord_less_eq_int
% 5.46/5.66 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 5.46/5.66 @ ( if_int
% 5.46/5.66 @ ( ( modulo_modulo_int @ B3 @ N )
% 5.46/5.66 = zero_zero_int )
% 5.46/5.66 @ one_one_int
% 5.46/5.66 @ zero_zero_int ) )
% 5.46/5.66 @ ( divide_divide_int @ B3 @ N ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % verit_le_mono_div_int
% 5.46/5.66 thf(fact_3327_split__pos__lemma,axiom,
% 5.46/5.66 ! [K: int,P: int > int > $o,N: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.66 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.46/5.66 = ( ! [I4: int,J3: int] :
% 5.46/5.66 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.46/5.66 & ( ord_less_int @ J3 @ K )
% 5.46/5.66 & ( N
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.46/5.66 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % split_pos_lemma
% 5.46/5.66 thf(fact_3328_split__neg__lemma,axiom,
% 5.46/5.66 ! [K: int,P: int > int > $o,N: int] :
% 5.46/5.66 ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.66 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.46/5.66 = ( ! [I4: int,J3: int] :
% 5.46/5.66 ( ( ( ord_less_int @ K @ J3 )
% 5.46/5.66 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.46/5.66 & ( N
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.46/5.66 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % split_neg_lemma
% 5.46/5.66 thf(fact_3329_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.46/5.66 ! [A: $o,B: $o] :
% 5.46/5.66 ( ( vEBT_T_m_a_x_t @ ( vEBT_Leaf @ A @ B ) )
% 5.46/5.66 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(1)
% 5.46/5.66 thf(fact_3330_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 5.46/5.66 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(3)
% 5.46/5.66 thf(fact_3331_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.46/5.66 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.66 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(2)
% 5.46/5.66 thf(fact_3332_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.46/5.66 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.66 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(2)
% 5.46/5.66 thf(fact_3333_eq__diff__eq_H,axiom,
% 5.46/5.66 ! [X2: real,Y2: real,Z: real] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( minus_minus_real @ Y2 @ Z ) )
% 5.46/5.66 = ( Y2
% 5.46/5.66 = ( plus_plus_real @ X2 @ Z ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % eq_diff_eq'
% 5.46/5.66 thf(fact_3334_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 5.46/5.66 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.46/5.66 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(4)
% 5.46/5.66 thf(fact_3335_pos__zdiv__mult__2,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.66 => ( ( 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 ) )
% 5.46/5.66 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pos_zdiv_mult_2
% 5.46/5.66 thf(fact_3336_neg__zdiv__mult__2,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.66 => ( ( 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 ) )
% 5.46/5.66 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % neg_zdiv_mult_2
% 5.46/5.66 thf(fact_3337_maxt__bound,axiom,
% 5.46/5.66 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % maxt_bound
% 5.46/5.66 thf(fact_3338_mint__bound,axiom,
% 5.46/5.66 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mint_bound
% 5.46/5.66 thf(fact_3339_pos__zmod__mult__2,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.66 => ( ( 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 ) )
% 5.46/5.66 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pos_zmod_mult_2
% 5.46/5.66 thf(fact_3340_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.46/5.66 ! [A: $o,B: $o] :
% 5.46/5.66 ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 5.46/5.66 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(1)
% 5.46/5.66 thf(fact_3341_member__bound__height_H,axiom,
% 5.46/5.66 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.46/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.66 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % member_bound_height'
% 5.46/5.66 thf(fact_3342_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.46/5.66 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.66 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(3)
% 5.46/5.66 thf(fact_3343_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.46/5.66 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.66 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(3)
% 5.46/5.66 thf(fact_3344_neg__zmod__mult__2,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.66 => ( ( 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 ) )
% 5.46/5.66 = ( 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 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % neg_zmod_mult_2
% 5.46/5.66 thf(fact_3345_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_i_n_s_e_r_t @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.66 @ ( if_nat
% 5.46/5.66 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 & ~ ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 ) ) )
% 5.46/5.66 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.46/5.66 @ one_one_nat ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.pelims
% 5.46/5.66 thf(fact_3346_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( if_nat
% 5.46/5.66 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 & ~ ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 ) ) )
% 5.46/5.66 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.46/5.66 @ one_one_nat ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.pelims
% 5.46/5.66 thf(fact_3347_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_m_e_m_b_e_r @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.pelims
% 5.46/5.66 thf(fact_3348_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: nat] :
% 5.46/5.66 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.66 => ( ( Y2 = one_one_nat )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( plus_plus_nat @ one_one_nat
% 5.46/5.66 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 5.46/5.66 @ ( if_nat
% 5.46/5.66 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 5.46/5.66 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 5.46/5.66 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.46/5.66 @ zero_zero_nat ) ) ) ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.pelims
% 5.46/5.66 thf(fact_3349_vebt__member_Opelims_I1_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.46/5.66 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ( ~ Y2
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ( ~ Y2
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.66 => ( ~ Y2
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( ( Xa2 != Mi2 )
% 5.46/5.66 => ( ( Xa2 != Ma2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_member.pelims(1)
% 5.46/5.66 thf(fact_3350_vebt__member_Opelims_I3_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.46/5.66 => ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.46/5.66 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.46/5.66 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.46/5.66 => ( ( Xa2 != Mi2 )
% 5.46/5.66 => ( ( Xa2 != Ma2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_member.pelims(3)
% 5.46/5.66 thf(fact_3351_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.46/5.66 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ( ~ Y2
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.naive_member.pelims(1)
% 5.46/5.66 thf(fact_3352_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.46/5.66 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.46/5.66 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ Xa2 ) )
% 5.46/5.66 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.naive_member.pelims(2)
% 5.46/5.66 thf(fact_3353_zero__one__enat__neq_I1_J,axiom,
% 5.46/5.66 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.46/5.66
% 5.46/5.66 % zero_one_enat_neq(1)
% 5.46/5.66 thf(fact_3354_imult__is__0,axiom,
% 5.46/5.66 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.66 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.46/5.66 = zero_z5237406670263579293d_enat )
% 5.46/5.66 = ( ( M = zero_z5237406670263579293d_enat )
% 5.46/5.66 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % imult_is_0
% 5.46/5.66 thf(fact_3355_vebt__member_Opelims_I2_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.46/5.66 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.46/5.66 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.46/5.66 => ~ ( ( Xa2 != Mi2 )
% 5.46/5.66 => ( ( Xa2 != Ma2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.46/5.66 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % vebt_member.pelims(2)
% 5.46/5.66 thf(fact_3356_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [A5: $o,B5: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.46/5.66 => ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.66 => A5 )
% 5.46/5.66 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.66 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.66 => B5 )
% 5.46/5.66 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.46/5.66 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.46/5.66 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ Xa2 ) )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.naive_member.pelims(3)
% 5.46/5.66 thf(fact_3357_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [Uu2: $o,Uv2: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 5.46/5.66 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.46/5.66 => ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 ) ) ) )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 5.46/5.66 => ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 )
% 5.46/5.66 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.46/5.66 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 5.46/5.66 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.membermima.pelims(3)
% 5.46/5.66 thf(fact_3358_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.46/5.66 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.46/5.66 = Y2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [Uu2: $o,Uv2: $o] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.66 => ( ~ Y2
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.46/5.66 => ( ~ Y2
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 )
% 5.46/5.66 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.46/5.66 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.46/5.66 => ( ( Y2
% 5.46/5.66 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.46/5.66 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.membermima.pelims(1)
% 5.46/5.66 thf(fact_3359_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.46/5.66 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.66 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.46/5.66 => ~ ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 ) ) ) )
% 5.46/5.66 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 5.46/5.66 => ~ ( ( Xa2 = Mi2 )
% 5.46/5.66 | ( Xa2 = Ma2 )
% 5.46/5.66 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.46/5.66 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.46/5.66 ( ( X2
% 5.46/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.46/5.66 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 5.46/5.66 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.66 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.66 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.membermima.pelims(2)
% 5.46/5.66 thf(fact_3360_infinite__Icc__iff,axiom,
% 5.46/5.66 ! [A: rat,B: rat] :
% 5.46/5.66 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.46/5.66 = ( ord_less_rat @ A @ B ) ) ).
% 5.46/5.66
% 5.46/5.66 % infinite_Icc_iff
% 5.46/5.66 thf(fact_3361_infinite__Icc__iff,axiom,
% 5.46/5.66 ! [A: real,B: real] :
% 5.46/5.66 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.46/5.66 = ( ord_less_real @ A @ B ) ) ).
% 5.46/5.66
% 5.46/5.66 % infinite_Icc_iff
% 5.46/5.66 thf(fact_3362_atLeastatMost__empty,axiom,
% 5.46/5.66 ! [B: rat,A: rat] :
% 5.46/5.66 ( ( ord_less_rat @ B @ A )
% 5.46/5.66 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.46/5.66 = bot_bot_set_rat ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty
% 5.46/5.66 thf(fact_3363_atLeastatMost__empty,axiom,
% 5.46/5.66 ! [B: num,A: num] :
% 5.46/5.66 ( ( ord_less_num @ B @ A )
% 5.46/5.66 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.46/5.66 = bot_bot_set_num ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty
% 5.46/5.66 thf(fact_3364_atLeastatMost__empty,axiom,
% 5.46/5.66 ! [B: nat,A: nat] :
% 5.46/5.66 ( ( ord_less_nat @ B @ A )
% 5.46/5.66 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.46/5.66 = bot_bot_set_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty
% 5.46/5.66 thf(fact_3365_atLeastatMost__empty,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ B @ A )
% 5.46/5.66 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.46/5.66 = bot_bot_set_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty
% 5.46/5.66 thf(fact_3366_atLeastatMost__empty,axiom,
% 5.46/5.66 ! [B: real,A: real] :
% 5.46/5.66 ( ( ord_less_real @ B @ A )
% 5.46/5.66 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.46/5.66 = bot_bot_set_real ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty
% 5.46/5.66 thf(fact_3367_atLeastatMost__subset__iff,axiom,
% 5.46/5.66 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 5.46/5.66 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.46/5.66 & ( ord_less_eq_set_nat @ B @ D2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_subset_iff
% 5.46/5.66 thf(fact_3368_atLeastatMost__subset__iff,axiom,
% 5.46/5.66 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.46/5.66 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_rat @ C @ A )
% 5.46/5.66 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_subset_iff
% 5.46/5.66 thf(fact_3369_atLeastatMost__subset__iff,axiom,
% 5.46/5.66 ! [A: num,B: num,C: num,D2: num] :
% 5.46/5.66 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_num @ C @ A )
% 5.46/5.66 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_subset_iff
% 5.46/5.66 thf(fact_3370_atLeastatMost__subset__iff,axiom,
% 5.46/5.66 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.46/5.66 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_nat @ C @ A )
% 5.46/5.66 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_subset_iff
% 5.46/5.66 thf(fact_3371_atLeastatMost__subset__iff,axiom,
% 5.46/5.66 ! [A: int,B: int,C: int,D2: int] :
% 5.46/5.66 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_int @ C @ A )
% 5.46/5.66 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_subset_iff
% 5.46/5.66 thf(fact_3372_atLeastatMost__subset__iff,axiom,
% 5.46/5.66 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.66 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D2 ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_real @ C @ A )
% 5.46/5.66 & ( ord_less_eq_real @ B @ D2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_subset_iff
% 5.46/5.66 thf(fact_3373_atLeastatMost__empty__iff,axiom,
% 5.46/5.66 ! [A: set_nat,B: set_nat] :
% 5.46/5.66 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 5.46/5.66 = bot_bot_set_set_nat )
% 5.46/5.66 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff
% 5.46/5.66 thf(fact_3374_atLeastatMost__empty__iff,axiom,
% 5.46/5.66 ! [A: rat,B: rat] :
% 5.46/5.66 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.46/5.66 = bot_bot_set_rat )
% 5.46/5.66 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff
% 5.46/5.66 thf(fact_3375_atLeastatMost__empty__iff,axiom,
% 5.46/5.66 ! [A: num,B: num] :
% 5.46/5.66 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.46/5.66 = bot_bot_set_num )
% 5.46/5.66 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff
% 5.46/5.66 thf(fact_3376_atLeastatMost__empty__iff,axiom,
% 5.46/5.66 ! [A: nat,B: nat] :
% 5.46/5.66 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.46/5.66 = bot_bot_set_nat )
% 5.46/5.66 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff
% 5.46/5.66 thf(fact_3377_atLeastatMost__empty__iff,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.46/5.66 = bot_bot_set_int )
% 5.46/5.66 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff
% 5.46/5.66 thf(fact_3378_atLeastatMost__empty__iff,axiom,
% 5.46/5.66 ! [A: real,B: real] :
% 5.46/5.66 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.46/5.66 = bot_bot_set_real )
% 5.46/5.66 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff
% 5.46/5.66 thf(fact_3379_atLeastatMost__empty__iff2,axiom,
% 5.46/5.66 ! [A: set_nat,B: set_nat] :
% 5.46/5.66 ( ( bot_bot_set_set_nat
% 5.46/5.66 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff2
% 5.46/5.66 thf(fact_3380_atLeastatMost__empty__iff2,axiom,
% 5.46/5.66 ! [A: rat,B: rat] :
% 5.46/5.66 ( ( bot_bot_set_rat
% 5.46/5.66 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff2
% 5.46/5.66 thf(fact_3381_atLeastatMost__empty__iff2,axiom,
% 5.46/5.66 ! [A: num,B: num] :
% 5.46/5.66 ( ( bot_bot_set_num
% 5.46/5.66 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff2
% 5.46/5.66 thf(fact_3382_atLeastatMost__empty__iff2,axiom,
% 5.46/5.66 ! [A: nat,B: nat] :
% 5.46/5.66 ( ( bot_bot_set_nat
% 5.46/5.66 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff2
% 5.46/5.66 thf(fact_3383_atLeastatMost__empty__iff2,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( bot_bot_set_int
% 5.46/5.66 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff2
% 5.46/5.66 thf(fact_3384_atLeastatMost__empty__iff2,axiom,
% 5.46/5.66 ! [A: real,B: real] :
% 5.46/5.66 ( ( bot_bot_set_real
% 5.46/5.66 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.46/5.66 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_empty_iff2
% 5.46/5.66 thf(fact_3385_Icc__eq__Icc,axiom,
% 5.46/5.66 ! [L2: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 5.46/5.66 ( ( ( set_or4548717258645045905et_nat @ L2 @ H2 )
% 5.46/5.66 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 5.46/5.66 = ( ( ( L2 = L3 )
% 5.46/5.66 & ( H2 = H3 ) )
% 5.46/5.66 | ( ~ ( ord_less_eq_set_nat @ L2 @ H2 )
% 5.46/5.66 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Icc_eq_Icc
% 5.46/5.66 thf(fact_3386_Icc__eq__Icc,axiom,
% 5.46/5.66 ! [L2: rat,H2: rat,L3: rat,H3: rat] :
% 5.46/5.66 ( ( ( set_or633870826150836451st_rat @ L2 @ H2 )
% 5.46/5.66 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.46/5.66 = ( ( ( L2 = L3 )
% 5.46/5.66 & ( H2 = H3 ) )
% 5.46/5.66 | ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.46/5.66 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Icc_eq_Icc
% 5.46/5.66 thf(fact_3387_Icc__eq__Icc,axiom,
% 5.46/5.66 ! [L2: num,H2: num,L3: num,H3: num] :
% 5.46/5.66 ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 5.46/5.66 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.46/5.66 = ( ( ( L2 = L3 )
% 5.46/5.66 & ( H2 = H3 ) )
% 5.46/5.66 | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.46/5.66 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Icc_eq_Icc
% 5.46/5.66 thf(fact_3388_Icc__eq__Icc,axiom,
% 5.46/5.66 ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 5.46/5.66 ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 5.46/5.66 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.46/5.66 = ( ( ( L2 = L3 )
% 5.46/5.66 & ( H2 = H3 ) )
% 5.46/5.66 | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.46/5.66 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Icc_eq_Icc
% 5.46/5.66 thf(fact_3389_Icc__eq__Icc,axiom,
% 5.46/5.66 ! [L2: int,H2: int,L3: int,H3: int] :
% 5.46/5.66 ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 5.46/5.66 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.46/5.66 = ( ( ( L2 = L3 )
% 5.46/5.66 & ( H2 = H3 ) )
% 5.46/5.66 | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.46/5.66 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Icc_eq_Icc
% 5.46/5.66 thf(fact_3390_Icc__eq__Icc,axiom,
% 5.46/5.66 ! [L2: real,H2: real,L3: real,H3: real] :
% 5.46/5.66 ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 5.46/5.66 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.46/5.66 = ( ( ( L2 = L3 )
% 5.46/5.66 & ( H2 = H3 ) )
% 5.46/5.66 | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.46/5.66 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Icc_eq_Icc
% 5.46/5.66 thf(fact_3391_atLeastAtMost__iff,axiom,
% 5.46/5.66 ! [I: set_nat,L2: set_nat,U: set_nat] :
% 5.46/5.66 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L2 @ U ) )
% 5.46/5.66 = ( ( ord_less_eq_set_nat @ L2 @ I )
% 5.46/5.66 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastAtMost_iff
% 5.46/5.66 thf(fact_3392_atLeastAtMost__iff,axiom,
% 5.46/5.66 ! [I: rat,L2: rat,U: rat] :
% 5.46/5.66 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L2 @ U ) )
% 5.46/5.66 = ( ( ord_less_eq_rat @ L2 @ I )
% 5.46/5.66 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastAtMost_iff
% 5.46/5.66 thf(fact_3393_atLeastAtMost__iff,axiom,
% 5.46/5.66 ! [I: num,L2: num,U: num] :
% 5.46/5.66 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 5.46/5.66 = ( ( ord_less_eq_num @ L2 @ I )
% 5.46/5.66 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastAtMost_iff
% 5.46/5.66 thf(fact_3394_atLeastAtMost__iff,axiom,
% 5.46/5.66 ! [I: nat,L2: nat,U: nat] :
% 5.46/5.66 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.46/5.66 = ( ( ord_less_eq_nat @ L2 @ I )
% 5.46/5.66 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastAtMost_iff
% 5.46/5.66 thf(fact_3395_atLeastAtMost__iff,axiom,
% 5.46/5.66 ! [I: int,L2: int,U: int] :
% 5.46/5.66 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.46/5.66 = ( ( ord_less_eq_int @ L2 @ I )
% 5.46/5.66 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastAtMost_iff
% 5.46/5.66 thf(fact_3396_atLeastAtMost__iff,axiom,
% 5.46/5.66 ! [I: real,L2: real,U: real] :
% 5.46/5.66 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 5.46/5.66 = ( ( ord_less_eq_real @ L2 @ I )
% 5.46/5.66 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastAtMost_iff
% 5.46/5.66 thf(fact_3397_bounded__Max__nat,axiom,
% 5.46/5.66 ! [P: nat > $o,X2: nat,M7: nat] :
% 5.46/5.66 ( ( P @ X2 )
% 5.46/5.66 => ( ! [X3: nat] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 => ( ord_less_eq_nat @ X3 @ M7 ) )
% 5.46/5.66 => ~ ! [M4: nat] :
% 5.46/5.66 ( ( P @ M4 )
% 5.46/5.66 => ~ ! [X4: nat] :
% 5.46/5.66 ( ( P @ X4 )
% 5.46/5.66 => ( ord_less_eq_nat @ X4 @ M4 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % bounded_Max_nat
% 5.46/5.66 thf(fact_3398_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.46/5.66 ! [X2: produc3368934014287244435at_num] :
% 5.46/5.66 ~ ! [F2: nat > num > num,A5: nat,B5: nat,Acc: num] :
% 5.46/5.66 ( X2
% 5.46/5.66 != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A5 @ ( product_Pair_nat_num @ B5 @ Acc ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % fold_atLeastAtMost_nat.cases
% 5.46/5.66 thf(fact_3399_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.46/5.66 ! [X2: produc4471711990508489141at_nat] :
% 5.46/5.66 ~ ! [F2: nat > nat > nat,A5: nat,B5: nat,Acc: nat] :
% 5.46/5.66 ( X2
% 5.46/5.66 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A5 @ ( product_Pair_nat_nat @ B5 @ Acc ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % fold_atLeastAtMost_nat.cases
% 5.46/5.66 thf(fact_3400_finite__nat__set__iff__bounded,axiom,
% 5.46/5.66 ( finite_finite_nat
% 5.46/5.66 = ( ^ [N6: set_nat] :
% 5.46/5.66 ? [M3: nat] :
% 5.46/5.66 ! [X: nat] :
% 5.46/5.66 ( ( member_nat @ X @ N6 )
% 5.46/5.66 => ( ord_less_nat @ X @ M3 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % finite_nat_set_iff_bounded
% 5.46/5.66 thf(fact_3401_bounded__nat__set__is__finite,axiom,
% 5.46/5.66 ! [N4: set_nat,N: nat] :
% 5.46/5.66 ( ! [X3: nat] :
% 5.46/5.66 ( ( member_nat @ X3 @ N4 )
% 5.46/5.66 => ( ord_less_nat @ X3 @ N ) )
% 5.46/5.66 => ( finite_finite_nat @ N4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % bounded_nat_set_is_finite
% 5.46/5.66 thf(fact_3402_finite__nat__set__iff__bounded__le,axiom,
% 5.46/5.66 ( finite_finite_nat
% 5.46/5.66 = ( ^ [N6: set_nat] :
% 5.46/5.66 ? [M3: nat] :
% 5.46/5.66 ! [X: nat] :
% 5.46/5.66 ( ( member_nat @ X @ N6 )
% 5.46/5.66 => ( ord_less_eq_nat @ X @ M3 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % finite_nat_set_iff_bounded_le
% 5.46/5.66 thf(fact_3403_finite__M__bounded__by__nat,axiom,
% 5.46/5.66 ! [P: nat > $o,I: nat] :
% 5.46/5.66 ( finite_finite_nat
% 5.46/5.66 @ ( collect_nat
% 5.46/5.66 @ ^ [K2: nat] :
% 5.46/5.66 ( ( P @ K2 )
% 5.46/5.66 & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % finite_M_bounded_by_nat
% 5.46/5.66 thf(fact_3404_finite__less__ub,axiom,
% 5.46/5.66 ! [F: nat > nat,U: nat] :
% 5.46/5.66 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.46/5.66 => ( finite_finite_nat
% 5.46/5.66 @ ( collect_nat
% 5.46/5.66 @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % finite_less_ub
% 5.46/5.66 thf(fact_3405_infinite__Icc,axiom,
% 5.46/5.66 ! [A: rat,B: rat] :
% 5.46/5.66 ( ( ord_less_rat @ A @ B )
% 5.46/5.66 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % infinite_Icc
% 5.46/5.66 thf(fact_3406_infinite__Icc,axiom,
% 5.46/5.66 ! [A: real,B: real] :
% 5.46/5.66 ( ( ord_less_real @ A @ B )
% 5.46/5.66 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % infinite_Icc
% 5.46/5.66 thf(fact_3407_atLeastatMost__psubset__iff,axiom,
% 5.46/5.66 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 5.46/5.66 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 5.46/5.66 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.46/5.66 & ( ord_less_eq_set_nat @ B @ D2 )
% 5.46/5.66 & ( ( ord_less_set_nat @ C @ A )
% 5.46/5.66 | ( ord_less_set_nat @ B @ D2 ) ) ) )
% 5.46/5.66 & ( ord_less_eq_set_nat @ C @ D2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_psubset_iff
% 5.46/5.66 thf(fact_3408_atLeastatMost__psubset__iff,axiom,
% 5.46/5.66 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.46/5.66 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 5.46/5.66 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_rat @ C @ A )
% 5.46/5.66 & ( ord_less_eq_rat @ B @ D2 )
% 5.46/5.66 & ( ( ord_less_rat @ C @ A )
% 5.46/5.66 | ( ord_less_rat @ B @ D2 ) ) ) )
% 5.46/5.66 & ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_psubset_iff
% 5.46/5.66 thf(fact_3409_atLeastatMost__psubset__iff,axiom,
% 5.46/5.66 ! [A: num,B: num,C: num,D2: num] :
% 5.46/5.66 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 5.46/5.66 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_num @ C @ A )
% 5.46/5.66 & ( ord_less_eq_num @ B @ D2 )
% 5.46/5.66 & ( ( ord_less_num @ C @ A )
% 5.46/5.66 | ( ord_less_num @ B @ D2 ) ) ) )
% 5.46/5.66 & ( ord_less_eq_num @ C @ D2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_psubset_iff
% 5.46/5.66 thf(fact_3410_atLeastatMost__psubset__iff,axiom,
% 5.46/5.66 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.46/5.66 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 5.46/5.66 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_nat @ C @ A )
% 5.46/5.66 & ( ord_less_eq_nat @ B @ D2 )
% 5.46/5.66 & ( ( ord_less_nat @ C @ A )
% 5.46/5.66 | ( ord_less_nat @ B @ D2 ) ) ) )
% 5.46/5.66 & ( ord_less_eq_nat @ C @ D2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_psubset_iff
% 5.46/5.66 thf(fact_3411_atLeastatMost__psubset__iff,axiom,
% 5.46/5.66 ! [A: int,B: int,C: int,D2: int] :
% 5.46/5.66 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 5.46/5.66 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_int @ C @ A )
% 5.46/5.66 & ( ord_less_eq_int @ B @ D2 )
% 5.46/5.66 & ( ( ord_less_int @ C @ A )
% 5.46/5.66 | ( ord_less_int @ B @ D2 ) ) ) )
% 5.46/5.66 & ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_psubset_iff
% 5.46/5.66 thf(fact_3412_atLeastatMost__psubset__iff,axiom,
% 5.46/5.66 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.66 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D2 ) )
% 5.46/5.66 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.46/5.66 | ( ( ord_less_eq_real @ C @ A )
% 5.46/5.66 & ( ord_less_eq_real @ B @ D2 )
% 5.46/5.66 & ( ( ord_less_real @ C @ A )
% 5.46/5.66 | ( ord_less_real @ B @ D2 ) ) ) )
% 5.46/5.66 & ( ord_less_eq_real @ C @ D2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % atLeastatMost_psubset_iff
% 5.46/5.66 thf(fact_3413_cppi,axiom,
% 5.46/5.66 ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ A2 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: int,K3: int] :
% 5.46/5.66 ( ( P6 @ X3 )
% 5.46/5.66 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ( ( ? [X5: int] : ( P @ X5 ) )
% 5.46/5.66 = ( ? [X: int] :
% 5.46/5.66 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 & ( P6 @ X ) )
% 5.46/5.66 | ? [X: int] :
% 5.46/5.66 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 & ? [Y: int] :
% 5.46/5.66 ( ( member_int @ Y @ A2 )
% 5.46/5.66 & ( P @ ( minus_minus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % cppi
% 5.46/5.66 thf(fact_3414_cpmi,axiom,
% 5.46/5.66 ! [D4: int,P: int > $o,P6: int > $o,B3: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ B3 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: int,K3: int] :
% 5.46/5.66 ( ( P6 @ X3 )
% 5.46/5.66 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ( ( ? [X5: int] : ( P @ X5 ) )
% 5.46/5.66 = ( ? [X: int] :
% 5.46/5.66 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 & ( P6 @ X ) )
% 5.46/5.66 | ? [X: int] :
% 5.46/5.66 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 & ? [Y: int] :
% 5.46/5.66 ( ( member_int @ Y @ B3 )
% 5.46/5.66 & ( P @ ( plus_plus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % cpmi
% 5.46/5.66 thf(fact_3415_bset_I6_J,axiom,
% 5.46/5.66 ! [D4: int,B3: set_int,T: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ X4 @ T )
% 5.46/5.66 => ( ord_less_eq_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % bset(6)
% 5.46/5.66 thf(fact_3416_bset_I8_J,axiom,
% 5.46/5.66 ! [D4: int,T: int,B3: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ T @ X4 )
% 5.46/5.66 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % bset(8)
% 5.46/5.66 thf(fact_3417_aset_I6_J,axiom,
% 5.46/5.66 ! [D4: int,T: int,A2: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ X4 @ T )
% 5.46/5.66 => ( ord_less_eq_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % aset(6)
% 5.46/5.66 thf(fact_3418_aset_I8_J,axiom,
% 5.46/5.66 ! [D4: int,A2: set_int,T: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ T @ X4 )
% 5.46/5.66 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % aset(8)
% 5.46/5.66 thf(fact_3419_bset_I3_J,axiom,
% 5.46/5.66 ! [D4: int,T: int,B3: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( X4 = T )
% 5.46/5.66 => ( ( minus_minus_int @ X4 @ D4 )
% 5.46/5.66 = T ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % bset(3)
% 5.46/5.66 thf(fact_3420_bset_I4_J,axiom,
% 5.46/5.66 ! [D4: int,T: int,B3: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ( member_int @ T @ B3 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( X4 != T )
% 5.46/5.66 => ( ( minus_minus_int @ X4 @ D4 )
% 5.46/5.66 != T ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % bset(4)
% 5.46/5.66 thf(fact_3421_minf_I7_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_real @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(7)
% 5.46/5.66 thf(fact_3422_minf_I7_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_rat @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(7)
% 5.46/5.66 thf(fact_3423_minf_I7_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_num @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(7)
% 5.46/5.66 thf(fact_3424_minf_I7_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_nat @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(7)
% 5.46/5.66 thf(fact_3425_minf_I7_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_int @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(7)
% 5.46/5.66 thf(fact_3426_minf_I5_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_real @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(5)
% 5.46/5.66 thf(fact_3427_minf_I5_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_rat @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(5)
% 5.46/5.66 thf(fact_3428_minf_I5_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_num @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(5)
% 5.46/5.66 thf(fact_3429_minf_I5_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_nat @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(5)
% 5.46/5.66 thf(fact_3430_minf_I5_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_int @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(5)
% 5.46/5.66 thf(fact_3431_minf_I4_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(4)
% 5.46/5.66 thf(fact_3432_minf_I4_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(4)
% 5.46/5.66 thf(fact_3433_minf_I4_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(4)
% 5.46/5.66 thf(fact_3434_minf_I4_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(4)
% 5.46/5.66 thf(fact_3435_minf_I4_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(4)
% 5.46/5.66 thf(fact_3436_minf_I3_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(3)
% 5.46/5.66 thf(fact_3437_minf_I3_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(3)
% 5.46/5.66 thf(fact_3438_minf_I3_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(3)
% 5.46/5.66 thf(fact_3439_minf_I3_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(3)
% 5.46/5.66 thf(fact_3440_minf_I3_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(3)
% 5.46/5.66 thf(fact_3441_minf_I2_J,axiom,
% 5.46/5.66 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.46/5.66 ( ? [Z2: real] :
% 5.46/5.66 ! [X3: real] :
% 5.46/5.66 ( ( ord_less_real @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: real] :
% 5.46/5.66 ! [X3: real] :
% 5.46/5.66 ( ( ord_less_real @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(2)
% 5.46/5.66 thf(fact_3442_minf_I2_J,axiom,
% 5.46/5.66 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.46/5.66 ( ? [Z2: rat] :
% 5.46/5.66 ! [X3: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: rat] :
% 5.46/5.66 ! [X3: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(2)
% 5.46/5.66 thf(fact_3443_minf_I2_J,axiom,
% 5.46/5.66 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.46/5.66 ( ? [Z2: num] :
% 5.46/5.66 ! [X3: num] :
% 5.46/5.66 ( ( ord_less_num @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: num] :
% 5.46/5.66 ! [X3: num] :
% 5.46/5.66 ( ( ord_less_num @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(2)
% 5.46/5.66 thf(fact_3444_minf_I2_J,axiom,
% 5.46/5.66 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.46/5.66 ( ? [Z2: nat] :
% 5.46/5.66 ! [X3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: nat] :
% 5.46/5.66 ! [X3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(2)
% 5.46/5.66 thf(fact_3445_minf_I2_J,axiom,
% 5.46/5.66 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.46/5.66 ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(2)
% 5.46/5.66 thf(fact_3446_minf_I1_J,axiom,
% 5.46/5.66 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.46/5.66 ( ? [Z2: real] :
% 5.46/5.66 ! [X3: real] :
% 5.46/5.66 ( ( ord_less_real @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: real] :
% 5.46/5.66 ! [X3: real] :
% 5.46/5.66 ( ( ord_less_real @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(1)
% 5.46/5.66 thf(fact_3447_minf_I1_J,axiom,
% 5.46/5.66 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.46/5.66 ( ? [Z2: rat] :
% 5.46/5.66 ! [X3: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: rat] :
% 5.46/5.66 ! [X3: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(1)
% 5.46/5.66 thf(fact_3448_minf_I1_J,axiom,
% 5.46/5.66 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.46/5.66 ( ? [Z2: num] :
% 5.46/5.66 ! [X3: num] :
% 5.46/5.66 ( ( ord_less_num @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: num] :
% 5.46/5.66 ! [X3: num] :
% 5.46/5.66 ( ( ord_less_num @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(1)
% 5.46/5.66 thf(fact_3449_minf_I1_J,axiom,
% 5.46/5.66 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.46/5.66 ( ? [Z2: nat] :
% 5.46/5.66 ! [X3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: nat] :
% 5.46/5.66 ! [X3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(1)
% 5.46/5.66 thf(fact_3450_minf_I1_J,axiom,
% 5.46/5.66 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.46/5.66 ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ X3 @ Z2 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(1)
% 5.46/5.66 thf(fact_3451_pinf_I7_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_real @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(7)
% 5.46/5.66 thf(fact_3452_pinf_I7_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_rat @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(7)
% 5.46/5.66 thf(fact_3453_pinf_I7_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_num @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(7)
% 5.46/5.66 thf(fact_3454_pinf_I7_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_nat @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(7)
% 5.46/5.66 thf(fact_3455_pinf_I7_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_int @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(7)
% 5.46/5.66 thf(fact_3456_pinf_I5_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_real @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(5)
% 5.46/5.66 thf(fact_3457_pinf_I5_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_rat @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(5)
% 5.46/5.66 thf(fact_3458_pinf_I5_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_num @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(5)
% 5.46/5.66 thf(fact_3459_pinf_I5_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_nat @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(5)
% 5.46/5.66 thf(fact_3460_pinf_I5_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_int @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(5)
% 5.46/5.66 thf(fact_3461_pinf_I4_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(4)
% 5.46/5.66 thf(fact_3462_pinf_I4_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(4)
% 5.46/5.66 thf(fact_3463_pinf_I4_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(4)
% 5.46/5.66 thf(fact_3464_pinf_I4_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(4)
% 5.46/5.66 thf(fact_3465_pinf_I4_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(4)
% 5.46/5.66 thf(fact_3466_pinf_I3_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(3)
% 5.46/5.66 thf(fact_3467_pinf_I3_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(3)
% 5.46/5.66 thf(fact_3468_pinf_I3_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(3)
% 5.46/5.66 thf(fact_3469_pinf_I3_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(3)
% 5.46/5.66 thf(fact_3470_pinf_I3_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.66 => ( X4 != T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(3)
% 5.46/5.66 thf(fact_3471_pinf_I2_J,axiom,
% 5.46/5.66 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.46/5.66 ( ? [Z2: real] :
% 5.46/5.66 ! [X3: real] :
% 5.46/5.66 ( ( ord_less_real @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: real] :
% 5.46/5.66 ! [X3: real] :
% 5.46/5.66 ( ( ord_less_real @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(2)
% 5.46/5.66 thf(fact_3472_pinf_I2_J,axiom,
% 5.46/5.66 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.46/5.66 ( ? [Z2: rat] :
% 5.46/5.66 ! [X3: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: rat] :
% 5.46/5.66 ! [X3: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(2)
% 5.46/5.66 thf(fact_3473_pinf_I2_J,axiom,
% 5.46/5.66 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.46/5.66 ( ? [Z2: num] :
% 5.46/5.66 ! [X3: num] :
% 5.46/5.66 ( ( ord_less_num @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: num] :
% 5.46/5.66 ! [X3: num] :
% 5.46/5.66 ( ( ord_less_num @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(2)
% 5.46/5.66 thf(fact_3474_pinf_I2_J,axiom,
% 5.46/5.66 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.46/5.66 ( ? [Z2: nat] :
% 5.46/5.66 ! [X3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: nat] :
% 5.46/5.66 ! [X3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(2)
% 5.46/5.66 thf(fact_3475_pinf_I2_J,axiom,
% 5.46/5.66 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.46/5.66 ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(2)
% 5.46/5.66 thf(fact_3476_pinf_I1_J,axiom,
% 5.46/5.66 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.46/5.66 ( ? [Z2: real] :
% 5.46/5.66 ! [X3: real] :
% 5.46/5.66 ( ( ord_less_real @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: real] :
% 5.46/5.66 ! [X3: real] :
% 5.46/5.66 ( ( ord_less_real @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(1)
% 5.46/5.66 thf(fact_3477_pinf_I1_J,axiom,
% 5.46/5.66 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.46/5.66 ( ? [Z2: rat] :
% 5.46/5.66 ! [X3: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: rat] :
% 5.46/5.66 ! [X3: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(1)
% 5.46/5.66 thf(fact_3478_pinf_I1_J,axiom,
% 5.46/5.66 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.46/5.66 ( ? [Z2: num] :
% 5.46/5.66 ! [X3: num] :
% 5.46/5.66 ( ( ord_less_num @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: num] :
% 5.46/5.66 ! [X3: num] :
% 5.46/5.66 ( ( ord_less_num @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(1)
% 5.46/5.66 thf(fact_3479_pinf_I1_J,axiom,
% 5.46/5.66 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.46/5.66 ( ? [Z2: nat] :
% 5.46/5.66 ! [X3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: nat] :
% 5.46/5.66 ! [X3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(1)
% 5.46/5.66 thf(fact_3480_pinf_I1_J,axiom,
% 5.46/5.66 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.46/5.66 ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ Z2 @ X3 )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 = ( Q6 @ X3 ) ) )
% 5.46/5.66 => ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P6 @ X4 )
% 5.46/5.66 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(1)
% 5.46/5.66 thf(fact_3481_pinf_I6_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_eq_real @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(6)
% 5.46/5.66 thf(fact_3482_pinf_I6_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_eq_rat @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(6)
% 5.46/5.66 thf(fact_3483_pinf_I6_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_eq_num @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(6)
% 5.46/5.66 thf(fact_3484_pinf_I6_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_eq_nat @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(6)
% 5.46/5.66 thf(fact_3485_pinf_I6_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.66 => ~ ( ord_less_eq_int @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(6)
% 5.46/5.66 thf(fact_3486_pinf_I8_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_eq_real @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(8)
% 5.46/5.66 thf(fact_3487_pinf_I8_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_eq_rat @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(8)
% 5.46/5.66 thf(fact_3488_pinf_I8_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_eq_num @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(8)
% 5.46/5.66 thf(fact_3489_pinf_I8_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_eq_nat @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(8)
% 5.46/5.66 thf(fact_3490_pinf_I8_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.66 => ( ord_less_eq_int @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % pinf(8)
% 5.46/5.66 thf(fact_3491_minf_I6_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_eq_real @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(6)
% 5.46/5.66 thf(fact_3492_minf_I6_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_eq_rat @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(6)
% 5.46/5.66 thf(fact_3493_minf_I6_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_eq_num @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(6)
% 5.46/5.66 thf(fact_3494_minf_I6_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_eq_nat @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(6)
% 5.46/5.66 thf(fact_3495_minf_I6_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.66 => ( ord_less_eq_int @ X4 @ T ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(6)
% 5.46/5.66 thf(fact_3496_minf_I8_J,axiom,
% 5.46/5.66 ! [T: real] :
% 5.46/5.66 ? [Z3: real] :
% 5.46/5.66 ! [X4: real] :
% 5.46/5.66 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_eq_real @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(8)
% 5.46/5.66 thf(fact_3497_minf_I8_J,axiom,
% 5.46/5.66 ! [T: rat] :
% 5.46/5.66 ? [Z3: rat] :
% 5.46/5.66 ! [X4: rat] :
% 5.46/5.66 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_eq_rat @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(8)
% 5.46/5.66 thf(fact_3498_minf_I8_J,axiom,
% 5.46/5.66 ! [T: num] :
% 5.46/5.66 ? [Z3: num] :
% 5.46/5.66 ! [X4: num] :
% 5.46/5.66 ( ( ord_less_num @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_eq_num @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(8)
% 5.46/5.66 thf(fact_3499_minf_I8_J,axiom,
% 5.46/5.66 ! [T: nat] :
% 5.46/5.66 ? [Z3: nat] :
% 5.46/5.66 ! [X4: nat] :
% 5.46/5.66 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_eq_nat @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(8)
% 5.46/5.66 thf(fact_3500_minf_I8_J,axiom,
% 5.46/5.66 ! [T: int] :
% 5.46/5.66 ? [Z3: int] :
% 5.46/5.66 ! [X4: int] :
% 5.46/5.66 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.66 => ~ ( ord_less_eq_int @ T @ X4 ) ) ).
% 5.46/5.66
% 5.46/5.66 % minf(8)
% 5.46/5.66 thf(fact_3501_inf__period_I1_J,axiom,
% 5.46/5.66 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.46/5.66 ( ! [X3: real,K3: real] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: real,K3: real] :
% 5.46/5.66 ( ( Q @ X3 )
% 5.46/5.66 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: real,K4: real] :
% 5.46/5.66 ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.46/5.66 & ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % inf_period(1)
% 5.46/5.66 thf(fact_3502_inf__period_I1_J,axiom,
% 5.46/5.66 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.46/5.66 ( ! [X3: rat,K3: rat] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: rat,K3: rat] :
% 5.46/5.66 ( ( Q @ X3 )
% 5.46/5.66 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: rat,K4: rat] :
% 5.46/5.66 ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.46/5.66 & ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % inf_period(1)
% 5.46/5.66 thf(fact_3503_inf__period_I1_J,axiom,
% 5.46/5.66 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.46/5.66 ( ! [X3: int,K3: int] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: int,K3: int] :
% 5.46/5.66 ( ( Q @ X3 )
% 5.46/5.66 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: int,K4: int] :
% 5.46/5.66 ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.46/5.66 & ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % inf_period(1)
% 5.46/5.66 thf(fact_3504_inf__period_I2_J,axiom,
% 5.46/5.66 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.46/5.66 ( ! [X3: real,K3: real] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: real,K3: real] :
% 5.46/5.66 ( ( Q @ X3 )
% 5.46/5.66 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: real,K4: real] :
% 5.46/5.66 ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.46/5.66 | ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % inf_period(2)
% 5.46/5.66 thf(fact_3505_inf__period_I2_J,axiom,
% 5.46/5.66 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.46/5.66 ( ! [X3: rat,K3: rat] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: rat,K3: rat] :
% 5.46/5.66 ( ( Q @ X3 )
% 5.46/5.66 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: rat,K4: rat] :
% 5.46/5.66 ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.46/5.66 | ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % inf_period(2)
% 5.46/5.66 thf(fact_3506_inf__period_I2_J,axiom,
% 5.46/5.66 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.46/5.66 ( ! [X3: int,K3: int] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: int,K3: int] :
% 5.46/5.66 ( ( Q @ X3 )
% 5.46/5.66 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: int,K4: int] :
% 5.46/5.66 ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.46/5.66 | ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % inf_period(2)
% 5.46/5.66 thf(fact_3507_aset_I2_J,axiom,
% 5.46/5.66 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.46/5.66 ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ A2 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ A2 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 => ( ( P @ ( plus_plus_int @ X4 @ D4 ) )
% 5.46/5.66 | ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % aset(2)
% 5.46/5.66 thf(fact_3508_aset_I1_J,axiom,
% 5.46/5.66 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.46/5.66 ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ A2 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ A2 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 => ( ( P @ ( plus_plus_int @ X4 @ D4 ) )
% 5.46/5.66 & ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % aset(1)
% 5.46/5.66 thf(fact_3509_bset_I2_J,axiom,
% 5.46/5.66 ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 5.46/5.66 ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ B3 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ B3 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 | ( Q @ X4 ) )
% 5.46/5.66 => ( ( P @ ( minus_minus_int @ X4 @ D4 ) )
% 5.46/5.66 | ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % bset(2)
% 5.46/5.66 thf(fact_3510_bset_I1_J,axiom,
% 5.46/5.66 ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 5.46/5.66 ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ B3 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ( ! [X3: int] :
% 5.46/5.66 ( ! [Xa: int] :
% 5.46/5.66 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb2: int] :
% 5.46/5.66 ( ( member_int @ Xb2 @ B3 )
% 5.46/5.66 => ( X3
% 5.46/5.66 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.46/5.66 => ( ( Q @ X3 )
% 5.46/5.66 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ( P @ X4 )
% 5.46/5.66 & ( Q @ X4 ) )
% 5.46/5.66 => ( ( P @ ( minus_minus_int @ X4 @ D4 ) )
% 5.46/5.66 & ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % bset(1)
% 5.46/5.66 thf(fact_3511_plusinfinity,axiom,
% 5.46/5.66 ! [D2: int,P6: int > $o,P: int > $o] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.46/5.66 => ( ! [X3: int,K3: int] :
% 5.46/5.66 ( ( P6 @ X3 )
% 5.46/5.66 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D2 ) ) ) )
% 5.46/5.66 => ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ Z2 @ X3 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P6 @ X3 ) ) )
% 5.46/5.66 => ( ? [X_12: int] : ( P6 @ X_12 )
% 5.46/5.66 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % plusinfinity
% 5.46/5.66 thf(fact_3512_minusinfinity,axiom,
% 5.46/5.66 ! [D2: int,P1: int > $o,P: int > $o] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.46/5.66 => ( ! [X3: int,K3: int] :
% 5.46/5.66 ( ( P1 @ X3 )
% 5.46/5.66 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D2 ) ) ) )
% 5.46/5.66 => ( ? [Z2: int] :
% 5.46/5.66 ! [X3: int] :
% 5.46/5.66 ( ( ord_less_int @ X3 @ Z2 )
% 5.46/5.66 => ( ( P @ X3 )
% 5.46/5.66 = ( P1 @ X3 ) ) )
% 5.46/5.66 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.46/5.66 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % minusinfinity
% 5.46/5.66 thf(fact_3513_incr__mult__lemma,axiom,
% 5.46/5.66 ! [D2: int,P: int > $o,K: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.46/5.66 => ( ! [X3: int] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 => ( P @ ( plus_plus_int @ X3 @ D2 ) ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ( P @ X4 )
% 5.46/5.66 => ( P @ ( plus_plus_int @ X4 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % incr_mult_lemma
% 5.46/5.66 thf(fact_3514_decr__mult__lemma,axiom,
% 5.46/5.66 ! [D2: int,P: int > $o,K: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.46/5.66 => ( ! [X3: int] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 => ( P @ ( minus_minus_int @ X3 @ D2 ) ) )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ( P @ X4 )
% 5.46/5.66 => ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % decr_mult_lemma
% 5.46/5.66 thf(fact_3515_periodic__finite__ex,axiom,
% 5.46/5.66 ! [D2: int,P: int > $o] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.46/5.66 => ( ! [X3: int,K3: int] :
% 5.46/5.66 ( ( P @ X3 )
% 5.46/5.66 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D2 ) ) ) )
% 5.46/5.66 => ( ( ? [X5: int] : ( P @ X5 ) )
% 5.46/5.66 = ( ? [X: int] :
% 5.46/5.66 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 5.46/5.66 & ( P @ X ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % periodic_finite_ex
% 5.46/5.66 thf(fact_3516_aset_I7_J,axiom,
% 5.46/5.66 ! [D4: int,A2: set_int,T: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ord_less_int @ T @ X4 )
% 5.46/5.66 => ( ord_less_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % aset(7)
% 5.46/5.66 thf(fact_3517_aset_I5_J,axiom,
% 5.46/5.66 ! [D4: int,T: int,A2: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ( member_int @ T @ A2 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ord_less_int @ X4 @ T )
% 5.46/5.66 => ( ord_less_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % aset(5)
% 5.46/5.66 thf(fact_3518_aset_I4_J,axiom,
% 5.46/5.66 ! [D4: int,T: int,A2: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ( member_int @ T @ A2 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( X4 != T )
% 5.46/5.66 => ( ( plus_plus_int @ X4 @ D4 )
% 5.46/5.66 != T ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % aset(4)
% 5.46/5.66 thf(fact_3519_aset_I3_J,axiom,
% 5.46/5.66 ! [D4: int,T: int,A2: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( X4 = T )
% 5.46/5.66 => ( ( plus_plus_int @ X4 @ D4 )
% 5.46/5.66 = T ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % aset(3)
% 5.46/5.66 thf(fact_3520_bset_I7_J,axiom,
% 5.46/5.66 ! [D4: int,T: int,B3: set_int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ( ( member_int @ T @ B3 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ord_less_int @ T @ X4 )
% 5.46/5.66 => ( ord_less_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % bset(7)
% 5.46/5.66 thf(fact_3521_bset_I5_J,axiom,
% 5.46/5.66 ! [D4: int,B3: set_int,T: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.66 => ! [X4: int] :
% 5.46/5.66 ( ! [Xa3: int] :
% 5.46/5.66 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.66 => ! [Xb3: int] :
% 5.46/5.66 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.66 => ( X4
% 5.46/5.66 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.66 => ( ( ord_less_int @ X4 @ T )
% 5.46/5.66 => ( ord_less_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % bset(5)
% 5.46/5.66 thf(fact_3522_Bolzano,axiom,
% 5.46/5.66 ! [A: real,B: real,P: real > real > $o] :
% 5.46/5.66 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.66 => ( ! [A5: real,B5: real,C2: real] :
% 5.46/5.66 ( ( P @ A5 @ B5 )
% 5.46/5.66 => ( ( P @ B5 @ C2 )
% 5.46/5.66 => ( ( ord_less_eq_real @ A5 @ B5 )
% 5.46/5.66 => ( ( ord_less_eq_real @ B5 @ C2 )
% 5.46/5.66 => ( P @ A5 @ C2 ) ) ) ) )
% 5.46/5.66 => ( ! [X3: real] :
% 5.46/5.66 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.66 => ( ( ord_less_eq_real @ X3 @ B )
% 5.46/5.66 => ? [D5: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.46/5.66 & ! [A5: real,B5: real] :
% 5.46/5.66 ( ( ( ord_less_eq_real @ A5 @ X3 )
% 5.46/5.66 & ( ord_less_eq_real @ X3 @ B5 )
% 5.46/5.66 & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D5 ) )
% 5.46/5.66 => ( P @ A5 @ B5 ) ) ) ) )
% 5.46/5.66 => ( P @ A @ B ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Bolzano
% 5.46/5.66 thf(fact_3523_divmod__algorithm__code_I7_J,axiom,
% 5.46/5.66 ! [M: num,N: num] :
% 5.46/5.66 ( ( ( ord_less_eq_num @ M @ N )
% 5.46/5.66 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.46/5.66 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.46/5.66 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(7)
% 5.46/5.66 thf(fact_3524_divmod__algorithm__code_I7_J,axiom,
% 5.46/5.66 ! [M: num,N: num] :
% 5.46/5.66 ( ( ( ord_less_eq_num @ M @ N )
% 5.46/5.66 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.46/5.66 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.46/5.66 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(7)
% 5.46/5.66 thf(fact_3525_divmod__algorithm__code_I7_J,axiom,
% 5.46/5.66 ! [M: num,N: num] :
% 5.46/5.66 ( ( ( ord_less_eq_num @ M @ N )
% 5.46/5.66 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.46/5.66 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.46/5.66 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(7)
% 5.46/5.66 thf(fact_3526_divmod__algorithm__code_I8_J,axiom,
% 5.46/5.66 ! [M: num,N: num] :
% 5.46/5.66 ( ( ( ord_less_num @ M @ N )
% 5.46/5.66 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.46/5.66 & ( ~ ( ord_less_num @ M @ N )
% 5.46/5.66 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(8)
% 5.46/5.66 thf(fact_3527_divmod__algorithm__code_I8_J,axiom,
% 5.46/5.66 ! [M: num,N: num] :
% 5.46/5.66 ( ( ( ord_less_num @ M @ N )
% 5.46/5.66 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.46/5.66 & ( ~ ( ord_less_num @ M @ N )
% 5.46/5.66 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(8)
% 5.46/5.66 thf(fact_3528_divmod__algorithm__code_I8_J,axiom,
% 5.46/5.66 ! [M: num,N: num] :
% 5.46/5.66 ( ( ( ord_less_num @ M @ N )
% 5.46/5.66 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.46/5.66 & ( ~ ( ord_less_num @ M @ N )
% 5.46/5.66 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.66 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(8)
% 5.46/5.66 thf(fact_3529_mult__le__cancel__iff2,axiom,
% 5.46/5.66 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.46/5.66 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X2 ) @ ( times_times_real @ Z @ Y2 ) )
% 5.46/5.66 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_le_cancel_iff2
% 5.46/5.66 thf(fact_3530_mult__le__cancel__iff2,axiom,
% 5.46/5.66 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.66 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.46/5.66 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X2 ) @ ( times_times_rat @ Z @ Y2 ) )
% 5.46/5.66 = ( ord_less_eq_rat @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_le_cancel_iff2
% 5.46/5.66 thf(fact_3531_mult__le__cancel__iff2,axiom,
% 5.46/5.66 ! [Z: int,X2: int,Y2: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.66 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X2 ) @ ( times_times_int @ Z @ Y2 ) )
% 5.46/5.66 = ( ord_less_eq_int @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_le_cancel_iff2
% 5.46/5.66 thf(fact_3532_mult__le__cancel__iff1,axiom,
% 5.46/5.66 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.46/5.66 => ( ( ord_less_eq_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 5.46/5.66 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_le_cancel_iff1
% 5.46/5.66 thf(fact_3533_mult__le__cancel__iff1,axiom,
% 5.46/5.66 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.66 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.46/5.66 => ( ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 5.46/5.66 = ( ord_less_eq_rat @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_le_cancel_iff1
% 5.46/5.66 thf(fact_3534_mult__le__cancel__iff1,axiom,
% 5.46/5.66 ! [Z: int,X2: int,Y2: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.66 => ( ( ord_less_eq_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 5.46/5.66 = ( ord_less_eq_int @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_le_cancel_iff1
% 5.46/5.66 thf(fact_3535_divides__aux__eq,axiom,
% 5.46/5.66 ! [Q2: nat,R: nat] :
% 5.46/5.66 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.46/5.66 = ( R = zero_zero_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % divides_aux_eq
% 5.46/5.66 thf(fact_3536_divides__aux__eq,axiom,
% 5.46/5.66 ! [Q2: int,R: int] :
% 5.46/5.66 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.66 = ( R = zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % divides_aux_eq
% 5.46/5.66 thf(fact_3537_divmod__algorithm__code_I2_J,axiom,
% 5.46/5.66 ! [M: num] :
% 5.46/5.66 ( ( unique5052692396658037445od_int @ M @ one )
% 5.46/5.66 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(2)
% 5.46/5.66 thf(fact_3538_divmod__algorithm__code_I2_J,axiom,
% 5.46/5.66 ! [M: num] :
% 5.46/5.66 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.46/5.66 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(2)
% 5.46/5.66 thf(fact_3539_divmod__algorithm__code_I2_J,axiom,
% 5.46/5.66 ! [M: num] :
% 5.46/5.66 ( ( unique3479559517661332726nteger @ M @ one )
% 5.46/5.66 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(2)
% 5.46/5.66 thf(fact_3540_divmod__algorithm__code_I3_J,axiom,
% 5.46/5.66 ! [N: num] :
% 5.46/5.66 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.46/5.66 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(3)
% 5.46/5.66 thf(fact_3541_divmod__algorithm__code_I3_J,axiom,
% 5.46/5.66 ! [N: num] :
% 5.46/5.66 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.46/5.66 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(3)
% 5.46/5.66 thf(fact_3542_divmod__algorithm__code_I3_J,axiom,
% 5.46/5.66 ! [N: num] :
% 5.46/5.66 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.46/5.66 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(3)
% 5.46/5.66 thf(fact_3543_divmod__algorithm__code_I4_J,axiom,
% 5.46/5.66 ! [N: num] :
% 5.46/5.66 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.46/5.66 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(4)
% 5.46/5.66 thf(fact_3544_divmod__algorithm__code_I4_J,axiom,
% 5.46/5.66 ! [N: num] :
% 5.46/5.66 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.46/5.66 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(4)
% 5.46/5.66 thf(fact_3545_divmod__algorithm__code_I4_J,axiom,
% 5.46/5.66 ! [N: num] :
% 5.46/5.66 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.46/5.66 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_algorithm_code(4)
% 5.46/5.66 thf(fact_3546_divmod__int__def,axiom,
% 5.46/5.66 ( unique5052692396658037445od_int
% 5.46/5.66 = ( ^ [M3: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_int_def
% 5.46/5.66 thf(fact_3547_divmod__def,axiom,
% 5.46/5.66 ( unique5052692396658037445od_int
% 5.46/5.66 = ( ^ [M3: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_def
% 5.46/5.66 thf(fact_3548_divmod__def,axiom,
% 5.46/5.66 ( unique5055182867167087721od_nat
% 5.46/5.66 = ( ^ [M3: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_def
% 5.46/5.66 thf(fact_3549_divmod__def,axiom,
% 5.46/5.66 ( unique3479559517661332726nteger
% 5.46/5.66 = ( ^ [M3: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_def
% 5.46/5.66 thf(fact_3550_divmod_H__nat__def,axiom,
% 5.46/5.66 ( unique5055182867167087721od_nat
% 5.46/5.66 = ( ^ [M3: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod'_nat_def
% 5.46/5.66 thf(fact_3551_divmod__divmod__step,axiom,
% 5.46/5.66 ( unique5055182867167087721od_nat
% 5.46/5.66 = ( ^ [M3: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_divmod_step
% 5.46/5.66 thf(fact_3552_divmod__divmod__step,axiom,
% 5.46/5.66 ( unique5052692396658037445od_int
% 5.46/5.66 = ( ^ [M3: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_divmod_step
% 5.46/5.66 thf(fact_3553_divmod__divmod__step,axiom,
% 5.46/5.66 ( unique3479559517661332726nteger
% 5.46/5.66 = ( ^ [M3: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_divmod_step
% 5.46/5.66 thf(fact_3554_mult__less__iff1,axiom,
% 5.46/5.66 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.66 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.46/5.66 => ( ( ord_less_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 5.46/5.66 = ( ord_less_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_less_iff1
% 5.46/5.66 thf(fact_3555_mult__less__iff1,axiom,
% 5.46/5.66 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.66 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.46/5.66 => ( ( ord_less_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 5.46/5.66 = ( ord_less_rat @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_less_iff1
% 5.46/5.66 thf(fact_3556_mult__less__iff1,axiom,
% 5.46/5.66 ! [Z: int,X2: int,Y2: int] :
% 5.46/5.66 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.66 => ( ( ord_less_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 5.46/5.66 = ( ord_less_int @ X2 @ Y2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % mult_less_iff1
% 5.46/5.66 thf(fact_3557_neg__eucl__rel__int__mult__2,axiom,
% 5.46/5.66 ! [B: int,A: int,Q2: int,R: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.46/5.66 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.66 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % neg_eucl_rel_int_mult_2
% 5.46/5.66 thf(fact_3558_old_Oprod_Oinject,axiom,
% 5.46/5.66 ! [A: code_integer,B: $o,A4: code_integer,B4: $o] :
% 5.46/5.66 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.46/5.66 = ( produc6677183202524767010eger_o @ A4 @ B4 ) )
% 5.46/5.66 = ( ( A = A4 )
% 5.46/5.66 & ( B = B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.inject
% 5.46/5.66 thf(fact_3559_old_Oprod_Oinject,axiom,
% 5.46/5.66 ! [A: num,B: num,A4: num,B4: num] :
% 5.46/5.66 ( ( ( product_Pair_num_num @ A @ B )
% 5.46/5.66 = ( product_Pair_num_num @ A4 @ B4 ) )
% 5.46/5.66 = ( ( A = A4 )
% 5.46/5.66 & ( B = B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.inject
% 5.46/5.66 thf(fact_3560_old_Oprod_Oinject,axiom,
% 5.46/5.66 ! [A: nat,B: num,A4: nat,B4: num] :
% 5.46/5.66 ( ( ( product_Pair_nat_num @ A @ B )
% 5.46/5.66 = ( product_Pair_nat_num @ A4 @ B4 ) )
% 5.46/5.66 = ( ( A = A4 )
% 5.46/5.66 & ( B = B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.inject
% 5.46/5.66 thf(fact_3561_old_Oprod_Oinject,axiom,
% 5.46/5.66 ! [A: nat,B: nat,A4: nat,B4: nat] :
% 5.46/5.66 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.46/5.66 = ( product_Pair_nat_nat @ A4 @ B4 ) )
% 5.46/5.66 = ( ( A = A4 )
% 5.46/5.66 & ( B = B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.inject
% 5.46/5.66 thf(fact_3562_old_Oprod_Oinject,axiom,
% 5.46/5.66 ! [A: int,B: int,A4: int,B4: int] :
% 5.46/5.66 ( ( ( product_Pair_int_int @ A @ B )
% 5.46/5.66 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.46/5.66 = ( ( A = A4 )
% 5.46/5.66 & ( B = B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.inject
% 5.46/5.66 thf(fact_3563_prod_Oinject,axiom,
% 5.46/5.66 ! [X1: code_integer,X23: $o,Y1: code_integer,Y22: $o] :
% 5.46/5.66 ( ( ( produc6677183202524767010eger_o @ X1 @ X23 )
% 5.46/5.66 = ( produc6677183202524767010eger_o @ Y1 @ Y22 ) )
% 5.46/5.66 = ( ( X1 = Y1 )
% 5.46/5.66 & ( X23 = Y22 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod.inject
% 5.46/5.66 thf(fact_3564_prod_Oinject,axiom,
% 5.46/5.66 ! [X1: num,X23: num,Y1: num,Y22: num] :
% 5.46/5.66 ( ( ( product_Pair_num_num @ X1 @ X23 )
% 5.46/5.66 = ( product_Pair_num_num @ Y1 @ Y22 ) )
% 5.46/5.66 = ( ( X1 = Y1 )
% 5.46/5.66 & ( X23 = Y22 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod.inject
% 5.46/5.66 thf(fact_3565_prod_Oinject,axiom,
% 5.46/5.66 ! [X1: nat,X23: num,Y1: nat,Y22: num] :
% 5.46/5.66 ( ( ( product_Pair_nat_num @ X1 @ X23 )
% 5.46/5.66 = ( product_Pair_nat_num @ Y1 @ Y22 ) )
% 5.46/5.66 = ( ( X1 = Y1 )
% 5.46/5.66 & ( X23 = Y22 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod.inject
% 5.46/5.66 thf(fact_3566_prod_Oinject,axiom,
% 5.46/5.66 ! [X1: nat,X23: nat,Y1: nat,Y22: nat] :
% 5.46/5.66 ( ( ( product_Pair_nat_nat @ X1 @ X23 )
% 5.46/5.66 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 5.46/5.66 = ( ( X1 = Y1 )
% 5.46/5.66 & ( X23 = Y22 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod.inject
% 5.46/5.66 thf(fact_3567_prod_Oinject,axiom,
% 5.46/5.66 ! [X1: int,X23: int,Y1: int,Y22: int] :
% 5.46/5.66 ( ( ( product_Pair_int_int @ X1 @ X23 )
% 5.46/5.66 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 5.46/5.66 = ( ( X1 = Y1 )
% 5.46/5.66 & ( X23 = Y22 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod.inject
% 5.46/5.66 thf(fact_3568_unique__quotient,axiom,
% 5.46/5.66 ! [A: int,B: int,Q2: int,R: int,Q5: int,R4: int] :
% 5.46/5.66 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.66 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.46/5.66 => ( Q2 = Q5 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % unique_quotient
% 5.46/5.66 thf(fact_3569_unique__remainder,axiom,
% 5.46/5.66 ! [A: int,B: int,Q2: int,R: int,Q5: int,R4: int] :
% 5.46/5.66 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.66 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.46/5.66 => ( R = R4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % unique_remainder
% 5.46/5.66 thf(fact_3570_eucl__rel__int__by0,axiom,
% 5.46/5.66 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.46/5.66
% 5.46/5.66 % eucl_rel_int_by0
% 5.46/5.66 thf(fact_3571_div__int__unique,axiom,
% 5.46/5.66 ! [K: int,L2: int,Q2: int,R: int] :
% 5.46/5.66 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.66 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.66 = Q2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % div_int_unique
% 5.46/5.66 thf(fact_3572_mod__int__unique,axiom,
% 5.46/5.66 ! [K: int,L2: int,Q2: int,R: int] :
% 5.46/5.66 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.66 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.66 = R ) ) ).
% 5.46/5.66
% 5.46/5.66 % mod_int_unique
% 5.46/5.66 thf(fact_3573_eucl__rel__int__dividesI,axiom,
% 5.46/5.66 ! [L2: int,K: int,Q2: int] :
% 5.46/5.66 ( ( L2 != zero_zero_int )
% 5.46/5.66 => ( ( K
% 5.46/5.66 = ( times_times_int @ Q2 @ L2 ) )
% 5.46/5.66 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % eucl_rel_int_dividesI
% 5.46/5.66 thf(fact_3574_Pair__inject,axiom,
% 5.46/5.66 ! [A: code_integer,B: $o,A4: code_integer,B4: $o] :
% 5.46/5.66 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.46/5.66 = ( produc6677183202524767010eger_o @ A4 @ B4 ) )
% 5.46/5.66 => ~ ( ( A = A4 )
% 5.46/5.66 => ( B = ~ B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Pair_inject
% 5.46/5.66 thf(fact_3575_Pair__inject,axiom,
% 5.46/5.66 ! [A: num,B: num,A4: num,B4: num] :
% 5.46/5.66 ( ( ( product_Pair_num_num @ A @ B )
% 5.46/5.66 = ( product_Pair_num_num @ A4 @ B4 ) )
% 5.46/5.66 => ~ ( ( A = A4 )
% 5.46/5.66 => ( B != B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Pair_inject
% 5.46/5.66 thf(fact_3576_Pair__inject,axiom,
% 5.46/5.66 ! [A: nat,B: num,A4: nat,B4: num] :
% 5.46/5.66 ( ( ( product_Pair_nat_num @ A @ B )
% 5.46/5.66 = ( product_Pair_nat_num @ A4 @ B4 ) )
% 5.46/5.66 => ~ ( ( A = A4 )
% 5.46/5.66 => ( B != B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Pair_inject
% 5.46/5.66 thf(fact_3577_Pair__inject,axiom,
% 5.46/5.66 ! [A: nat,B: nat,A4: nat,B4: nat] :
% 5.46/5.66 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.46/5.66 = ( product_Pair_nat_nat @ A4 @ B4 ) )
% 5.46/5.66 => ~ ( ( A = A4 )
% 5.46/5.66 => ( B != B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Pair_inject
% 5.46/5.66 thf(fact_3578_Pair__inject,axiom,
% 5.46/5.66 ! [A: int,B: int,A4: int,B4: int] :
% 5.46/5.66 ( ( ( product_Pair_int_int @ A @ B )
% 5.46/5.66 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.46/5.66 => ~ ( ( A = A4 )
% 5.46/5.66 => ( B != B4 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % Pair_inject
% 5.46/5.66 thf(fact_3579_prod__cases,axiom,
% 5.46/5.66 ! [P: produc6271795597528267376eger_o > $o,P2: produc6271795597528267376eger_o] :
% 5.46/5.66 ( ! [A5: code_integer,B5: $o] : ( P @ ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.46/5.66 => ( P @ P2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod_cases
% 5.46/5.66 thf(fact_3580_prod__cases,axiom,
% 5.46/5.66 ! [P: product_prod_num_num > $o,P2: product_prod_num_num] :
% 5.46/5.66 ( ! [A5: num,B5: num] : ( P @ ( product_Pair_num_num @ A5 @ B5 ) )
% 5.46/5.66 => ( P @ P2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod_cases
% 5.46/5.66 thf(fact_3581_prod__cases,axiom,
% 5.46/5.66 ! [P: product_prod_nat_num > $o,P2: product_prod_nat_num] :
% 5.46/5.66 ( ! [A5: nat,B5: num] : ( P @ ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.46/5.66 => ( P @ P2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod_cases
% 5.46/5.66 thf(fact_3582_prod__cases,axiom,
% 5.46/5.66 ! [P: product_prod_nat_nat > $o,P2: product_prod_nat_nat] :
% 5.46/5.66 ( ! [A5: nat,B5: nat] : ( P @ ( product_Pair_nat_nat @ A5 @ B5 ) )
% 5.46/5.66 => ( P @ P2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod_cases
% 5.46/5.66 thf(fact_3583_prod__cases,axiom,
% 5.46/5.66 ! [P: product_prod_int_int > $o,P2: product_prod_int_int] :
% 5.46/5.66 ( ! [A5: int,B5: int] : ( P @ ( product_Pair_int_int @ A5 @ B5 ) )
% 5.46/5.66 => ( P @ P2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % prod_cases
% 5.46/5.66 thf(fact_3584_surj__pair,axiom,
% 5.46/5.66 ! [P2: produc6271795597528267376eger_o] :
% 5.46/5.66 ? [X3: code_integer,Y3: $o] :
% 5.46/5.66 ( P2
% 5.46/5.66 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) ) ).
% 5.46/5.66
% 5.46/5.66 % surj_pair
% 5.46/5.66 thf(fact_3585_surj__pair,axiom,
% 5.46/5.66 ! [P2: product_prod_num_num] :
% 5.46/5.66 ? [X3: num,Y3: num] :
% 5.46/5.66 ( P2
% 5.46/5.66 = ( product_Pair_num_num @ X3 @ Y3 ) ) ).
% 5.46/5.66
% 5.46/5.66 % surj_pair
% 5.46/5.66 thf(fact_3586_surj__pair,axiom,
% 5.46/5.66 ! [P2: product_prod_nat_num] :
% 5.46/5.66 ? [X3: nat,Y3: num] :
% 5.46/5.66 ( P2
% 5.46/5.66 = ( product_Pair_nat_num @ X3 @ Y3 ) ) ).
% 5.46/5.66
% 5.46/5.66 % surj_pair
% 5.46/5.66 thf(fact_3587_surj__pair,axiom,
% 5.46/5.66 ! [P2: product_prod_nat_nat] :
% 5.46/5.66 ? [X3: nat,Y3: nat] :
% 5.46/5.66 ( P2
% 5.46/5.66 = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 5.46/5.66
% 5.46/5.66 % surj_pair
% 5.46/5.66 thf(fact_3588_surj__pair,axiom,
% 5.46/5.66 ! [P2: product_prod_int_int] :
% 5.46/5.66 ? [X3: int,Y3: int] :
% 5.46/5.66 ( P2
% 5.46/5.66 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 5.46/5.66
% 5.46/5.66 % surj_pair
% 5.46/5.66 thf(fact_3589_old_Oprod_Oexhaust,axiom,
% 5.46/5.66 ! [Y2: produc6271795597528267376eger_o] :
% 5.46/5.66 ~ ! [A5: code_integer,B5: $o] :
% 5.46/5.66 ( Y2
% 5.46/5.66 != ( produc6677183202524767010eger_o @ A5 @ B5 ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.exhaust
% 5.46/5.66 thf(fact_3590_old_Oprod_Oexhaust,axiom,
% 5.46/5.66 ! [Y2: product_prod_num_num] :
% 5.46/5.66 ~ ! [A5: num,B5: num] :
% 5.46/5.66 ( Y2
% 5.46/5.66 != ( product_Pair_num_num @ A5 @ B5 ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.exhaust
% 5.46/5.66 thf(fact_3591_old_Oprod_Oexhaust,axiom,
% 5.46/5.66 ! [Y2: product_prod_nat_num] :
% 5.46/5.66 ~ ! [A5: nat,B5: num] :
% 5.46/5.66 ( Y2
% 5.46/5.66 != ( product_Pair_nat_num @ A5 @ B5 ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.exhaust
% 5.46/5.66 thf(fact_3592_old_Oprod_Oexhaust,axiom,
% 5.46/5.66 ! [Y2: product_prod_nat_nat] :
% 5.46/5.66 ~ ! [A5: nat,B5: nat] :
% 5.46/5.66 ( Y2
% 5.46/5.66 != ( product_Pair_nat_nat @ A5 @ B5 ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.exhaust
% 5.46/5.66 thf(fact_3593_old_Oprod_Oexhaust,axiom,
% 5.46/5.66 ! [Y2: product_prod_int_int] :
% 5.46/5.66 ~ ! [A5: int,B5: int] :
% 5.46/5.66 ( Y2
% 5.46/5.66 != ( product_Pair_int_int @ A5 @ B5 ) ) ).
% 5.46/5.66
% 5.46/5.66 % old.prod.exhaust
% 5.46/5.66 thf(fact_3594_eucl__rel__int,axiom,
% 5.46/5.66 ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % eucl_rel_int
% 5.46/5.66 thf(fact_3595_eucl__rel__int__iff,axiom,
% 5.46/5.66 ! [K: int,L2: int,Q2: int,R: int] :
% 5.46/5.66 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.66 = ( ( K
% 5.46/5.66 = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R ) )
% 5.46/5.66 & ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.46/5.66 & ( ord_less_int @ R @ L2 ) ) )
% 5.46/5.66 & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.66 => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.66 => ( ( ord_less_int @ L2 @ R )
% 5.46/5.66 & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 5.46/5.66 & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.66 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % eucl_rel_int_iff
% 5.46/5.66 thf(fact_3596_pos__eucl__rel__int__mult__2,axiom,
% 5.46/5.66 ! [B: int,A: int,Q2: int,R: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.46/5.66 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.66 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % pos_eucl_rel_int_mult_2
% 5.46/5.66 thf(fact_3597_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 5.46/5.66 ! [A: $o,B: $o] :
% 5.46/5.66 ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 5.46/5.66 = zero_zero_nat ) ).
% 5.46/5.66
% 5.46/5.66 % VEBT_internal.height.simps(1)
% 5.46/5.66 thf(fact_3598_divmod__BitM__2__eq,axiom,
% 5.46/5.66 ! [M: num] :
% 5.46/5.66 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.46/5.66 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % divmod_BitM_2_eq
% 5.46/5.66 thf(fact_3599_insert__simp__norm,axiom,
% 5.46/5.66 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.46/5.66 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.46/5.66 => ( ( ord_less_nat @ Mi @ X2 )
% 5.46/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.66 => ( ( X2 != Ma )
% 5.46/5.66 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X2 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % insert_simp_norm
% 5.46/5.66 thf(fact_3600_insert__simp__excp,axiom,
% 5.46/5.66 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X2: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.46/5.66 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.46/5.66 => ( ( ord_less_nat @ X2 @ Mi )
% 5.46/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.66 => ( ( X2 != Ma )
% 5.46/5.66 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.46/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % insert_simp_excp
% 5.46/5.66 thf(fact_3601_gcd__nat__induct,axiom,
% 5.46/5.66 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.46/5.66 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 5.46/5.66 => ( ! [M4: nat,N3: nat] :
% 5.46/5.66 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.46/5.66 => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 5.46/5.66 => ( P @ M4 @ N3 ) ) )
% 5.46/5.66 => ( P @ M @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % gcd_nat_induct
% 5.46/5.66 thf(fact_3602_concat__bit__Suc,axiom,
% 5.46/5.66 ! [N: nat,K: int,L2: int] :
% 5.46/5.66 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 5.46/5.66 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % concat_bit_Suc
% 5.46/5.66 thf(fact_3603_dbl__simps_I3_J,axiom,
% 5.46/5.66 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.46/5.66 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(3)
% 5.46/5.66 thf(fact_3604_dbl__simps_I3_J,axiom,
% 5.46/5.66 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.46/5.66 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(3)
% 5.46/5.66 thf(fact_3605_dbl__simps_I3_J,axiom,
% 5.46/5.66 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.46/5.66 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(3)
% 5.46/5.66 thf(fact_3606_dbl__simps_I3_J,axiom,
% 5.46/5.66 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.46/5.66 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(3)
% 5.46/5.66 thf(fact_3607_max_Oabsorb1,axiom,
% 5.46/5.66 ! [B: extended_enat,A: extended_enat] :
% 5.46/5.66 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.46/5.66 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb1
% 5.46/5.66 thf(fact_3608_max_Oabsorb1,axiom,
% 5.46/5.66 ! [B: rat,A: rat] :
% 5.46/5.66 ( ( ord_less_eq_rat @ B @ A )
% 5.46/5.66 => ( ( ord_max_rat @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb1
% 5.46/5.66 thf(fact_3609_max_Oabsorb1,axiom,
% 5.46/5.66 ! [B: num,A: num] :
% 5.46/5.66 ( ( ord_less_eq_num @ B @ A )
% 5.46/5.66 => ( ( ord_max_num @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb1
% 5.46/5.66 thf(fact_3610_max_Oabsorb1,axiom,
% 5.46/5.66 ! [B: nat,A: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ B @ A )
% 5.46/5.66 => ( ( ord_max_nat @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb1
% 5.46/5.66 thf(fact_3611_max_Oabsorb1,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ B @ A )
% 5.46/5.66 => ( ( ord_max_int @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb1
% 5.46/5.66 thf(fact_3612_max_Oabsorb2,axiom,
% 5.46/5.66 ! [A: extended_enat,B: extended_enat] :
% 5.46/5.66 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.46/5.66 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb2
% 5.46/5.66 thf(fact_3613_max_Oabsorb2,axiom,
% 5.46/5.66 ! [A: rat,B: rat] :
% 5.46/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.66 => ( ( ord_max_rat @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb2
% 5.46/5.66 thf(fact_3614_max_Oabsorb2,axiom,
% 5.46/5.66 ! [A: num,B: num] :
% 5.46/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.46/5.66 => ( ( ord_max_num @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb2
% 5.46/5.66 thf(fact_3615_max_Oabsorb2,axiom,
% 5.46/5.66 ! [A: nat,B: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ A @ B )
% 5.46/5.66 => ( ( ord_max_nat @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb2
% 5.46/5.66 thf(fact_3616_max_Oabsorb2,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ A @ B )
% 5.46/5.66 => ( ( ord_max_int @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb2
% 5.46/5.66 thf(fact_3617_max_Obounded__iff,axiom,
% 5.46/5.66 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.46/5.66 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.46/5.66 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.46/5.66 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.bounded_iff
% 5.46/5.66 thf(fact_3618_max_Obounded__iff,axiom,
% 5.46/5.66 ! [B: rat,C: rat,A: rat] :
% 5.46/5.66 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.46/5.66 = ( ( ord_less_eq_rat @ B @ A )
% 5.46/5.66 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.bounded_iff
% 5.46/5.66 thf(fact_3619_max_Obounded__iff,axiom,
% 5.46/5.66 ! [B: num,C: num,A: num] :
% 5.46/5.66 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.46/5.66 = ( ( ord_less_eq_num @ B @ A )
% 5.46/5.66 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.bounded_iff
% 5.46/5.66 thf(fact_3620_max_Obounded__iff,axiom,
% 5.46/5.66 ! [B: nat,C: nat,A: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.46/5.66 = ( ( ord_less_eq_nat @ B @ A )
% 5.46/5.66 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.bounded_iff
% 5.46/5.66 thf(fact_3621_max_Obounded__iff,axiom,
% 5.46/5.66 ! [B: int,C: int,A: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.46/5.66 = ( ( ord_less_eq_int @ B @ A )
% 5.46/5.66 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.bounded_iff
% 5.46/5.66 thf(fact_3622_max__less__iff__conj,axiom,
% 5.46/5.66 ! [X2: extended_enat,Y2: extended_enat,Z: extended_enat] :
% 5.46/5.66 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X2 @ Y2 ) @ Z )
% 5.46/5.66 = ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 5.46/5.66 & ( ord_le72135733267957522d_enat @ Y2 @ Z ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_less_iff_conj
% 5.46/5.66 thf(fact_3623_max__less__iff__conj,axiom,
% 5.46/5.66 ! [X2: real,Y2: real,Z: real] :
% 5.46/5.66 ( ( ord_less_real @ ( ord_max_real @ X2 @ Y2 ) @ Z )
% 5.46/5.66 = ( ( ord_less_real @ X2 @ Z )
% 5.46/5.66 & ( ord_less_real @ Y2 @ Z ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_less_iff_conj
% 5.46/5.66 thf(fact_3624_max__less__iff__conj,axiom,
% 5.46/5.66 ! [X2: rat,Y2: rat,Z: rat] :
% 5.46/5.66 ( ( ord_less_rat @ ( ord_max_rat @ X2 @ Y2 ) @ Z )
% 5.46/5.66 = ( ( ord_less_rat @ X2 @ Z )
% 5.46/5.66 & ( ord_less_rat @ Y2 @ Z ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_less_iff_conj
% 5.46/5.66 thf(fact_3625_max__less__iff__conj,axiom,
% 5.46/5.66 ! [X2: num,Y2: num,Z: num] :
% 5.46/5.66 ( ( ord_less_num @ ( ord_max_num @ X2 @ Y2 ) @ Z )
% 5.46/5.66 = ( ( ord_less_num @ X2 @ Z )
% 5.46/5.66 & ( ord_less_num @ Y2 @ Z ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_less_iff_conj
% 5.46/5.66 thf(fact_3626_max__less__iff__conj,axiom,
% 5.46/5.66 ! [X2: nat,Y2: nat,Z: nat] :
% 5.46/5.66 ( ( ord_less_nat @ ( ord_max_nat @ X2 @ Y2 ) @ Z )
% 5.46/5.66 = ( ( ord_less_nat @ X2 @ Z )
% 5.46/5.66 & ( ord_less_nat @ Y2 @ Z ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_less_iff_conj
% 5.46/5.66 thf(fact_3627_max__less__iff__conj,axiom,
% 5.46/5.66 ! [X2: int,Y2: int,Z: int] :
% 5.46/5.66 ( ( ord_less_int @ ( ord_max_int @ X2 @ Y2 ) @ Z )
% 5.46/5.66 = ( ( ord_less_int @ X2 @ Z )
% 5.46/5.66 & ( ord_less_int @ Y2 @ Z ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_less_iff_conj
% 5.46/5.66 thf(fact_3628_max_Oabsorb4,axiom,
% 5.46/5.66 ! [A: extended_enat,B: extended_enat] :
% 5.46/5.66 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.46/5.66 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb4
% 5.46/5.66 thf(fact_3629_max_Oabsorb4,axiom,
% 5.46/5.66 ! [A: real,B: real] :
% 5.46/5.66 ( ( ord_less_real @ A @ B )
% 5.46/5.66 => ( ( ord_max_real @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb4
% 5.46/5.66 thf(fact_3630_max_Oabsorb4,axiom,
% 5.46/5.66 ! [A: rat,B: rat] :
% 5.46/5.66 ( ( ord_less_rat @ A @ B )
% 5.46/5.66 => ( ( ord_max_rat @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb4
% 5.46/5.66 thf(fact_3631_max_Oabsorb4,axiom,
% 5.46/5.66 ! [A: num,B: num] :
% 5.46/5.66 ( ( ord_less_num @ A @ B )
% 5.46/5.66 => ( ( ord_max_num @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb4
% 5.46/5.66 thf(fact_3632_max_Oabsorb4,axiom,
% 5.46/5.66 ! [A: nat,B: nat] :
% 5.46/5.66 ( ( ord_less_nat @ A @ B )
% 5.46/5.66 => ( ( ord_max_nat @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb4
% 5.46/5.66 thf(fact_3633_max_Oabsorb4,axiom,
% 5.46/5.66 ! [A: int,B: int] :
% 5.46/5.66 ( ( ord_less_int @ A @ B )
% 5.46/5.66 => ( ( ord_max_int @ A @ B )
% 5.46/5.66 = B ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb4
% 5.46/5.66 thf(fact_3634_max_Oabsorb3,axiom,
% 5.46/5.66 ! [B: extended_enat,A: extended_enat] :
% 5.46/5.66 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.46/5.66 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb3
% 5.46/5.66 thf(fact_3635_max_Oabsorb3,axiom,
% 5.46/5.66 ! [B: real,A: real] :
% 5.46/5.66 ( ( ord_less_real @ B @ A )
% 5.46/5.66 => ( ( ord_max_real @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb3
% 5.46/5.66 thf(fact_3636_max_Oabsorb3,axiom,
% 5.46/5.66 ! [B: rat,A: rat] :
% 5.46/5.66 ( ( ord_less_rat @ B @ A )
% 5.46/5.66 => ( ( ord_max_rat @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb3
% 5.46/5.66 thf(fact_3637_max_Oabsorb3,axiom,
% 5.46/5.66 ! [B: num,A: num] :
% 5.46/5.66 ( ( ord_less_num @ B @ A )
% 5.46/5.66 => ( ( ord_max_num @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb3
% 5.46/5.66 thf(fact_3638_max_Oabsorb3,axiom,
% 5.46/5.66 ! [B: nat,A: nat] :
% 5.46/5.66 ( ( ord_less_nat @ B @ A )
% 5.46/5.66 => ( ( ord_max_nat @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb3
% 5.46/5.66 thf(fact_3639_max_Oabsorb3,axiom,
% 5.46/5.66 ! [B: int,A: int] :
% 5.46/5.66 ( ( ord_less_int @ B @ A )
% 5.46/5.66 => ( ( ord_max_int @ A @ B )
% 5.46/5.66 = A ) ) ).
% 5.46/5.66
% 5.46/5.66 % max.absorb3
% 5.46/5.66 thf(fact_3640_length__list__update,axiom,
% 5.46/5.66 ! [Xs2: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] :
% 5.46/5.66 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) )
% 5.46/5.66 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % length_list_update
% 5.46/5.66 thf(fact_3641_length__list__update,axiom,
% 5.46/5.66 ! [Xs2: list_o,I: nat,X2: $o] :
% 5.46/5.66 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I @ X2 ) )
% 5.46/5.66 = ( size_size_list_o @ Xs2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % length_list_update
% 5.46/5.66 thf(fact_3642_length__list__update,axiom,
% 5.46/5.66 ! [Xs2: list_nat,I: nat,X2: nat] :
% 5.46/5.66 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) )
% 5.46/5.66 = ( size_size_list_nat @ Xs2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % length_list_update
% 5.46/5.66 thf(fact_3643_length__list__update,axiom,
% 5.46/5.66 ! [Xs2: list_int,I: nat,X2: int] :
% 5.46/5.66 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I @ X2 ) )
% 5.46/5.66 = ( size_size_list_int @ Xs2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % length_list_update
% 5.46/5.66 thf(fact_3644_max__Suc__Suc,axiom,
% 5.46/5.66 ! [M: nat,N: nat] :
% 5.46/5.66 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.46/5.66 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_Suc_Suc
% 5.46/5.66 thf(fact_3645_max__nat_Oeq__neutr__iff,axiom,
% 5.46/5.66 ! [A: nat,B: nat] :
% 5.46/5.66 ( ( ( ord_max_nat @ A @ B )
% 5.46/5.66 = zero_zero_nat )
% 5.46/5.66 = ( ( A = zero_zero_nat )
% 5.46/5.66 & ( B = zero_zero_nat ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_nat.eq_neutr_iff
% 5.46/5.66 thf(fact_3646_max__nat_Oleft__neutral,axiom,
% 5.46/5.66 ! [A: nat] :
% 5.46/5.66 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.46/5.66 = A ) ).
% 5.46/5.66
% 5.46/5.66 % max_nat.left_neutral
% 5.46/5.66 thf(fact_3647_max__nat_Oneutr__eq__iff,axiom,
% 5.46/5.66 ! [A: nat,B: nat] :
% 5.46/5.66 ( ( zero_zero_nat
% 5.46/5.66 = ( ord_max_nat @ A @ B ) )
% 5.46/5.66 = ( ( A = zero_zero_nat )
% 5.46/5.66 & ( B = zero_zero_nat ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_nat.neutr_eq_iff
% 5.46/5.66 thf(fact_3648_max__nat_Oright__neutral,axiom,
% 5.46/5.66 ! [A: nat] :
% 5.46/5.66 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.46/5.66 = A ) ).
% 5.46/5.66
% 5.46/5.66 % max_nat.right_neutral
% 5.46/5.66 thf(fact_3649_max__0L,axiom,
% 5.46/5.66 ! [N: nat] :
% 5.46/5.66 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.46/5.66 = N ) ).
% 5.46/5.66
% 5.46/5.66 % max_0L
% 5.46/5.66 thf(fact_3650_max__0R,axiom,
% 5.46/5.66 ! [N: nat] :
% 5.46/5.66 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.46/5.66 = N ) ).
% 5.46/5.66
% 5.46/5.66 % max_0R
% 5.46/5.66 thf(fact_3651_nth__list__update__neq,axiom,
% 5.46/5.66 ! [I: nat,J: nat,Xs2: list_nat,X2: nat] :
% 5.46/5.66 ( ( I != J )
% 5.46/5.66 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ J )
% 5.46/5.66 = ( nth_nat @ Xs2 @ J ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % nth_list_update_neq
% 5.46/5.66 thf(fact_3652_nth__list__update__neq,axiom,
% 5.46/5.66 ! [I: nat,J: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.46/5.66 ( ( I != J )
% 5.46/5.66 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ J )
% 5.46/5.66 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % nth_list_update_neq
% 5.46/5.66 thf(fact_3653_list__update__id,axiom,
% 5.46/5.66 ! [Xs2: list_nat,I: nat] :
% 5.46/5.66 ( ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ I ) )
% 5.46/5.66 = Xs2 ) ).
% 5.46/5.66
% 5.46/5.66 % list_update_id
% 5.46/5.66 thf(fact_3654_list__update__id,axiom,
% 5.46/5.66 ! [Xs2: list_VEBT_VEBT,I: nat] :
% 5.46/5.66 ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 5.46/5.66 = Xs2 ) ).
% 5.46/5.66
% 5.46/5.66 % list_update_id
% 5.46/5.66 thf(fact_3655_concat__bit__0,axiom,
% 5.46/5.66 ! [K: int,L2: int] :
% 5.46/5.66 ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 5.46/5.66 = L2 ) ).
% 5.46/5.66
% 5.46/5.66 % concat_bit_0
% 5.46/5.66 thf(fact_3656_dbl__simps_I2_J,axiom,
% 5.46/5.66 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.46/5.66 = zero_zero_complex ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(2)
% 5.46/5.66 thf(fact_3657_dbl__simps_I2_J,axiom,
% 5.46/5.66 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.46/5.66 = zero_zero_real ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(2)
% 5.46/5.66 thf(fact_3658_dbl__simps_I2_J,axiom,
% 5.46/5.66 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.46/5.66 = zero_zero_rat ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(2)
% 5.46/5.66 thf(fact_3659_dbl__simps_I2_J,axiom,
% 5.46/5.66 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.46/5.66 = zero_zero_int ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(2)
% 5.46/5.66 thf(fact_3660_max__number__of_I1_J,axiom,
% 5.46/5.66 ! [U: num,V: num] :
% 5.46/5.66 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.46/5.66 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.46/5.66 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.46/5.66 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.46/5.66 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.46/5.66 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_number_of(1)
% 5.46/5.66 thf(fact_3661_max__number__of_I1_J,axiom,
% 5.46/5.66 ! [U: num,V: num] :
% 5.46/5.66 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.46/5.66 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.46/5.66 = ( numeral_numeral_real @ V ) ) )
% 5.46/5.66 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.46/5.66 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.46/5.66 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_number_of(1)
% 5.46/5.66 thf(fact_3662_max__number__of_I1_J,axiom,
% 5.46/5.66 ! [U: num,V: num] :
% 5.46/5.66 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.46/5.66 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.46/5.66 = ( numeral_numeral_rat @ V ) ) )
% 5.46/5.66 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.46/5.66 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.46/5.66 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_number_of(1)
% 5.46/5.66 thf(fact_3663_max__number__of_I1_J,axiom,
% 5.46/5.66 ! [U: num,V: num] :
% 5.46/5.66 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.46/5.66 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.46/5.66 = ( numeral_numeral_nat @ V ) ) )
% 5.46/5.66 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.46/5.66 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.46/5.66 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_number_of(1)
% 5.46/5.66 thf(fact_3664_max__number__of_I1_J,axiom,
% 5.46/5.66 ! [U: num,V: num] :
% 5.46/5.66 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.66 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.66 = ( numeral_numeral_int @ V ) ) )
% 5.46/5.66 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.66 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.66 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_number_of(1)
% 5.46/5.66 thf(fact_3665_max__0__1_I4_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ zero_z5237406670263579293d_enat )
% 5.46/5.66 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(4)
% 5.46/5.66 thf(fact_3666_max__0__1_I4_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ zero_zero_real )
% 5.46/5.66 = ( numeral_numeral_real @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(4)
% 5.46/5.66 thf(fact_3667_max__0__1_I4_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ zero_zero_rat )
% 5.46/5.66 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(4)
% 5.46/5.66 thf(fact_3668_max__0__1_I4_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ zero_zero_nat )
% 5.46/5.66 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(4)
% 5.46/5.66 thf(fact_3669_max__0__1_I4_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ zero_zero_int )
% 5.46/5.66 = ( numeral_numeral_int @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(4)
% 5.46/5.66 thf(fact_3670_max__0__1_I3_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X2 ) )
% 5.46/5.66 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(3)
% 5.46/5.66 thf(fact_3671_max__0__1_I3_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X2 ) )
% 5.46/5.66 = ( numeral_numeral_real @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(3)
% 5.46/5.66 thf(fact_3672_max__0__1_I3_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.46/5.66 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(3)
% 5.46/5.66 thf(fact_3673_max__0__1_I3_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.46/5.66 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(3)
% 5.46/5.66 thf(fact_3674_max__0__1_I3_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X2 ) )
% 5.46/5.66 = ( numeral_numeral_int @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(3)
% 5.46/5.66 thf(fact_3675_max__0__1_I2_J,axiom,
% 5.46/5.66 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.46/5.66 = one_one_real ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(2)
% 5.46/5.66 thf(fact_3676_max__0__1_I2_J,axiom,
% 5.46/5.66 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.46/5.66 = one_one_rat ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(2)
% 5.46/5.66 thf(fact_3677_max__0__1_I2_J,axiom,
% 5.46/5.66 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(2)
% 5.46/5.66 thf(fact_3678_max__0__1_I2_J,axiom,
% 5.46/5.66 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.46/5.66 = one_on7984719198319812577d_enat ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(2)
% 5.46/5.66 thf(fact_3679_max__0__1_I2_J,axiom,
% 5.46/5.66 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.46/5.66 = one_one_int ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(2)
% 5.46/5.66 thf(fact_3680_max__0__1_I1_J,axiom,
% 5.46/5.66 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.46/5.66 = one_one_real ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(1)
% 5.46/5.66 thf(fact_3681_max__0__1_I1_J,axiom,
% 5.46/5.66 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.46/5.66 = one_one_rat ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(1)
% 5.46/5.66 thf(fact_3682_max__0__1_I1_J,axiom,
% 5.46/5.66 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.46/5.66 = one_one_nat ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(1)
% 5.46/5.66 thf(fact_3683_max__0__1_I1_J,axiom,
% 5.46/5.66 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.46/5.66 = one_on7984719198319812577d_enat ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(1)
% 5.46/5.66 thf(fact_3684_max__0__1_I1_J,axiom,
% 5.46/5.66 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.46/5.66 = one_one_int ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(1)
% 5.46/5.66 thf(fact_3685_max__0__1_I6_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ one_on7984719198319812577d_enat )
% 5.46/5.66 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(6)
% 5.46/5.66 thf(fact_3686_max__0__1_I6_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ one_one_real )
% 5.46/5.66 = ( numeral_numeral_real @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(6)
% 5.46/5.66 thf(fact_3687_max__0__1_I6_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat )
% 5.46/5.66 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(6)
% 5.46/5.66 thf(fact_3688_max__0__1_I6_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat )
% 5.46/5.66 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(6)
% 5.46/5.66 thf(fact_3689_max__0__1_I6_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ one_one_int )
% 5.46/5.66 = ( numeral_numeral_int @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(6)
% 5.46/5.66 thf(fact_3690_max__0__1_I5_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X2 ) )
% 5.46/5.66 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(5)
% 5.46/5.66 thf(fact_3691_max__0__1_I5_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 5.46/5.66 = ( numeral_numeral_real @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(5)
% 5.46/5.66 thf(fact_3692_max__0__1_I5_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.46/5.66 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(5)
% 5.46/5.66 thf(fact_3693_max__0__1_I5_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.46/5.66 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(5)
% 5.46/5.66 thf(fact_3694_max__0__1_I5_J,axiom,
% 5.46/5.66 ! [X2: num] :
% 5.46/5.66 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 5.46/5.66 = ( numeral_numeral_int @ X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % max_0_1(5)
% 5.46/5.66 thf(fact_3695_list__update__beyond,axiom,
% 5.46/5.66 ! [Xs2: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] :
% 5.46/5.66 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I )
% 5.46/5.66 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 )
% 5.46/5.66 = Xs2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % list_update_beyond
% 5.46/5.66 thf(fact_3696_list__update__beyond,axiom,
% 5.46/5.66 ! [Xs2: list_o,I: nat,X2: $o] :
% 5.46/5.66 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I )
% 5.46/5.66 => ( ( list_update_o @ Xs2 @ I @ X2 )
% 5.46/5.66 = Xs2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % list_update_beyond
% 5.46/5.66 thf(fact_3697_list__update__beyond,axiom,
% 5.46/5.66 ! [Xs2: list_nat,I: nat,X2: nat] :
% 5.46/5.66 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I )
% 5.46/5.66 => ( ( list_update_nat @ Xs2 @ I @ X2 )
% 5.46/5.66 = Xs2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % list_update_beyond
% 5.46/5.66 thf(fact_3698_list__update__beyond,axiom,
% 5.46/5.66 ! [Xs2: list_int,I: nat,X2: int] :
% 5.46/5.66 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I )
% 5.46/5.66 => ( ( list_update_int @ Xs2 @ I @ X2 )
% 5.46/5.66 = Xs2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % list_update_beyond
% 5.46/5.66 thf(fact_3699_concat__bit__nonnegative__iff,axiom,
% 5.46/5.66 ! [N: nat,K: int,L2: int] :
% 5.46/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 5.46/5.66 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % concat_bit_nonnegative_iff
% 5.46/5.66 thf(fact_3700_concat__bit__negative__iff,axiom,
% 5.46/5.66 ! [N: nat,K: int,L2: int] :
% 5.46/5.66 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 5.46/5.66 = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 5.46/5.66
% 5.46/5.66 % concat_bit_negative_iff
% 5.46/5.66 thf(fact_3701_dbl__simps_I5_J,axiom,
% 5.46/5.66 ! [K: num] :
% 5.46/5.66 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.46/5.66 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(5)
% 5.46/5.66 thf(fact_3702_dbl__simps_I5_J,axiom,
% 5.46/5.66 ! [K: num] :
% 5.46/5.66 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.46/5.66 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(5)
% 5.46/5.66 thf(fact_3703_dbl__simps_I5_J,axiom,
% 5.46/5.66 ! [K: num] :
% 5.46/5.66 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.46/5.66 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(5)
% 5.46/5.66 thf(fact_3704_dbl__simps_I5_J,axiom,
% 5.46/5.66 ! [K: num] :
% 5.46/5.66 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.46/5.66 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % dbl_simps(5)
% 5.46/5.66 thf(fact_3705_nth__list__update__eq,axiom,
% 5.46/5.66 ! [I: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.46/5.66 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.66 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ I )
% 5.46/5.66 = X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % nth_list_update_eq
% 5.46/5.66 thf(fact_3706_nth__list__update__eq,axiom,
% 5.46/5.66 ! [I: nat,Xs2: list_o,X2: $o] :
% 5.46/5.66 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.66 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X2 ) @ I )
% 5.46/5.66 = X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % nth_list_update_eq
% 5.46/5.66 thf(fact_3707_nth__list__update__eq,axiom,
% 5.46/5.66 ! [I: nat,Xs2: list_nat,X2: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.66 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ I )
% 5.46/5.66 = X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % nth_list_update_eq
% 5.46/5.66 thf(fact_3708_nth__list__update__eq,axiom,
% 5.46/5.66 ! [I: nat,Xs2: list_int,X2: int] :
% 5.46/5.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.66 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X2 ) @ I )
% 5.46/5.66 = X2 ) ) ).
% 5.46/5.66
% 5.46/5.66 % nth_list_update_eq
% 5.46/5.66 thf(fact_3709_set__swap,axiom,
% 5.46/5.66 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.66 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.66 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) )
% 5.46/5.66 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % set_swap
% 5.46/5.66 thf(fact_3710_set__swap,axiom,
% 5.46/5.66 ! [I: nat,Xs2: list_o,J: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.66 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.66 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I ) ) )
% 5.46/5.66 = ( set_o2 @ Xs2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % set_swap
% 5.46/5.66 thf(fact_3711_set__swap,axiom,
% 5.46/5.66 ! [I: nat,Xs2: list_nat,J: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.66 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.66 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I ) ) )
% 5.46/5.66 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 5.46/5.66
% 5.46/5.66 % set_swap
% 5.46/5.66 thf(fact_3712_set__swap,axiom,
% 5.46/5.66 ! [I: nat,Xs2: list_int,J: nat] :
% 5.46/5.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.66 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.66 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I ) ) )
% 5.46/5.67 = ( set_int2 @ Xs2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_swap
% 5.46/5.67 thf(fact_3713_max_Omono,axiom,
% 5.46/5.67 ! [C: extended_enat,A: extended_enat,D2: extended_enat,B: extended_enat] :
% 5.46/5.67 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.46/5.67 => ( ( ord_le2932123472753598470d_enat @ D2 @ B )
% 5.46/5.67 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D2 ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.mono
% 5.46/5.67 thf(fact_3714_max_Omono,axiom,
% 5.46/5.67 ! [C: rat,A: rat,D2: rat,B: rat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ C @ A )
% 5.46/5.67 => ( ( ord_less_eq_rat @ D2 @ B )
% 5.46/5.67 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D2 ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.mono
% 5.46/5.67 thf(fact_3715_max_Omono,axiom,
% 5.46/5.67 ! [C: num,A: num,D2: num,B: num] :
% 5.46/5.67 ( ( ord_less_eq_num @ C @ A )
% 5.46/5.67 => ( ( ord_less_eq_num @ D2 @ B )
% 5.46/5.67 => ( ord_less_eq_num @ ( ord_max_num @ C @ D2 ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.mono
% 5.46/5.67 thf(fact_3716_max_Omono,axiom,
% 5.46/5.67 ! [C: nat,A: nat,D2: nat,B: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ C @ A )
% 5.46/5.67 => ( ( ord_less_eq_nat @ D2 @ B )
% 5.46/5.67 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D2 ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.mono
% 5.46/5.67 thf(fact_3717_max_Omono,axiom,
% 5.46/5.67 ! [C: int,A: int,D2: int,B: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ C @ A )
% 5.46/5.67 => ( ( ord_less_eq_int @ D2 @ B )
% 5.46/5.67 => ( ord_less_eq_int @ ( ord_max_int @ C @ D2 ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.mono
% 5.46/5.67 thf(fact_3718_max_OorderE,axiom,
% 5.46/5.67 ! [B: extended_enat,A: extended_enat] :
% 5.46/5.67 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.46/5.67 => ( A
% 5.46/5.67 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderE
% 5.46/5.67 thf(fact_3719_max_OorderE,axiom,
% 5.46/5.67 ! [B: rat,A: rat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ B @ A )
% 5.46/5.67 => ( A
% 5.46/5.67 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderE
% 5.46/5.67 thf(fact_3720_max_OorderE,axiom,
% 5.46/5.67 ! [B: num,A: num] :
% 5.46/5.67 ( ( ord_less_eq_num @ B @ A )
% 5.46/5.67 => ( A
% 5.46/5.67 = ( ord_max_num @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderE
% 5.46/5.67 thf(fact_3721_max_OorderE,axiom,
% 5.46/5.67 ! [B: nat,A: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ B @ A )
% 5.46/5.67 => ( A
% 5.46/5.67 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderE
% 5.46/5.67 thf(fact_3722_max_OorderE,axiom,
% 5.46/5.67 ! [B: int,A: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ B @ A )
% 5.46/5.67 => ( A
% 5.46/5.67 = ( ord_max_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderE
% 5.46/5.67 thf(fact_3723_max_OorderI,axiom,
% 5.46/5.67 ! [A: extended_enat,B: extended_enat] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.46/5.67 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderI
% 5.46/5.67 thf(fact_3724_max_OorderI,axiom,
% 5.46/5.67 ! [A: rat,B: rat] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( ord_max_rat @ A @ B ) )
% 5.46/5.67 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderI
% 5.46/5.67 thf(fact_3725_max_OorderI,axiom,
% 5.46/5.67 ! [A: num,B: num] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( ord_max_num @ A @ B ) )
% 5.46/5.67 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderI
% 5.46/5.67 thf(fact_3726_max_OorderI,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( ord_max_nat @ A @ B ) )
% 5.46/5.67 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderI
% 5.46/5.67 thf(fact_3727_max_OorderI,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( ord_max_int @ A @ B ) )
% 5.46/5.67 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.orderI
% 5.46/5.67 thf(fact_3728_max_OboundedE,axiom,
% 5.46/5.67 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.46/5.67 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.46/5.67 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedE
% 5.46/5.67 thf(fact_3729_max_OboundedE,axiom,
% 5.46/5.67 ! [B: rat,C: rat,A: rat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.46/5.67 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedE
% 5.46/5.67 thf(fact_3730_max_OboundedE,axiom,
% 5.46/5.67 ! [B: num,C: num,A: num] :
% 5.46/5.67 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.46/5.67 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedE
% 5.46/5.67 thf(fact_3731_max_OboundedE,axiom,
% 5.46/5.67 ! [B: nat,C: nat,A: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.46/5.67 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedE
% 5.46/5.67 thf(fact_3732_max_OboundedE,axiom,
% 5.46/5.67 ! [B: int,C: int,A: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.46/5.67 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedE
% 5.46/5.67 thf(fact_3733_max_OboundedI,axiom,
% 5.46/5.67 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.46/5.67 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.46/5.67 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.46/5.67 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedI
% 5.46/5.67 thf(fact_3734_max_OboundedI,axiom,
% 5.46/5.67 ! [B: rat,A: rat,C: rat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ B @ A )
% 5.46/5.67 => ( ( ord_less_eq_rat @ C @ A )
% 5.46/5.67 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedI
% 5.46/5.67 thf(fact_3735_max_OboundedI,axiom,
% 5.46/5.67 ! [B: num,A: num,C: num] :
% 5.46/5.67 ( ( ord_less_eq_num @ B @ A )
% 5.46/5.67 => ( ( ord_less_eq_num @ C @ A )
% 5.46/5.67 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedI
% 5.46/5.67 thf(fact_3736_max_OboundedI,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ B @ A )
% 5.46/5.67 => ( ( ord_less_eq_nat @ C @ A )
% 5.46/5.67 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedI
% 5.46/5.67 thf(fact_3737_max_OboundedI,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ B @ A )
% 5.46/5.67 => ( ( ord_less_eq_int @ C @ A )
% 5.46/5.67 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.boundedI
% 5.46/5.67 thf(fact_3738_max_Oorder__iff,axiom,
% 5.46/5.67 ( ord_le2932123472753598470d_enat
% 5.46/5.67 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.order_iff
% 5.46/5.67 thf(fact_3739_max_Oorder__iff,axiom,
% 5.46/5.67 ( ord_less_eq_rat
% 5.46/5.67 = ( ^ [B2: rat,A3: rat] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( ord_max_rat @ A3 @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.order_iff
% 5.46/5.67 thf(fact_3740_max_Oorder__iff,axiom,
% 5.46/5.67 ( ord_less_eq_num
% 5.46/5.67 = ( ^ [B2: num,A3: num] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( ord_max_num @ A3 @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.order_iff
% 5.46/5.67 thf(fact_3741_max_Oorder__iff,axiom,
% 5.46/5.67 ( ord_less_eq_nat
% 5.46/5.67 = ( ^ [B2: nat,A3: nat] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( ord_max_nat @ A3 @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.order_iff
% 5.46/5.67 thf(fact_3742_max_Oorder__iff,axiom,
% 5.46/5.67 ( ord_less_eq_int
% 5.46/5.67 = ( ^ [B2: int,A3: int] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( ord_max_int @ A3 @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.order_iff
% 5.46/5.67 thf(fact_3743_max_Ocobounded1,axiom,
% 5.46/5.67 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded1
% 5.46/5.67 thf(fact_3744_max_Ocobounded1,axiom,
% 5.46/5.67 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded1
% 5.46/5.67 thf(fact_3745_max_Ocobounded1,axiom,
% 5.46/5.67 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded1
% 5.46/5.67 thf(fact_3746_max_Ocobounded1,axiom,
% 5.46/5.67 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded1
% 5.46/5.67 thf(fact_3747_max_Ocobounded1,axiom,
% 5.46/5.67 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded1
% 5.46/5.67 thf(fact_3748_max_Ocobounded2,axiom,
% 5.46/5.67 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded2
% 5.46/5.67 thf(fact_3749_max_Ocobounded2,axiom,
% 5.46/5.67 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded2
% 5.46/5.67 thf(fact_3750_max_Ocobounded2,axiom,
% 5.46/5.67 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded2
% 5.46/5.67 thf(fact_3751_max_Ocobounded2,axiom,
% 5.46/5.67 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded2
% 5.46/5.67 thf(fact_3752_max_Ocobounded2,axiom,
% 5.46/5.67 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.cobounded2
% 5.46/5.67 thf(fact_3753_le__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: extended_enat,X2: extended_enat,Y2: extended_enat] :
% 5.46/5.67 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_le2932123472753598470d_enat @ Z @ X2 )
% 5.46/5.67 | ( ord_le2932123472753598470d_enat @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_max_iff_disj
% 5.46/5.67 thf(fact_3754_le__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_less_eq_rat @ Z @ X2 )
% 5.46/5.67 | ( ord_less_eq_rat @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_max_iff_disj
% 5.46/5.67 thf(fact_3755_le__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: num,X2: num,Y2: num] :
% 5.46/5.67 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_less_eq_num @ Z @ X2 )
% 5.46/5.67 | ( ord_less_eq_num @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_max_iff_disj
% 5.46/5.67 thf(fact_3756_le__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: nat,X2: nat,Y2: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_less_eq_nat @ Z @ X2 )
% 5.46/5.67 | ( ord_less_eq_nat @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_max_iff_disj
% 5.46/5.67 thf(fact_3757_le__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: int,X2: int,Y2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_less_eq_int @ Z @ X2 )
% 5.46/5.67 | ( ord_less_eq_int @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_max_iff_disj
% 5.46/5.67 thf(fact_3758_max_Oabsorb__iff1,axiom,
% 5.46/5.67 ( ord_le2932123472753598470d_enat
% 5.46/5.67 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.46/5.67 ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 5.46/5.67 = A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff1
% 5.46/5.67 thf(fact_3759_max_Oabsorb__iff1,axiom,
% 5.46/5.67 ( ord_less_eq_rat
% 5.46/5.67 = ( ^ [B2: rat,A3: rat] :
% 5.46/5.67 ( ( ord_max_rat @ A3 @ B2 )
% 5.46/5.67 = A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff1
% 5.46/5.67 thf(fact_3760_max_Oabsorb__iff1,axiom,
% 5.46/5.67 ( ord_less_eq_num
% 5.46/5.67 = ( ^ [B2: num,A3: num] :
% 5.46/5.67 ( ( ord_max_num @ A3 @ B2 )
% 5.46/5.67 = A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff1
% 5.46/5.67 thf(fact_3761_max_Oabsorb__iff1,axiom,
% 5.46/5.67 ( ord_less_eq_nat
% 5.46/5.67 = ( ^ [B2: nat,A3: nat] :
% 5.46/5.67 ( ( ord_max_nat @ A3 @ B2 )
% 5.46/5.67 = A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff1
% 5.46/5.67 thf(fact_3762_max_Oabsorb__iff1,axiom,
% 5.46/5.67 ( ord_less_eq_int
% 5.46/5.67 = ( ^ [B2: int,A3: int] :
% 5.46/5.67 ( ( ord_max_int @ A3 @ B2 )
% 5.46/5.67 = A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff1
% 5.46/5.67 thf(fact_3763_max_Oabsorb__iff2,axiom,
% 5.46/5.67 ( ord_le2932123472753598470d_enat
% 5.46/5.67 = ( ^ [A3: extended_enat,B2: extended_enat] :
% 5.46/5.67 ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 5.46/5.67 = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff2
% 5.46/5.67 thf(fact_3764_max_Oabsorb__iff2,axiom,
% 5.46/5.67 ( ord_less_eq_rat
% 5.46/5.67 = ( ^ [A3: rat,B2: rat] :
% 5.46/5.67 ( ( ord_max_rat @ A3 @ B2 )
% 5.46/5.67 = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff2
% 5.46/5.67 thf(fact_3765_max_Oabsorb__iff2,axiom,
% 5.46/5.67 ( ord_less_eq_num
% 5.46/5.67 = ( ^ [A3: num,B2: num] :
% 5.46/5.67 ( ( ord_max_num @ A3 @ B2 )
% 5.46/5.67 = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff2
% 5.46/5.67 thf(fact_3766_max_Oabsorb__iff2,axiom,
% 5.46/5.67 ( ord_less_eq_nat
% 5.46/5.67 = ( ^ [A3: nat,B2: nat] :
% 5.46/5.67 ( ( ord_max_nat @ A3 @ B2 )
% 5.46/5.67 = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff2
% 5.46/5.67 thf(fact_3767_max_Oabsorb__iff2,axiom,
% 5.46/5.67 ( ord_less_eq_int
% 5.46/5.67 = ( ^ [A3: int,B2: int] :
% 5.46/5.67 ( ( ord_max_int @ A3 @ B2 )
% 5.46/5.67 = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.absorb_iff2
% 5.46/5.67 thf(fact_3768_max_OcoboundedI1,axiom,
% 5.46/5.67 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.46/5.67 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.46/5.67 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI1
% 5.46/5.67 thf(fact_3769_max_OcoboundedI1,axiom,
% 5.46/5.67 ! [C: rat,A: rat,B: rat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ C @ A )
% 5.46/5.67 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI1
% 5.46/5.67 thf(fact_3770_max_OcoboundedI1,axiom,
% 5.46/5.67 ! [C: num,A: num,B: num] :
% 5.46/5.67 ( ( ord_less_eq_num @ C @ A )
% 5.46/5.67 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI1
% 5.46/5.67 thf(fact_3771_max_OcoboundedI1,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ C @ A )
% 5.46/5.67 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI1
% 5.46/5.67 thf(fact_3772_max_OcoboundedI1,axiom,
% 5.46/5.67 ! [C: int,A: int,B: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ C @ A )
% 5.46/5.67 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI1
% 5.46/5.67 thf(fact_3773_max_OcoboundedI2,axiom,
% 5.46/5.67 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.46/5.67 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.46/5.67 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI2
% 5.46/5.67 thf(fact_3774_max_OcoboundedI2,axiom,
% 5.46/5.67 ! [C: rat,B: rat,A: rat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ C @ B )
% 5.46/5.67 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI2
% 5.46/5.67 thf(fact_3775_max_OcoboundedI2,axiom,
% 5.46/5.67 ! [C: num,B: num,A: num] :
% 5.46/5.67 ( ( ord_less_eq_num @ C @ B )
% 5.46/5.67 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI2
% 5.46/5.67 thf(fact_3776_max_OcoboundedI2,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ C @ B )
% 5.46/5.67 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI2
% 5.46/5.67 thf(fact_3777_max_OcoboundedI2,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ C @ B )
% 5.46/5.67 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.coboundedI2
% 5.46/5.67 thf(fact_3778_less__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: extended_enat,X2: extended_enat,Y2: extended_enat] :
% 5.46/5.67 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 5.46/5.67 | ( ord_le72135733267957522d_enat @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % less_max_iff_disj
% 5.46/5.67 thf(fact_3779_less__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.67 ( ( ord_less_real @ Z @ ( ord_max_real @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_less_real @ Z @ X2 )
% 5.46/5.67 | ( ord_less_real @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % less_max_iff_disj
% 5.46/5.67 thf(fact_3780_less__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.67 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_less_rat @ Z @ X2 )
% 5.46/5.67 | ( ord_less_rat @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % less_max_iff_disj
% 5.46/5.67 thf(fact_3781_less__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: num,X2: num,Y2: num] :
% 5.46/5.67 ( ( ord_less_num @ Z @ ( ord_max_num @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_less_num @ Z @ X2 )
% 5.46/5.67 | ( ord_less_num @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % less_max_iff_disj
% 5.46/5.67 thf(fact_3782_less__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: nat,X2: nat,Y2: nat] :
% 5.46/5.67 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_less_nat @ Z @ X2 )
% 5.46/5.67 | ( ord_less_nat @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % less_max_iff_disj
% 5.46/5.67 thf(fact_3783_less__max__iff__disj,axiom,
% 5.46/5.67 ! [Z: int,X2: int,Y2: int] :
% 5.46/5.67 ( ( ord_less_int @ Z @ ( ord_max_int @ X2 @ Y2 ) )
% 5.46/5.67 = ( ( ord_less_int @ Z @ X2 )
% 5.46/5.67 | ( ord_less_int @ Z @ Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % less_max_iff_disj
% 5.46/5.67 thf(fact_3784_max_Ostrict__boundedE,axiom,
% 5.46/5.67 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.46/5.67 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.46/5.67 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_boundedE
% 5.46/5.67 thf(fact_3785_max_Ostrict__boundedE,axiom,
% 5.46/5.67 ! [B: real,C: real,A: real] :
% 5.46/5.67 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_less_real @ B @ A )
% 5.46/5.67 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_boundedE
% 5.46/5.67 thf(fact_3786_max_Ostrict__boundedE,axiom,
% 5.46/5.67 ! [B: rat,C: rat,A: rat] :
% 5.46/5.67 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_less_rat @ B @ A )
% 5.46/5.67 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_boundedE
% 5.46/5.67 thf(fact_3787_max_Ostrict__boundedE,axiom,
% 5.46/5.67 ! [B: num,C: num,A: num] :
% 5.46/5.67 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_less_num @ B @ A )
% 5.46/5.67 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_boundedE
% 5.46/5.67 thf(fact_3788_max_Ostrict__boundedE,axiom,
% 5.46/5.67 ! [B: nat,C: nat,A: nat] :
% 5.46/5.67 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_less_nat @ B @ A )
% 5.46/5.67 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_boundedE
% 5.46/5.67 thf(fact_3789_max_Ostrict__boundedE,axiom,
% 5.46/5.67 ! [B: int,C: int,A: int] :
% 5.46/5.67 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.46/5.67 => ~ ( ( ord_less_int @ B @ A )
% 5.46/5.67 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_boundedE
% 5.46/5.67 thf(fact_3790_max_Ostrict__order__iff,axiom,
% 5.46/5.67 ( ord_le72135733267957522d_enat
% 5.46/5.67 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.46/5.67 ( ( A3
% 5.46/5.67 = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) )
% 5.46/5.67 & ( A3 != B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_order_iff
% 5.46/5.67 thf(fact_3791_max_Ostrict__order__iff,axiom,
% 5.46/5.67 ( ord_less_real
% 5.46/5.67 = ( ^ [B2: real,A3: real] :
% 5.46/5.67 ( ( A3
% 5.46/5.67 = ( ord_max_real @ A3 @ B2 ) )
% 5.46/5.67 & ( A3 != B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_order_iff
% 5.46/5.67 thf(fact_3792_max_Ostrict__order__iff,axiom,
% 5.46/5.67 ( ord_less_rat
% 5.46/5.67 = ( ^ [B2: rat,A3: rat] :
% 5.46/5.67 ( ( A3
% 5.46/5.67 = ( ord_max_rat @ A3 @ B2 ) )
% 5.46/5.67 & ( A3 != B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_order_iff
% 5.46/5.67 thf(fact_3793_max_Ostrict__order__iff,axiom,
% 5.46/5.67 ( ord_less_num
% 5.46/5.67 = ( ^ [B2: num,A3: num] :
% 5.46/5.67 ( ( A3
% 5.46/5.67 = ( ord_max_num @ A3 @ B2 ) )
% 5.46/5.67 & ( A3 != B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_order_iff
% 5.46/5.67 thf(fact_3794_max_Ostrict__order__iff,axiom,
% 5.46/5.67 ( ord_less_nat
% 5.46/5.67 = ( ^ [B2: nat,A3: nat] :
% 5.46/5.67 ( ( A3
% 5.46/5.67 = ( ord_max_nat @ A3 @ B2 ) )
% 5.46/5.67 & ( A3 != B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_order_iff
% 5.46/5.67 thf(fact_3795_max_Ostrict__order__iff,axiom,
% 5.46/5.67 ( ord_less_int
% 5.46/5.67 = ( ^ [B2: int,A3: int] :
% 5.46/5.67 ( ( A3
% 5.46/5.67 = ( ord_max_int @ A3 @ B2 ) )
% 5.46/5.67 & ( A3 != B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_order_iff
% 5.46/5.67 thf(fact_3796_max_Ostrict__coboundedI1,axiom,
% 5.46/5.67 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.46/5.67 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.46/5.67 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI1
% 5.46/5.67 thf(fact_3797_max_Ostrict__coboundedI1,axiom,
% 5.46/5.67 ! [C: real,A: real,B: real] :
% 5.46/5.67 ( ( ord_less_real @ C @ A )
% 5.46/5.67 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI1
% 5.46/5.67 thf(fact_3798_max_Ostrict__coboundedI1,axiom,
% 5.46/5.67 ! [C: rat,A: rat,B: rat] :
% 5.46/5.67 ( ( ord_less_rat @ C @ A )
% 5.46/5.67 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI1
% 5.46/5.67 thf(fact_3799_max_Ostrict__coboundedI1,axiom,
% 5.46/5.67 ! [C: num,A: num,B: num] :
% 5.46/5.67 ( ( ord_less_num @ C @ A )
% 5.46/5.67 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI1
% 5.46/5.67 thf(fact_3800_max_Ostrict__coboundedI1,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B: nat] :
% 5.46/5.67 ( ( ord_less_nat @ C @ A )
% 5.46/5.67 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI1
% 5.46/5.67 thf(fact_3801_max_Ostrict__coboundedI1,axiom,
% 5.46/5.67 ! [C: int,A: int,B: int] :
% 5.46/5.67 ( ( ord_less_int @ C @ A )
% 5.46/5.67 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI1
% 5.46/5.67 thf(fact_3802_max_Ostrict__coboundedI2,axiom,
% 5.46/5.67 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.46/5.67 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.46/5.67 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI2
% 5.46/5.67 thf(fact_3803_max_Ostrict__coboundedI2,axiom,
% 5.46/5.67 ! [C: real,B: real,A: real] :
% 5.46/5.67 ( ( ord_less_real @ C @ B )
% 5.46/5.67 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI2
% 5.46/5.67 thf(fact_3804_max_Ostrict__coboundedI2,axiom,
% 5.46/5.67 ! [C: rat,B: rat,A: rat] :
% 5.46/5.67 ( ( ord_less_rat @ C @ B )
% 5.46/5.67 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI2
% 5.46/5.67 thf(fact_3805_max_Ostrict__coboundedI2,axiom,
% 5.46/5.67 ! [C: num,B: num,A: num] :
% 5.46/5.67 ( ( ord_less_num @ C @ B )
% 5.46/5.67 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI2
% 5.46/5.67 thf(fact_3806_max_Ostrict__coboundedI2,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( ord_less_nat @ C @ B )
% 5.46/5.67 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI2
% 5.46/5.67 thf(fact_3807_max_Ostrict__coboundedI2,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( ord_less_int @ C @ B )
% 5.46/5.67 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max.strict_coboundedI2
% 5.46/5.67 thf(fact_3808_max__add__distrib__left,axiom,
% 5.46/5.67 ! [X2: real,Y2: real,Z: real] :
% 5.46/5.67 ( ( plus_plus_real @ ( ord_max_real @ X2 @ Y2 ) @ Z )
% 5.46/5.67 = ( ord_max_real @ ( plus_plus_real @ X2 @ Z ) @ ( plus_plus_real @ Y2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_add_distrib_left
% 5.46/5.67 thf(fact_3809_max__add__distrib__left,axiom,
% 5.46/5.67 ! [X2: rat,Y2: rat,Z: rat] :
% 5.46/5.67 ( ( plus_plus_rat @ ( ord_max_rat @ X2 @ Y2 ) @ Z )
% 5.46/5.67 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Z ) @ ( plus_plus_rat @ Y2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_add_distrib_left
% 5.46/5.67 thf(fact_3810_max__add__distrib__left,axiom,
% 5.46/5.67 ! [X2: nat,Y2: nat,Z: nat] :
% 5.46/5.67 ( ( plus_plus_nat @ ( ord_max_nat @ X2 @ Y2 ) @ Z )
% 5.46/5.67 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Z ) @ ( plus_plus_nat @ Y2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_add_distrib_left
% 5.46/5.67 thf(fact_3811_max__add__distrib__left,axiom,
% 5.46/5.67 ! [X2: int,Y2: int,Z: int] :
% 5.46/5.67 ( ( plus_plus_int @ ( ord_max_int @ X2 @ Y2 ) @ Z )
% 5.46/5.67 = ( ord_max_int @ ( plus_plus_int @ X2 @ Z ) @ ( plus_plus_int @ Y2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_add_distrib_left
% 5.46/5.67 thf(fact_3812_max__add__distrib__right,axiom,
% 5.46/5.67 ! [X2: real,Y2: real,Z: real] :
% 5.46/5.67 ( ( plus_plus_real @ X2 @ ( ord_max_real @ Y2 @ Z ) )
% 5.46/5.67 = ( ord_max_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( plus_plus_real @ X2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_add_distrib_right
% 5.46/5.67 thf(fact_3813_max__add__distrib__right,axiom,
% 5.46/5.67 ! [X2: rat,Y2: rat,Z: rat] :
% 5.46/5.67 ( ( plus_plus_rat @ X2 @ ( ord_max_rat @ Y2 @ Z ) )
% 5.46/5.67 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Y2 ) @ ( plus_plus_rat @ X2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_add_distrib_right
% 5.46/5.67 thf(fact_3814_max__add__distrib__right,axiom,
% 5.46/5.67 ! [X2: nat,Y2: nat,Z: nat] :
% 5.46/5.67 ( ( plus_plus_nat @ X2 @ ( ord_max_nat @ Y2 @ Z ) )
% 5.46/5.67 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Y2 ) @ ( plus_plus_nat @ X2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_add_distrib_right
% 5.46/5.67 thf(fact_3815_max__add__distrib__right,axiom,
% 5.46/5.67 ! [X2: int,Y2: int,Z: int] :
% 5.46/5.67 ( ( plus_plus_int @ X2 @ ( ord_max_int @ Y2 @ Z ) )
% 5.46/5.67 = ( ord_max_int @ ( plus_plus_int @ X2 @ Y2 ) @ ( plus_plus_int @ X2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_add_distrib_right
% 5.46/5.67 thf(fact_3816_max__diff__distrib__left,axiom,
% 5.46/5.67 ! [X2: rat,Y2: rat,Z: rat] :
% 5.46/5.67 ( ( minus_minus_rat @ ( ord_max_rat @ X2 @ Y2 ) @ Z )
% 5.46/5.67 = ( ord_max_rat @ ( minus_minus_rat @ X2 @ Z ) @ ( minus_minus_rat @ Y2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_diff_distrib_left
% 5.46/5.67 thf(fact_3817_max__diff__distrib__left,axiom,
% 5.46/5.67 ! [X2: int,Y2: int,Z: int] :
% 5.46/5.67 ( ( minus_minus_int @ ( ord_max_int @ X2 @ Y2 ) @ Z )
% 5.46/5.67 = ( ord_max_int @ ( minus_minus_int @ X2 @ Z ) @ ( minus_minus_int @ Y2 @ Z ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_diff_distrib_left
% 5.46/5.67 thf(fact_3818_nat__add__max__left,axiom,
% 5.46/5.67 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.67 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.46/5.67 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_add_max_left
% 5.46/5.67 thf(fact_3819_nat__add__max__right,axiom,
% 5.46/5.67 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.67 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.46/5.67 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_add_max_right
% 5.46/5.67 thf(fact_3820_nat__mult__max__left,axiom,
% 5.46/5.67 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.67 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.46/5.67 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_mult_max_left
% 5.46/5.67 thf(fact_3821_nat__mult__max__right,axiom,
% 5.46/5.67 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.67 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.46/5.67 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_mult_max_right
% 5.46/5.67 thf(fact_3822_semiring__norm_I26_J,axiom,
% 5.46/5.67 ( ( bitM @ one )
% 5.46/5.67 = one ) ).
% 5.46/5.67
% 5.46/5.67 % semiring_norm(26)
% 5.46/5.67 thf(fact_3823_max__def__raw,axiom,
% 5.46/5.67 ( ord_ma741700101516333627d_enat
% 5.46/5.67 = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_def_raw
% 5.46/5.67 thf(fact_3824_max__def__raw,axiom,
% 5.46/5.67 ( ord_max_set_nat
% 5.46/5.67 = ( ^ [A3: set_nat,B2: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_def_raw
% 5.46/5.67 thf(fact_3825_max__def__raw,axiom,
% 5.46/5.67 ( ord_max_rat
% 5.46/5.67 = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_def_raw
% 5.46/5.67 thf(fact_3826_max__def__raw,axiom,
% 5.46/5.67 ( ord_max_num
% 5.46/5.67 = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_def_raw
% 5.46/5.67 thf(fact_3827_max__def__raw,axiom,
% 5.46/5.67 ( ord_max_nat
% 5.46/5.67 = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_def_raw
% 5.46/5.67 thf(fact_3828_max__def__raw,axiom,
% 5.46/5.67 ( ord_max_int
% 5.46/5.67 = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % max_def_raw
% 5.46/5.67 thf(fact_3829_concat__bit__assoc,axiom,
% 5.46/5.67 ! [N: nat,K: int,M: nat,L2: int,R: int] :
% 5.46/5.67 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
% 5.46/5.67 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R ) ) ).
% 5.46/5.67
% 5.46/5.67 % concat_bit_assoc
% 5.46/5.67 thf(fact_3830_nat__minus__add__max,axiom,
% 5.46/5.67 ! [N: nat,M: nat] :
% 5.46/5.67 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.46/5.67 = ( ord_max_nat @ N @ M ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_minus_add_max
% 5.46/5.67 thf(fact_3831_set__update__subsetI,axiom,
% 5.46/5.67 ! [Xs2: list_P6011104703257516679at_nat,A2: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,I: nat] :
% 5.46/5.67 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 )
% 5.46/5.67 => ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.46/5.67 => ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I @ X2 ) ) @ A2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_subsetI
% 5.46/5.67 thf(fact_3832_set__update__subsetI,axiom,
% 5.46/5.67 ! [Xs2: list_complex,A2: set_complex,X2: complex,I: nat] :
% 5.46/5.67 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 5.46/5.67 => ( ( member_complex @ X2 @ A2 )
% 5.46/5.67 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I @ X2 ) ) @ A2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_subsetI
% 5.46/5.67 thf(fact_3833_set__update__subsetI,axiom,
% 5.46/5.67 ! [Xs2: list_real,A2: set_real,X2: real,I: nat] :
% 5.46/5.67 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A2 )
% 5.46/5.67 => ( ( member_real @ X2 @ A2 )
% 5.46/5.67 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I @ X2 ) ) @ A2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_subsetI
% 5.46/5.67 thf(fact_3834_set__update__subsetI,axiom,
% 5.46/5.67 ! [Xs2: list_int,A2: set_int,X2: int,I: nat] :
% 5.46/5.67 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 5.46/5.67 => ( ( member_int @ X2 @ A2 )
% 5.46/5.67 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I @ X2 ) ) @ A2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_subsetI
% 5.46/5.67 thf(fact_3835_set__update__subsetI,axiom,
% 5.46/5.67 ! [Xs2: list_VEBT_VEBT,A2: set_VEBT_VEBT,X2: vEBT_VEBT,I: nat] :
% 5.46/5.67 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 5.46/5.67 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.67 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) ) @ A2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_subsetI
% 5.46/5.67 thf(fact_3836_set__update__subsetI,axiom,
% 5.46/5.67 ! [Xs2: list_nat,A2: set_nat,X2: nat,I: nat] :
% 5.46/5.67 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 5.46/5.67 => ( ( member_nat @ X2 @ A2 )
% 5.46/5.67 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I @ X2 ) ) @ A2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_subsetI
% 5.46/5.67 thf(fact_3837_dbl__def,axiom,
% 5.46/5.67 ( neg_numeral_dbl_real
% 5.46/5.67 = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dbl_def
% 5.46/5.67 thf(fact_3838_dbl__def,axiom,
% 5.46/5.67 ( neg_numeral_dbl_rat
% 5.46/5.67 = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dbl_def
% 5.46/5.67 thf(fact_3839_dbl__def,axiom,
% 5.46/5.67 ( neg_numeral_dbl_int
% 5.46/5.67 = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dbl_def
% 5.46/5.67 thf(fact_3840_semiring__norm_I28_J,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( ( bitM @ ( bit1 @ N ) )
% 5.46/5.67 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % semiring_norm(28)
% 5.46/5.67 thf(fact_3841_semiring__norm_I27_J,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( ( bitM @ ( bit0 @ N ) )
% 5.46/5.67 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % semiring_norm(27)
% 5.46/5.67 thf(fact_3842_set__update__memI,axiom,
% 5.46/5.67 ! [N: nat,Xs2: list_P6011104703257516679at_nat,X2: product_prod_nat_nat] :
% 5.46/5.67 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.46/5.67 => ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_memI
% 5.46/5.67 thf(fact_3843_set__update__memI,axiom,
% 5.46/5.67 ! [N: nat,Xs2: list_complex,X2: complex] :
% 5.46/5.67 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.46/5.67 => ( member_complex @ X2 @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_memI
% 5.46/5.67 thf(fact_3844_set__update__memI,axiom,
% 5.46/5.67 ! [N: nat,Xs2: list_real,X2: real] :
% 5.46/5.67 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.46/5.67 => ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_memI
% 5.46/5.67 thf(fact_3845_set__update__memI,axiom,
% 5.46/5.67 ! [N: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.46/5.67 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.67 => ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_memI
% 5.46/5.67 thf(fact_3846_set__update__memI,axiom,
% 5.46/5.67 ! [N: nat,Xs2: list_o,X2: $o] :
% 5.46/5.67 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.67 => ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_memI
% 5.46/5.67 thf(fact_3847_set__update__memI,axiom,
% 5.46/5.67 ! [N: nat,Xs2: list_nat,X2: nat] :
% 5.46/5.67 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.67 => ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_memI
% 5.46/5.67 thf(fact_3848_set__update__memI,axiom,
% 5.46/5.67 ! [N: nat,Xs2: list_int,X2: int] :
% 5.46/5.67 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.67 => ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_update_memI
% 5.46/5.67 thf(fact_3849_list__update__same__conv,axiom,
% 5.46/5.67 ! [I: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.46/5.67 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.67 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 )
% 5.46/5.67 = Xs2 )
% 5.46/5.67 = ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 5.46/5.67 = X2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % list_update_same_conv
% 5.46/5.67 thf(fact_3850_list__update__same__conv,axiom,
% 5.46/5.67 ! [I: nat,Xs2: list_o,X2: $o] :
% 5.46/5.67 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.67 => ( ( ( list_update_o @ Xs2 @ I @ X2 )
% 5.46/5.67 = Xs2 )
% 5.46/5.67 = ( ( nth_o @ Xs2 @ I )
% 5.46/5.67 = X2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % list_update_same_conv
% 5.46/5.67 thf(fact_3851_list__update__same__conv,axiom,
% 5.46/5.67 ! [I: nat,Xs2: list_nat,X2: nat] :
% 5.46/5.67 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.67 => ( ( ( list_update_nat @ Xs2 @ I @ X2 )
% 5.46/5.67 = Xs2 )
% 5.46/5.67 = ( ( nth_nat @ Xs2 @ I )
% 5.46/5.67 = X2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % list_update_same_conv
% 5.46/5.67 thf(fact_3852_list__update__same__conv,axiom,
% 5.46/5.67 ! [I: nat,Xs2: list_int,X2: int] :
% 5.46/5.67 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.67 => ( ( ( list_update_int @ Xs2 @ I @ X2 )
% 5.46/5.67 = Xs2 )
% 5.46/5.67 = ( ( nth_int @ Xs2 @ I )
% 5.46/5.67 = X2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % list_update_same_conv
% 5.46/5.67 thf(fact_3853_nth__list__update,axiom,
% 5.46/5.67 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat,X2: vEBT_VEBT] :
% 5.46/5.67 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.67 => ( ( ( I = J )
% 5.46/5.67 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ J )
% 5.46/5.67 = X2 ) )
% 5.46/5.67 & ( ( I != J )
% 5.46/5.67 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ J )
% 5.46/5.67 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nth_list_update
% 5.46/5.67 thf(fact_3854_nth__list__update,axiom,
% 5.46/5.67 ! [I: nat,Xs2: list_o,X2: $o,J: nat] :
% 5.46/5.67 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.67 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X2 ) @ J )
% 5.46/5.67 = ( ( ( I = J )
% 5.46/5.67 => X2 )
% 5.46/5.67 & ( ( I != J )
% 5.46/5.67 => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nth_list_update
% 5.46/5.67 thf(fact_3855_nth__list__update,axiom,
% 5.46/5.67 ! [I: nat,Xs2: list_nat,J: nat,X2: nat] :
% 5.46/5.67 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.67 => ( ( ( I = J )
% 5.46/5.67 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ J )
% 5.46/5.67 = X2 ) )
% 5.46/5.67 & ( ( I != J )
% 5.46/5.67 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ J )
% 5.46/5.67 = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nth_list_update
% 5.46/5.67 thf(fact_3856_nth__list__update,axiom,
% 5.46/5.67 ! [I: nat,Xs2: list_int,J: nat,X2: int] :
% 5.46/5.67 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.67 => ( ( ( I = J )
% 5.46/5.67 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X2 ) @ J )
% 5.46/5.67 = X2 ) )
% 5.46/5.67 & ( ( I != J )
% 5.46/5.67 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X2 ) @ J )
% 5.46/5.67 = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nth_list_update
% 5.46/5.67 thf(fact_3857_eval__nat__numeral_I2_J,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.46/5.67 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % eval_nat_numeral(2)
% 5.46/5.67 thf(fact_3858_BitM__plus__one,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.46/5.67 = ( bit0 @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % BitM_plus_one
% 5.46/5.67 thf(fact_3859_one__plus__BitM,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.46/5.67 = ( bit0 @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % one_plus_BitM
% 5.46/5.67 thf(fact_3860_numeral__BitM,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 5.46/5.67 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 5.46/5.67
% 5.46/5.67 % numeral_BitM
% 5.46/5.67 thf(fact_3861_numeral__BitM,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( ( numeral_numeral_real @ ( bitM @ N ) )
% 5.46/5.67 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 5.46/5.67
% 5.46/5.67 % numeral_BitM
% 5.46/5.67 thf(fact_3862_numeral__BitM,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 5.46/5.67 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 5.46/5.67
% 5.46/5.67 % numeral_BitM
% 5.46/5.67 thf(fact_3863_numeral__BitM,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 5.46/5.67 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % numeral_BitM
% 5.46/5.67 thf(fact_3864_Euclid__induct,axiom,
% 5.46/5.67 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.46/5.67 ( ! [A5: nat,B5: nat] :
% 5.46/5.67 ( ( P @ A5 @ B5 )
% 5.46/5.67 = ( P @ B5 @ A5 ) )
% 5.46/5.67 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 5.46/5.67 => ( ! [A5: nat,B5: nat] :
% 5.46/5.67 ( ( P @ A5 @ B5 )
% 5.46/5.67 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 5.46/5.67 => ( P @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % Euclid_induct
% 5.46/5.67 thf(fact_3865_VEBT__internal_Oheight_Ocases,axiom,
% 5.46/5.67 ! [X2: vEBT_VEBT] :
% 5.46/5.67 ( ! [A5: $o,B5: $o] :
% 5.46/5.67 ( X2
% 5.46/5.67 != ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.67 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.67 ( X2
% 5.46/5.67 != ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % VEBT_internal.height.cases
% 5.46/5.67 thf(fact_3866_vebt__insert_Osimps_I5_J,axiom,
% 5.46/5.67 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.46/5.67 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.46/5.67 = ( if_VEBT_VEBT
% 5.46/5.67 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.46/5.67 & ~ ( ( X2 = Mi )
% 5.46/5.67 | ( X2 = Ma ) ) )
% 5.46/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ X2 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.46/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % vebt_insert.simps(5)
% 5.46/5.67 thf(fact_3867_vebt__insert_Oelims,axiom,
% 5.46/5.67 ! [X2: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 5.46/5.67 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 5.46/5.67 = Y2 )
% 5.46/5.67 => ( ! [A5: $o,B5: $o] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.67 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.67 => ( Y2
% 5.46/5.67 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.46/5.67 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.67 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.67 => ( Y2
% 5.46/5.67 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.46/5.67 & ( ( Xa2 != one_one_nat )
% 5.46/5.67 => ( Y2
% 5.46/5.67 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) ) )
% 5.46/5.67 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 5.46/5.67 => ( Y2
% 5.46/5.67 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) ) )
% 5.46/5.67 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.46/5.67 => ( Y2
% 5.46/5.67 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) ) )
% 5.46/5.67 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.67 => ( Y2
% 5.46/5.67 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.46/5.67 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.67 => ( Y2
% 5.46/5.67 != ( if_VEBT_VEBT
% 5.46/5.67 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.67 & ~ ( ( Xa2 = Mi2 )
% 5.46/5.67 | ( Xa2 = Ma2 ) ) )
% 5.46/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.46/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % vebt_insert.elims
% 5.46/5.67 thf(fact_3868_vebt__insert_Opelims,axiom,
% 5.46/5.67 ! [X2: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 5.46/5.67 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 5.46/5.67 = Y2 )
% 5.46/5.67 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.67 => ( ! [A5: $o,B5: $o] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.67 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.67 => ( Y2
% 5.46/5.67 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.46/5.67 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.67 => ( ( ( Xa2 = one_one_nat )
% 5.46/5.67 => ( Y2
% 5.46/5.67 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.46/5.67 & ( ( Xa2 != one_one_nat )
% 5.46/5.67 => ( Y2
% 5.46/5.67 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) )
% 5.46/5.67 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.46/5.67 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 5.46/5.67 => ( ( Y2
% 5.46/5.67 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 5.46/5.67 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa2 ) ) ) )
% 5.46/5.67 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.46/5.67 => ( ( Y2
% 5.46/5.67 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.46/5.67 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa2 ) ) ) )
% 5.46/5.67 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.67 => ( ( Y2
% 5.46/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.67 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 5.46/5.67 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) )
% 5.46/5.67 => ( ( Y2
% 5.46/5.67 = ( if_VEBT_VEBT
% 5.46/5.67 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.67 & ~ ( ( Xa2 = Mi2 )
% 5.46/5.67 | ( Xa2 = Ma2 ) ) )
% 5.46/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.46/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.46/5.67 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % vebt_insert.pelims
% 5.46/5.67 thf(fact_3869_even__succ__mod__exp,axiom,
% 5.46/5.67 ! [A: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_mod_exp
% 5.46/5.67 thf(fact_3870_even__succ__mod__exp,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_mod_exp
% 5.46/5.67 thf(fact_3871_even__succ__mod__exp,axiom,
% 5.46/5.67 ! [A: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_mod_exp
% 5.46/5.67 thf(fact_3872_divmod__algorithm__code_I6_J,axiom,
% 5.46/5.67 ! [M: num,N: num] :
% 5.46/5.67 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.67 = ( produc4245557441103728435nt_int
% 5.46/5.67 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.46/5.67 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_algorithm_code(6)
% 5.46/5.67 thf(fact_3873_divmod__algorithm__code_I6_J,axiom,
% 5.46/5.67 ! [M: num,N: num] :
% 5.46/5.67 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.67 = ( produc2626176000494625587at_nat
% 5.46/5.67 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.46/5.67 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_algorithm_code(6)
% 5.46/5.67 thf(fact_3874_divmod__algorithm__code_I6_J,axiom,
% 5.46/5.67 ! [M: num,N: num] :
% 5.46/5.67 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.67 = ( produc6916734918728496179nteger
% 5.46/5.67 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 5.46/5.67 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_algorithm_code(6)
% 5.46/5.67 thf(fact_3875_even__succ__div__exp,axiom,
% 5.46/5.67 ! [A: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_exp
% 5.46/5.67 thf(fact_3876_even__succ__div__exp,axiom,
% 5.46/5.67 ! [A: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_exp
% 5.46/5.67 thf(fact_3877_even__succ__div__exp,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_exp
% 5.46/5.67 thf(fact_3878_option_Osize__gen_I2_J,axiom,
% 5.46/5.67 ! [X2: product_prod_nat_nat > nat,X23: product_prod_nat_nat] :
% 5.46/5.67 ( ( size_o8335143837870341156at_nat @ X2 @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.46/5.67 = ( plus_plus_nat @ ( X2 @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % option.size_gen(2)
% 5.46/5.67 thf(fact_3879_option_Osize__gen_I2_J,axiom,
% 5.46/5.67 ! [X2: nat > nat,X23: nat] :
% 5.46/5.67 ( ( size_option_nat @ X2 @ ( some_nat @ X23 ) )
% 5.46/5.67 = ( plus_plus_nat @ ( X2 @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % option.size_gen(2)
% 5.46/5.67 thf(fact_3880_option_Osize__gen_I2_J,axiom,
% 5.46/5.67 ! [X2: num > nat,X23: num] :
% 5.46/5.67 ( ( size_option_num @ X2 @ ( some_num @ X23 ) )
% 5.46/5.67 = ( plus_plus_nat @ ( X2 @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % option.size_gen(2)
% 5.46/5.67 thf(fact_3881_signed__take__bit__Suc,axiom,
% 5.46/5.67 ! [N: nat,A: code_integer] :
% 5.46/5.67 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.46/5.67 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_Suc
% 5.46/5.67 thf(fact_3882_signed__take__bit__Suc,axiom,
% 5.46/5.67 ! [N: nat,A: int] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.46/5.67 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_Suc
% 5.46/5.67 thf(fact_3883_nat__dvd__1__iff__1,axiom,
% 5.46/5.67 ! [M: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.46/5.67 = ( M = one_one_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_dvd_1_iff_1
% 5.46/5.67 thf(fact_3884_max__enat__simps_I2_J,axiom,
% 5.46/5.67 ! [Q2: extended_enat] :
% 5.46/5.67 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.46/5.67 = Q2 ) ).
% 5.46/5.67
% 5.46/5.67 % max_enat_simps(2)
% 5.46/5.67 thf(fact_3885_max__enat__simps_I3_J,axiom,
% 5.46/5.67 ! [Q2: extended_enat] :
% 5.46/5.67 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.46/5.67 = Q2 ) ).
% 5.46/5.67
% 5.46/5.67 % max_enat_simps(3)
% 5.46/5.67 thf(fact_3886_dvd__0__left__iff,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.46/5.67 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left_iff
% 5.46/5.67 thf(fact_3887_dvd__0__left__iff,axiom,
% 5.46/5.67 ! [A: complex] :
% 5.46/5.67 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.46/5.67 = ( A = zero_zero_complex ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left_iff
% 5.46/5.67 thf(fact_3888_dvd__0__left__iff,axiom,
% 5.46/5.67 ! [A: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.46/5.67 = ( A = zero_zero_real ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left_iff
% 5.46/5.67 thf(fact_3889_dvd__0__left__iff,axiom,
% 5.46/5.67 ! [A: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.46/5.67 = ( A = zero_zero_rat ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left_iff
% 5.46/5.67 thf(fact_3890_dvd__0__left__iff,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.46/5.67 = ( A = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left_iff
% 5.46/5.67 thf(fact_3891_dvd__0__left__iff,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.46/5.67 = ( A = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left_iff
% 5.46/5.67 thf(fact_3892_dvd__0__right,axiom,
% 5.46/5.67 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_right
% 5.46/5.67 thf(fact_3893_dvd__0__right,axiom,
% 5.46/5.67 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_right
% 5.46/5.67 thf(fact_3894_dvd__0__right,axiom,
% 5.46/5.67 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_right
% 5.46/5.67 thf(fact_3895_dvd__0__right,axiom,
% 5.46/5.67 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_right
% 5.46/5.67 thf(fact_3896_dvd__0__right,axiom,
% 5.46/5.67 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_right
% 5.46/5.67 thf(fact_3897_dvd__0__right,axiom,
% 5.46/5.67 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_right
% 5.46/5.67 thf(fact_3898_dvd__1__iff__1,axiom,
% 5.46/5.67 ! [M: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.46/5.67 = ( M
% 5.46/5.67 = ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_1_iff_1
% 5.46/5.67 thf(fact_3899_dvd__1__left,axiom,
% 5.46/5.67 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_1_left
% 5.46/5.67 thf(fact_3900_dvd__add__triv__right__iff,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_right_iff
% 5.46/5.67 thf(fact_3901_dvd__add__triv__right__iff,axiom,
% 5.46/5.67 ! [A: real,B: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.46/5.67 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_right_iff
% 5.46/5.67 thf(fact_3902_dvd__add__triv__right__iff,axiom,
% 5.46/5.67 ! [A: rat,B: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.46/5.67 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_right_iff
% 5.46/5.67 thf(fact_3903_dvd__add__triv__right__iff,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_right_iff
% 5.46/5.67 thf(fact_3904_dvd__add__triv__right__iff,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_right_iff
% 5.46/5.67 thf(fact_3905_dvd__add__triv__left__iff,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_left_iff
% 5.46/5.67 thf(fact_3906_dvd__add__triv__left__iff,axiom,
% 5.46/5.67 ! [A: real,B: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_left_iff
% 5.46/5.67 thf(fact_3907_dvd__add__triv__left__iff,axiom,
% 5.46/5.67 ! [A: rat,B: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_left_iff
% 5.46/5.67 thf(fact_3908_dvd__add__triv__left__iff,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_left_iff
% 5.46/5.67 thf(fact_3909_dvd__add__triv__left__iff,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_triv_left_iff
% 5.46/5.67 thf(fact_3910_div__dvd__div,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_dvd_div
% 5.46/5.67 thf(fact_3911_div__dvd__div,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.46/5.67 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_dvd_div
% 5.46/5.67 thf(fact_3912_div__dvd__div,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.46/5.67 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_dvd_div
% 5.46/5.67 thf(fact_3913_nat__mult__dvd__cancel__disj,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.67 = ( ( K = zero_zero_nat )
% 5.46/5.67 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_mult_dvd_cancel_disj
% 5.46/5.67 thf(fact_3914_signed__take__bit__of__0,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.46/5.67 = zero_zero_int ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_of_0
% 5.46/5.67 thf(fact_3915_case__prod__conv,axiom,
% 5.46/5.67 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.46/5.67 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.46/5.67 = ( F @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_conv
% 5.46/5.67 thf(fact_3916_case__prod__conv,axiom,
% 5.46/5.67 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.46/5.67 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.46/5.67 = ( F @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_conv
% 5.46/5.67 thf(fact_3917_case__prod__conv,axiom,
% 5.46/5.67 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.46/5.67 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.46/5.67 = ( F @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_conv
% 5.46/5.67 thf(fact_3918_case__prod__conv,axiom,
% 5.46/5.67 ! [F: int > int > $o,A: int,B: int] :
% 5.46/5.67 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.46/5.67 = ( F @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_conv
% 5.46/5.67 thf(fact_3919_case__prod__conv,axiom,
% 5.46/5.67 ! [F: int > int > int,A: int,B: int] :
% 5.46/5.67 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.46/5.67 = ( F @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_conv
% 5.46/5.67 thf(fact_3920_dvd__mult__cancel__left,axiom,
% 5.46/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.46/5.67 = ( ( C = zero_z3403309356797280102nteger )
% 5.46/5.67 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_left
% 5.46/5.67 thf(fact_3921_dvd__mult__cancel__left,axiom,
% 5.46/5.67 ! [C: complex,A: complex,B: complex] :
% 5.46/5.67 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.46/5.67 = ( ( C = zero_zero_complex )
% 5.46/5.67 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_left
% 5.46/5.67 thf(fact_3922_dvd__mult__cancel__left,axiom,
% 5.46/5.67 ! [C: real,A: real,B: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.46/5.67 = ( ( C = zero_zero_real )
% 5.46/5.67 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_left
% 5.46/5.67 thf(fact_3923_dvd__mult__cancel__left,axiom,
% 5.46/5.67 ! [C: rat,A: rat,B: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.46/5.67 = ( ( C = zero_zero_rat )
% 5.46/5.67 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_left
% 5.46/5.67 thf(fact_3924_dvd__mult__cancel__left,axiom,
% 5.46/5.67 ! [C: int,A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.46/5.67 = ( ( C = zero_zero_int )
% 5.46/5.67 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_left
% 5.46/5.67 thf(fact_3925_dvd__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.46/5.67 = ( ( C = zero_z3403309356797280102nteger )
% 5.46/5.67 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_right
% 5.46/5.67 thf(fact_3926_dvd__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: complex,C: complex,B: complex] :
% 5.46/5.67 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.46/5.67 = ( ( C = zero_zero_complex )
% 5.46/5.67 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_right
% 5.46/5.67 thf(fact_3927_dvd__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: real,C: real,B: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.46/5.67 = ( ( C = zero_zero_real )
% 5.46/5.67 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_right
% 5.46/5.67 thf(fact_3928_dvd__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: rat,C: rat,B: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.46/5.67 = ( ( C = zero_zero_rat )
% 5.46/5.67 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_right
% 5.46/5.67 thf(fact_3929_dvd__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: int,C: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.46/5.67 = ( ( C = zero_zero_int )
% 5.46/5.67 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel_right
% 5.46/5.67 thf(fact_3930_dvd__times__left__cancel__iff,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_times_left_cancel_iff
% 5.46/5.67 thf(fact_3931_dvd__times__left__cancel__iff,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.46/5.67 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_times_left_cancel_iff
% 5.46/5.67 thf(fact_3932_dvd__times__left__cancel__iff,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.46/5.67 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_times_left_cancel_iff
% 5.46/5.67 thf(fact_3933_dvd__times__right__cancel__iff,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_times_right_cancel_iff
% 5.46/5.67 thf(fact_3934_dvd__times__right__cancel__iff,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.46/5.67 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_times_right_cancel_iff
% 5.46/5.67 thf(fact_3935_dvd__times__right__cancel__iff,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.46/5.67 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_times_right_cancel_iff
% 5.46/5.67 thf(fact_3936_unit__prod,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_prod
% 5.46/5.67 thf(fact_3937_unit__prod,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_prod
% 5.46/5.67 thf(fact_3938_unit__prod,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_prod
% 5.46/5.67 thf(fact_3939_dvd__add__times__triv__right__iff,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_right_iff
% 5.46/5.67 thf(fact_3940_dvd__add__times__triv__right__iff,axiom,
% 5.46/5.67 ! [A: real,B: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.46/5.67 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_right_iff
% 5.46/5.67 thf(fact_3941_dvd__add__times__triv__right__iff,axiom,
% 5.46/5.67 ! [A: rat,B: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.46/5.67 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_right_iff
% 5.46/5.67 thf(fact_3942_dvd__add__times__triv__right__iff,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_right_iff
% 5.46/5.67 thf(fact_3943_dvd__add__times__triv__right__iff,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_right_iff
% 5.46/5.67 thf(fact_3944_dvd__add__times__triv__left__iff,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_left_iff
% 5.46/5.67 thf(fact_3945_dvd__add__times__triv__left__iff,axiom,
% 5.46/5.67 ! [A: real,C: real,B: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.46/5.67 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_left_iff
% 5.46/5.67 thf(fact_3946_dvd__add__times__triv__left__iff,axiom,
% 5.46/5.67 ! [A: rat,C: rat,B: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.46/5.67 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_left_iff
% 5.46/5.67 thf(fact_3947_dvd__add__times__triv__left__iff,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_left_iff
% 5.46/5.67 thf(fact_3948_dvd__add__times__triv__left__iff,axiom,
% 5.46/5.67 ! [A: int,C: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_times_triv_left_iff
% 5.46/5.67 thf(fact_3949_dvd__mult__div__cancel,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.46/5.67 = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_div_cancel
% 5.46/5.67 thf(fact_3950_dvd__mult__div__cancel,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.46/5.67 = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_div_cancel
% 5.46/5.67 thf(fact_3951_dvd__mult__div__cancel,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.46/5.67 = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_div_cancel
% 5.46/5.67 thf(fact_3952_dvd__div__mult__self,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.46/5.67 = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_mult_self
% 5.46/5.67 thf(fact_3953_dvd__div__mult__self,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.46/5.67 = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_mult_self
% 5.46/5.67 thf(fact_3954_dvd__div__mult__self,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.46/5.67 = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_mult_self
% 5.46/5.67 thf(fact_3955_unit__div__1__div__1,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.46/5.67 = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_1_div_1
% 5.46/5.67 thf(fact_3956_unit__div__1__div__1,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.46/5.67 = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_1_div_1
% 5.46/5.67 thf(fact_3957_unit__div__1__div__1,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.46/5.67 = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_1_div_1
% 5.46/5.67 thf(fact_3958_unit__div__1__unit,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_1_unit
% 5.46/5.67 thf(fact_3959_unit__div__1__unit,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_1_unit
% 5.46/5.67 thf(fact_3960_unit__div__1__unit,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_1_unit
% 5.46/5.67 thf(fact_3961_unit__div,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div
% 5.46/5.67 thf(fact_3962_unit__div,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div
% 5.46/5.67 thf(fact_3963_unit__div,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div
% 5.46/5.67 thf(fact_3964_div__add,axiom,
% 5.46/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.46/5.67 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_add
% 5.46/5.67 thf(fact_3965_div__add,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.46/5.67 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_add
% 5.46/5.67 thf(fact_3966_div__add,axiom,
% 5.46/5.67 ! [C: int,A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.46/5.67 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_add
% 5.46/5.67 thf(fact_3967_div__diff,axiom,
% 5.46/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.46/5.67 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_diff
% 5.46/5.67 thf(fact_3968_div__diff,axiom,
% 5.46/5.67 ! [C: int,A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.46/5.67 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_diff
% 5.46/5.67 thf(fact_3969_dvd__imp__mod__0,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( modulo_modulo_nat @ B @ A )
% 5.46/5.67 = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_imp_mod_0
% 5.46/5.67 thf(fact_3970_dvd__imp__mod__0,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( modulo_modulo_int @ B @ A )
% 5.46/5.67 = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_imp_mod_0
% 5.46/5.67 thf(fact_3971_dvd__imp__mod__0,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ B @ A )
% 5.46/5.67 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_imp_mod_0
% 5.46/5.67 thf(fact_3972_signed__take__bit__Suc__1,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.46/5.67 = one_one_int ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_Suc_1
% 5.46/5.67 thf(fact_3973_signed__take__bit__numeral__of__1,axiom,
% 5.46/5.67 ! [K: num] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.46/5.67 = one_one_int ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_numeral_of_1
% 5.46/5.67 thf(fact_3974_even__Suc__Suc__iff,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.46/5.67 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_Suc_Suc_iff
% 5.46/5.67 thf(fact_3975_even__Suc,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_Suc
% 5.46/5.67 thf(fact_3976_unit__div__mult__self,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.46/5.67 = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_mult_self
% 5.46/5.67 thf(fact_3977_unit__div__mult__self,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.46/5.67 = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_mult_self
% 5.46/5.67 thf(fact_3978_unit__div__mult__self,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.46/5.67 = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_mult_self
% 5.46/5.67 thf(fact_3979_unit__mult__div__div,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_mult_div_div
% 5.46/5.67 thf(fact_3980_unit__mult__div__div,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.46/5.67 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_mult_div_div
% 5.46/5.67 thf(fact_3981_unit__mult__div__div,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.46/5.67 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_mult_div_div
% 5.46/5.67 thf(fact_3982_pow__divides__pow__iff,axiom,
% 5.46/5.67 ! [N: nat,A: nat,B: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pow_divides_pow_iff
% 5.46/5.67 thf(fact_3983_pow__divides__pow__iff,axiom,
% 5.46/5.67 ! [N: nat,A: int,B: int] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pow_divides_pow_iff
% 5.46/5.67 thf(fact_3984_even__mult__iff,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mult_iff
% 5.46/5.67 thf(fact_3985_even__mult__iff,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mult_iff
% 5.46/5.67 thf(fact_3986_even__mult__iff,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mult_iff
% 5.46/5.67 thf(fact_3987_even__add,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_add
% 5.46/5.67 thf(fact_3988_even__add,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_add
% 5.46/5.67 thf(fact_3989_even__add,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_add
% 5.46/5.67 thf(fact_3990_odd__add,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.46/5.67 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.67 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_add
% 5.46/5.67 thf(fact_3991_odd__add,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.46/5.67 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.67 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_add
% 5.46/5.67 thf(fact_3992_odd__add,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.46/5.67 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.67 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_add
% 5.46/5.67 thf(fact_3993_even__mod__2__iff,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.67 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mod_2_iff
% 5.46/5.67 thf(fact_3994_even__mod__2__iff,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.46/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mod_2_iff
% 5.46/5.67 thf(fact_3995_even__mod__2__iff,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mod_2_iff
% 5.46/5.67 thf(fact_3996_even__Suc__div__two,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_Suc_div_two
% 5.46/5.67 thf(fact_3997_odd__Suc__div__two,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_Suc_div_two
% 5.46/5.67 thf(fact_3998_signed__take__bit__Suc__bit0,axiom,
% 5.46/5.67 ! [N: nat,K: num] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.46/5.67 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_Suc_bit0
% 5.46/5.67 thf(fact_3999_dvd__numeral__simp,axiom,
% 5.46/5.67 ! [M: num,N: num] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.67 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_numeral_simp
% 5.46/5.67 thf(fact_4000_dvd__numeral__simp,axiom,
% 5.46/5.67 ! [M: num,N: num] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.67 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_numeral_simp
% 5.46/5.67 thf(fact_4001_dvd__numeral__simp,axiom,
% 5.46/5.67 ! [M: num,N: num] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.67 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_numeral_simp
% 5.46/5.67 thf(fact_4002_zero__le__power__eq__numeral,axiom,
% 5.46/5.67 ! [A: real,W: num] :
% 5.46/5.67 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_power_eq_numeral
% 5.46/5.67 thf(fact_4003_zero__le__power__eq__numeral,axiom,
% 5.46/5.67 ! [A: rat,W: num] :
% 5.46/5.67 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_power_eq_numeral
% 5.46/5.67 thf(fact_4004_zero__le__power__eq__numeral,axiom,
% 5.46/5.67 ! [A: int,W: num] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_power_eq_numeral
% 5.46/5.67 thf(fact_4005_power__less__zero__eq__numeral,axiom,
% 5.46/5.67 ! [A: real,W: num] :
% 5.46/5.67 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_less_zero_eq_numeral
% 5.46/5.67 thf(fact_4006_power__less__zero__eq__numeral,axiom,
% 5.46/5.67 ! [A: rat,W: num] :
% 5.46/5.67 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_less_zero_eq_numeral
% 5.46/5.67 thf(fact_4007_power__less__zero__eq__numeral,axiom,
% 5.46/5.67 ! [A: int,W: num] :
% 5.46/5.67 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_less_zero_eq_numeral
% 5.46/5.67 thf(fact_4008_power__less__zero__eq,axiom,
% 5.46/5.67 ! [A: real,N: nat] :
% 5.46/5.67 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_less_zero_eq
% 5.46/5.67 thf(fact_4009_power__less__zero__eq,axiom,
% 5.46/5.67 ! [A: rat,N: nat] :
% 5.46/5.67 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_less_zero_eq
% 5.46/5.67 thf(fact_4010_power__less__zero__eq,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_less_zero_eq
% 5.46/5.67 thf(fact_4011_even__plus__one__iff,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_plus_one_iff
% 5.46/5.67 thf(fact_4012_even__plus__one__iff,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_plus_one_iff
% 5.46/5.67 thf(fact_4013_even__plus__one__iff,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_plus_one_iff
% 5.46/5.67 thf(fact_4014_even__diff,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_diff
% 5.46/5.67 thf(fact_4015_even__diff,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_diff
% 5.46/5.67 thf(fact_4016_odd__Suc__minus__one,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.46/5.67 = N ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_Suc_minus_one
% 5.46/5.67 thf(fact_4017_even__diff__nat,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.67 = ( ( ord_less_nat @ M @ N )
% 5.46/5.67 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_diff_nat
% 5.46/5.67 thf(fact_4018_zero__less__power__eq__numeral,axiom,
% 5.46/5.67 ! [A: real,W: num] :
% 5.46/5.67 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.46/5.67 = ( ( ( numeral_numeral_nat @ W )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( A != zero_zero_real ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_power_eq_numeral
% 5.46/5.67 thf(fact_4019_zero__less__power__eq__numeral,axiom,
% 5.46/5.67 ! [A: rat,W: num] :
% 5.46/5.67 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.46/5.67 = ( ( ( numeral_numeral_nat @ W )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( A != zero_zero_rat ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_power_eq_numeral
% 5.46/5.67 thf(fact_4020_zero__less__power__eq__numeral,axiom,
% 5.46/5.67 ! [A: int,W: num] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.46/5.67 = ( ( ( numeral_numeral_nat @ W )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( A != zero_zero_int ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_power_eq_numeral
% 5.46/5.67 thf(fact_4021_even__succ__div__2,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_2
% 5.46/5.67 thf(fact_4022_even__succ__div__2,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_2
% 5.46/5.67 thf(fact_4023_even__succ__div__2,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_2
% 5.46/5.67 thf(fact_4024_even__succ__div__two,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_two
% 5.46/5.67 thf(fact_4025_even__succ__div__two,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_two
% 5.46/5.67 thf(fact_4026_even__succ__div__two,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_two
% 5.46/5.67 thf(fact_4027_odd__succ__div__two,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_succ_div_two
% 5.46/5.67 thf(fact_4028_odd__succ__div__two,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_succ_div_two
% 5.46/5.67 thf(fact_4029_odd__succ__div__two,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_succ_div_two
% 5.46/5.67 thf(fact_4030_even__power,axiom,
% 5.46/5.67 ! [A: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_power
% 5.46/5.67 thf(fact_4031_even__power,axiom,
% 5.46/5.67 ! [A: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_power
% 5.46/5.67 thf(fact_4032_even__power,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_power
% 5.46/5.67 thf(fact_4033_odd__two__times__div__two__nat,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.67 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_two_times_div_two_nat
% 5.46/5.67 thf(fact_4034_divmod__algorithm__code_I5_J,axiom,
% 5.46/5.67 ! [M: num,N: num] :
% 5.46/5.67 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.46/5.67 = ( produc4245557441103728435nt_int
% 5.46/5.67 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.46/5.67 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_algorithm_code(5)
% 5.46/5.67 thf(fact_4035_divmod__algorithm__code_I5_J,axiom,
% 5.46/5.67 ! [M: num,N: num] :
% 5.46/5.67 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.46/5.67 = ( produc2626176000494625587at_nat
% 5.46/5.67 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.46/5.67 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_algorithm_code(5)
% 5.46/5.67 thf(fact_4036_divmod__algorithm__code_I5_J,axiom,
% 5.46/5.67 ! [M: num,N: num] :
% 5.46/5.67 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.46/5.67 = ( produc6916734918728496179nteger
% 5.46/5.67 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 5.46/5.67 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_algorithm_code(5)
% 5.46/5.67 thf(fact_4037_odd__two__times__div__two__succ,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.46/5.67 = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_two_times_div_two_succ
% 5.46/5.67 thf(fact_4038_odd__two__times__div__two__succ,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.46/5.67 = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_two_times_div_two_succ
% 5.46/5.67 thf(fact_4039_odd__two__times__div__two__succ,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.46/5.67 = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_two_times_div_two_succ
% 5.46/5.67 thf(fact_4040_power__le__zero__eq__numeral,axiom,
% 5.46/5.67 ! [A: real,W: num] :
% 5.46/5.67 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq_numeral
% 5.46/5.67 thf(fact_4041_power__le__zero__eq__numeral,axiom,
% 5.46/5.67 ! [A: rat,W: num] :
% 5.46/5.67 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq_numeral
% 5.46/5.67 thf(fact_4042_power__le__zero__eq__numeral,axiom,
% 5.46/5.67 ! [A: int,W: num] :
% 5.46/5.67 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq_numeral
% 5.46/5.67 thf(fact_4043_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.46/5.67 = ( N = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % semiring_parity_class.even_mask_iff
% 5.46/5.67 thf(fact_4044_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.46/5.67 = ( N = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % semiring_parity_class.even_mask_iff
% 5.46/5.67 thf(fact_4045_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.46/5.67 = ( N = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % semiring_parity_class.even_mask_iff
% 5.46/5.67 thf(fact_4046_signed__take__bit__Suc__bit1,axiom,
% 5.46/5.67 ! [N: nat,K: num] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_Suc_bit1
% 5.46/5.67 thf(fact_4047_dvd__trans,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_trans
% 5.46/5.67 thf(fact_4048_dvd__trans,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ C )
% 5.46/5.67 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_trans
% 5.46/5.67 thf(fact_4049_dvd__trans,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_trans
% 5.46/5.67 thf(fact_4050_dvd__refl,axiom,
% 5.46/5.67 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_refl
% 5.46/5.67 thf(fact_4051_dvd__refl,axiom,
% 5.46/5.67 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_refl
% 5.46/5.67 thf(fact_4052_dvd__refl,axiom,
% 5.46/5.67 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_refl
% 5.46/5.67 thf(fact_4053_dvd__0__left,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.46/5.67 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_4054_dvd__0__left,axiom,
% 5.46/5.67 ! [A: complex] :
% 5.46/5.67 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.46/5.67 => ( A = zero_zero_complex ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_4055_dvd__0__left,axiom,
% 5.46/5.67 ! [A: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.46/5.67 => ( A = zero_zero_real ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_4056_dvd__0__left,axiom,
% 5.46/5.67 ! [A: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.46/5.67 => ( A = zero_zero_rat ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_4057_dvd__0__left,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.46/5.67 => ( A = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_4058_dvd__0__left,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.46/5.67 => ( A = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_4059_dvd__field__iff,axiom,
% 5.46/5.67 ( dvd_dvd_complex
% 5.46/5.67 = ( ^ [A3: complex,B2: complex] :
% 5.46/5.67 ( ( A3 = zero_zero_complex )
% 5.46/5.67 => ( B2 = zero_zero_complex ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_field_iff
% 5.46/5.67 thf(fact_4060_dvd__field__iff,axiom,
% 5.46/5.67 ( dvd_dvd_real
% 5.46/5.67 = ( ^ [A3: real,B2: real] :
% 5.46/5.67 ( ( A3 = zero_zero_real )
% 5.46/5.67 => ( B2 = zero_zero_real ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_field_iff
% 5.46/5.67 thf(fact_4061_dvd__field__iff,axiom,
% 5.46/5.67 ( dvd_dvd_rat
% 5.46/5.67 = ( ^ [A3: rat,B2: rat] :
% 5.46/5.67 ( ( A3 = zero_zero_rat )
% 5.46/5.67 => ( B2 = zero_zero_rat ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_field_iff
% 5.46/5.67 thf(fact_4062_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_4063_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_4064_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_4065_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_4066_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_4067_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_4068_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: real,B: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_4069_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: rat,B: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_4070_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_4071_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_4072_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_4073_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_real @ C @ D2 )
% 5.46/5.67 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_4074_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_rat @ C @ D2 )
% 5.46/5.67 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_4075_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ D2 )
% 5.46/5.67 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_4076_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int,D2: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ D2 )
% 5.46/5.67 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_4077_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_4078_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_4079_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_4080_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_4081_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_4082_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_4083_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: real,B: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_4084_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: rat,B: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_4085_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_4086_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.46/5.67 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_4087_dvd__mult2,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_4088_dvd__mult2,axiom,
% 5.46/5.67 ! [A: real,B: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ B )
% 5.46/5.67 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_4089_dvd__mult2,axiom,
% 5.46/5.67 ! [A: rat,B: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ B )
% 5.46/5.67 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_4090_dvd__mult2,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_4091_dvd__mult2,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_4092_dvd__mult,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_4093_dvd__mult,axiom,
% 5.46/5.67 ! [A: real,C: real,B: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ C )
% 5.46/5.67 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_4094_dvd__mult,axiom,
% 5.46/5.67 ! [A: rat,C: rat,B: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ C )
% 5.46/5.67 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_4095_dvd__mult,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_4096_dvd__mult,axiom,
% 5.46/5.67 ! [A: int,C: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ C )
% 5.46/5.67 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_4097_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_Code_integer
% 5.46/5.67 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.46/5.67 ? [K2: code_integer] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( times_3573771949741848930nteger @ B2 @ K2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_4098_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_real
% 5.46/5.67 = ( ^ [B2: real,A3: real] :
% 5.46/5.67 ? [K2: real] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( times_times_real @ B2 @ K2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_4099_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_rat
% 5.46/5.67 = ( ^ [B2: rat,A3: rat] :
% 5.46/5.67 ? [K2: rat] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( times_times_rat @ B2 @ K2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_4100_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_nat
% 5.46/5.67 = ( ^ [B2: nat,A3: nat] :
% 5.46/5.67 ? [K2: nat] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( times_times_nat @ B2 @ K2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_4101_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_int
% 5.46/5.67 = ( ^ [B2: int,A3: int] :
% 5.46/5.67 ? [K2: int] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( times_times_int @ B2 @ K2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_4102_dvdI,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_4103_dvdI,axiom,
% 5.46/5.67 ! [A: real,B: real,K: real] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_real @ B @ K ) )
% 5.46/5.67 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_4104_dvdI,axiom,
% 5.46/5.67 ! [A: rat,B: rat,K: rat] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_rat @ B @ K ) )
% 5.46/5.67 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_4105_dvdI,axiom,
% 5.46/5.67 ! [A: nat,B: nat,K: nat] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_nat @ B @ K ) )
% 5.46/5.67 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_4106_dvdI,axiom,
% 5.46/5.67 ! [A: int,B: int,K: int] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_int @ B @ K ) )
% 5.46/5.67 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_4107_dvdE,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.67 => ~ ! [K3: code_integer] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_3573771949741848930nteger @ B @ K3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_4108_dvdE,axiom,
% 5.46/5.67 ! [B: real,A: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ B @ A )
% 5.46/5.67 => ~ ! [K3: real] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_real @ B @ K3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_4109_dvdE,axiom,
% 5.46/5.67 ! [B: rat,A: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ B @ A )
% 5.46/5.67 => ~ ! [K3: rat] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_rat @ B @ K3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_4110_dvdE,axiom,
% 5.46/5.67 ! [B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ A )
% 5.46/5.67 => ~ ! [K3: nat] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_nat @ B @ K3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_4111_dvdE,axiom,
% 5.46/5.67 ! [B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ A )
% 5.46/5.67 => ~ ! [K3: int] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_int @ B @ K3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_4112_division__decomp,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.46/5.67 => ? [B8: nat,C5: nat] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_nat @ B8 @ C5 ) )
% 5.46/5.67 & ( dvd_dvd_nat @ B8 @ B )
% 5.46/5.67 & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % division_decomp
% 5.46/5.67 thf(fact_4113_division__decomp,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.46/5.67 => ? [B8: int,C5: int] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_int @ B8 @ C5 ) )
% 5.46/5.67 & ( dvd_dvd_int @ B8 @ B )
% 5.46/5.67 & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % division_decomp
% 5.46/5.67 thf(fact_4114_dvd__productE,axiom,
% 5.46/5.67 ! [P2: nat,A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ P2 @ ( times_times_nat @ A @ B ) )
% 5.46/5.67 => ~ ! [X3: nat,Y3: nat] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( times_times_nat @ X3 @ Y3 ) )
% 5.46/5.67 => ( ( dvd_dvd_nat @ X3 @ A )
% 5.46/5.67 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_productE
% 5.46/5.67 thf(fact_4115_dvd__productE,axiom,
% 5.46/5.67 ! [P2: int,A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ P2 @ ( times_times_int @ A @ B ) )
% 5.46/5.67 => ~ ! [X3: int,Y3: int] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( times_times_int @ X3 @ Y3 ) )
% 5.46/5.67 => ( ( dvd_dvd_int @ X3 @ A )
% 5.46/5.67 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_productE
% 5.46/5.67 thf(fact_4116_dvd__unit__imp__unit,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_unit_imp_unit
% 5.46/5.67 thf(fact_4117_dvd__unit__imp__unit,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_unit_imp_unit
% 5.46/5.67 thf(fact_4118_dvd__unit__imp__unit,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_unit_imp_unit
% 5.46/5.67 thf(fact_4119_unit__imp__dvd,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_dvd
% 5.46/5.67 thf(fact_4120_unit__imp__dvd,axiom,
% 5.46/5.67 ! [B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_dvd
% 5.46/5.67 thf(fact_4121_unit__imp__dvd,axiom,
% 5.46/5.67 ! [B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_dvd
% 5.46/5.67 thf(fact_4122_one__dvd,axiom,
% 5.46/5.67 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_4123_one__dvd,axiom,
% 5.46/5.67 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_4124_one__dvd,axiom,
% 5.46/5.67 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_4125_one__dvd,axiom,
% 5.46/5.67 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_4126_one__dvd,axiom,
% 5.46/5.67 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_4127_one__dvd,axiom,
% 5.46/5.67 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_4128_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_4129_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: real,B: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_4130_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: rat,B: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_4131_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_4132_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_4133_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_4134_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: real,C: real,B: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_4135_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: rat,C: rat,B: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_4136_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_4137_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: int,C: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_4138_dvd__add,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_4139_dvd__add,axiom,
% 5.46/5.67 ! [A: real,B: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_real @ A @ C )
% 5.46/5.67 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_4140_dvd__add,axiom,
% 5.46/5.67 ! [A: rat,B: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_rat @ A @ C )
% 5.46/5.67 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_4141_dvd__add,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_4142_dvd__add,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ C )
% 5.46/5.67 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_4143_dvd__diff__commute,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff_commute
% 5.46/5.67 thf(fact_4144_dvd__diff__commute,axiom,
% 5.46/5.67 ! [A: int,C: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff_commute
% 5.46/5.67 thf(fact_4145_dvd__diff,axiom,
% 5.46/5.67 ! [X2: code_integer,Y2: code_integer,Z: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ X2 @ Y2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ X2 @ Z )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ X2 @ ( minus_8373710615458151222nteger @ Y2 @ Z ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff
% 5.46/5.67 thf(fact_4146_dvd__diff,axiom,
% 5.46/5.67 ! [X2: rat,Y2: rat,Z: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ X2 @ Y2 )
% 5.46/5.67 => ( ( dvd_dvd_rat @ X2 @ Z )
% 5.46/5.67 => ( dvd_dvd_rat @ X2 @ ( minus_minus_rat @ Y2 @ Z ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff
% 5.46/5.67 thf(fact_4147_dvd__diff,axiom,
% 5.46/5.67 ! [X2: int,Y2: int,Z: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ X2 @ Y2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ X2 @ Z )
% 5.46/5.67 => ( dvd_dvd_int @ X2 @ ( minus_minus_int @ Y2 @ Z ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff
% 5.46/5.67 thf(fact_4148_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.46/5.67 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.46/5.67 = ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_4149_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: complex,A: complex,B: complex] :
% 5.46/5.67 ( ( dvd_dvd_complex @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_complex @ C @ B )
% 5.46/5.67 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.46/5.67 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.46/5.67 = ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_4150_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: real,A: real,B: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_real @ C @ B )
% 5.46/5.67 => ( ( ( divide_divide_real @ A @ C )
% 5.46/5.67 = ( divide_divide_real @ B @ C ) )
% 5.46/5.67 = ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_4151_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: rat,A: rat,B: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_rat @ C @ B )
% 5.46/5.67 => ( ( ( divide_divide_rat @ A @ C )
% 5.46/5.67 = ( divide_divide_rat @ B @ C ) )
% 5.46/5.67 = ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_4152_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( ( ( divide_divide_nat @ A @ C )
% 5.46/5.67 = ( divide_divide_nat @ B @ C ) )
% 5.46/5.67 = ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_4153_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: int,A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( ( divide_divide_int @ A @ C )
% 5.46/5.67 = ( divide_divide_int @ B @ C ) )
% 5.46/5.67 = ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_4154_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.46/5.67 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.46/5.67 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_4155_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: complex,C: complex,B: complex] :
% 5.46/5.67 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.46/5.67 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_complex @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_complex @ C @ B )
% 5.46/5.67 => ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_4156_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: real,C: real,B: real] :
% 5.46/5.67 ( ( ( divide_divide_real @ A @ C )
% 5.46/5.67 = ( divide_divide_real @ B @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_real @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_real @ C @ B )
% 5.46/5.67 => ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_4157_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: rat,C: rat,B: rat] :
% 5.46/5.67 ( ( ( divide_divide_rat @ A @ C )
% 5.46/5.67 = ( divide_divide_rat @ B @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_rat @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_rat @ C @ B )
% 5.46/5.67 => ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_4158_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B: nat] :
% 5.46/5.67 ( ( ( divide_divide_nat @ A @ C )
% 5.46/5.67 = ( divide_divide_nat @ B @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_4159_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: int,C: int,B: int] :
% 5.46/5.67 ( ( ( divide_divide_int @ A @ C )
% 5.46/5.67 = ( divide_divide_int @ B @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( A = B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_4160_div__div__div__same,axiom,
% 5.46/5.67 ! [D2: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ D2 @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D2 ) @ ( divide6298287555418463151nteger @ B @ D2 ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_div_div_same
% 5.46/5.67 thf(fact_4161_div__div__div__same,axiom,
% 5.46/5.67 ! [D2: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ D2 @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ A )
% 5.46/5.67 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D2 ) @ ( divide_divide_nat @ B @ D2 ) )
% 5.46/5.67 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_div_div_same
% 5.46/5.67 thf(fact_4162_div__div__div__same,axiom,
% 5.46/5.67 ! [D2: int,B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ D2 @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ A )
% 5.46/5.67 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D2 ) @ ( divide_divide_int @ B @ D2 ) )
% 5.46/5.67 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_div_div_same
% 5.46/5.67 thf(fact_4163_dvd__power__same,axiom,
% 5.46/5.67 ! [X2: code_integer,Y2: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ X2 @ Y2 )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_4164_dvd__power__same,axiom,
% 5.46/5.67 ! [X2: nat,Y2: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ X2 @ Y2 )
% 5.46/5.67 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_4165_dvd__power__same,axiom,
% 5.46/5.67 ! [X2: real,Y2: real,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_real @ X2 @ Y2 )
% 5.46/5.67 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_4166_dvd__power__same,axiom,
% 5.46/5.67 ! [X2: complex,Y2: complex,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_complex @ X2 @ Y2 )
% 5.46/5.67 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_4167_dvd__power__same,axiom,
% 5.46/5.67 ! [X2: int,Y2: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ X2 @ Y2 )
% 5.46/5.67 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_4168_old_Oprod_Ocase,axiom,
% 5.46/5.67 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X23: nat] :
% 5.46/5.67 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 5.46/5.67 = ( F @ X1 @ X23 ) ) ).
% 5.46/5.67
% 5.46/5.67 % old.prod.case
% 5.46/5.67 thf(fact_4169_old_Oprod_Ocase,axiom,
% 5.46/5.67 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X23: nat] :
% 5.46/5.67 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X23 ) )
% 5.46/5.67 = ( F @ X1 @ X23 ) ) ).
% 5.46/5.67
% 5.46/5.67 % old.prod.case
% 5.46/5.67 thf(fact_4170_old_Oprod_Ocase,axiom,
% 5.46/5.67 ! [F: int > int > product_prod_int_int,X1: int,X23: int] :
% 5.46/5.67 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 5.46/5.67 = ( F @ X1 @ X23 ) ) ).
% 5.46/5.67
% 5.46/5.67 % old.prod.case
% 5.46/5.67 thf(fact_4171_old_Oprod_Ocase,axiom,
% 5.46/5.67 ! [F: int > int > $o,X1: int,X23: int] :
% 5.46/5.67 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 5.46/5.67 = ( F @ X1 @ X23 ) ) ).
% 5.46/5.67
% 5.46/5.67 % old.prod.case
% 5.46/5.67 thf(fact_4172_old_Oprod_Ocase,axiom,
% 5.46/5.67 ! [F: int > int > int,X1: int,X23: int] :
% 5.46/5.67 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X23 ) )
% 5.46/5.67 = ( F @ X1 @ X23 ) ) ).
% 5.46/5.67
% 5.46/5.67 % old.prod.case
% 5.46/5.67 thf(fact_4173_mod__mod__cancel,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.46/5.67 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_mod_cancel
% 5.46/5.67 thf(fact_4174_mod__mod__cancel,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.46/5.67 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_mod_cancel
% 5.46/5.67 thf(fact_4175_mod__mod__cancel,axiom,
% 5.46/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.46/5.67 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_mod_cancel
% 5.46/5.67 thf(fact_4176_dvd__mod,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ K @ M )
% 5.46/5.67 => ( ( dvd_dvd_nat @ K @ N )
% 5.46/5.67 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod
% 5.46/5.67 thf(fact_4177_dvd__mod,axiom,
% 5.46/5.67 ! [K: int,M: int,N: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ K @ M )
% 5.46/5.67 => ( ( dvd_dvd_int @ K @ N )
% 5.46/5.67 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod
% 5.46/5.67 thf(fact_4178_dvd__mod,axiom,
% 5.46/5.67 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod
% 5.46/5.67 thf(fact_4179_dvd__mod__imp__dvd,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_imp_dvd
% 5.46/5.67 thf(fact_4180_dvd__mod__imp__dvd,axiom,
% 5.46/5.67 ! [C: int,A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_imp_dvd
% 5.46/5.67 thf(fact_4181_dvd__mod__imp__dvd,axiom,
% 5.46/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_imp_dvd
% 5.46/5.67 thf(fact_4182_dvd__mod__iff,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_iff
% 5.46/5.67 thf(fact_4183_dvd__mod__iff,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_iff
% 5.46/5.67 thf(fact_4184_dvd__mod__iff,axiom,
% 5.46/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_iff
% 5.46/5.67 thf(fact_4185_signed__take__bit__mult,axiom,
% 5.46/5.67 ! [N: nat,K: int,L2: int] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.46/5.67 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_mult
% 5.46/5.67 thf(fact_4186_signed__take__bit__add,axiom,
% 5.46/5.67 ! [N: nat,K: int,L2: int] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.46/5.67 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_add
% 5.46/5.67 thf(fact_4187_dvd__diff__nat,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ K @ M )
% 5.46/5.67 => ( ( dvd_dvd_nat @ K @ N )
% 5.46/5.67 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff_nat
% 5.46/5.67 thf(fact_4188_signed__take__bit__diff,axiom,
% 5.46/5.67 ! [N: nat,K: int,L2: int] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.46/5.67 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_diff
% 5.46/5.67 thf(fact_4189_zdvd__zdiffD,axiom,
% 5.46/5.67 ! [K: int,M: int,N: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 5.46/5.67 => ( ( dvd_dvd_int @ K @ N )
% 5.46/5.67 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdvd_zdiffD
% 5.46/5.67 thf(fact_4190_subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: complex,B: complex] :
% 5.46/5.67 ( ( ord_le211207098394363844omplex
% 5.46/5.67 @ ( collect_complex
% 5.46/5.67 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 5.46/5.67 @ ( collect_complex
% 5.46/5.67 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 5.46/5.67 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % subset_divisors_dvd
% 5.46/5.67 thf(fact_4191_subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: real,B: real] :
% 5.46/5.67 ( ( ord_less_eq_set_real
% 5.46/5.67 @ ( collect_real
% 5.46/5.67 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 5.46/5.67 @ ( collect_real
% 5.46/5.67 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 5.46/5.67 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % subset_divisors_dvd
% 5.46/5.67 thf(fact_4192_subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( ord_less_eq_set_int
% 5.46/5.67 @ ( collect_int
% 5.46/5.67 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.46/5.67 @ ( collect_int
% 5.46/5.67 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % subset_divisors_dvd
% 5.46/5.67 thf(fact_4193_subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( ord_le7084787975880047091nteger
% 5.46/5.67 @ ( collect_Code_integer
% 5.46/5.67 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.46/5.67 @ ( collect_Code_integer
% 5.46/5.67 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % subset_divisors_dvd
% 5.46/5.67 thf(fact_4194_subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( ord_less_eq_set_nat
% 5.46/5.67 @ ( collect_nat
% 5.46/5.67 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.46/5.67 @ ( collect_nat
% 5.46/5.67 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % subset_divisors_dvd
% 5.46/5.67 thf(fact_4195_case__prodE2,axiom,
% 5.46/5.67 ! [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] :
% 5.46/5.67 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.46/5.67 => ~ ! [X3: nat,Y3: nat] :
% 5.46/5.67 ( ( Z
% 5.46/5.67 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.46/5.67 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodE2
% 5.46/5.67 thf(fact_4196_case__prodE2,axiom,
% 5.46/5.67 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.46/5.67 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.46/5.67 => ~ ! [X3: nat,Y3: nat] :
% 5.46/5.67 ( ( Z
% 5.46/5.67 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.46/5.67 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodE2
% 5.46/5.67 thf(fact_4197_case__prodE2,axiom,
% 5.46/5.67 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.46/5.67 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.46/5.67 => ~ ! [X3: int,Y3: int] :
% 5.46/5.67 ( ( Z
% 5.46/5.67 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.46/5.67 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodE2
% 5.46/5.67 thf(fact_4198_case__prodE2,axiom,
% 5.46/5.67 ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 5.46/5.67 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 5.46/5.67 => ~ ! [X3: int,Y3: int] :
% 5.46/5.67 ( ( Z
% 5.46/5.67 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.46/5.67 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodE2
% 5.46/5.67 thf(fact_4199_case__prodE2,axiom,
% 5.46/5.67 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 5.46/5.67 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 5.46/5.67 => ~ ! [X3: int,Y3: int] :
% 5.46/5.67 ( ( Z
% 5.46/5.67 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.46/5.67 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodE2
% 5.46/5.67 thf(fact_4200_case__prod__eta,axiom,
% 5.46/5.67 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.46/5.67 ( ( produc27273713700761075at_nat
% 5.46/5.67 @ ^ [X: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 5.46/5.67 = F ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_eta
% 5.46/5.67 thf(fact_4201_case__prod__eta,axiom,
% 5.46/5.67 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.46/5.67 ( ( produc8739625826339149834_nat_o
% 5.46/5.67 @ ^ [X: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 5.46/5.67 = F ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_eta
% 5.46/5.67 thf(fact_4202_case__prod__eta,axiom,
% 5.46/5.67 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.46/5.67 ( ( produc4245557441103728435nt_int
% 5.46/5.67 @ ^ [X: int,Y: int] : ( F @ ( product_Pair_int_int @ X @ Y ) ) )
% 5.46/5.67 = F ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_eta
% 5.46/5.67 thf(fact_4203_case__prod__eta,axiom,
% 5.46/5.67 ! [F: product_prod_int_int > $o] :
% 5.46/5.67 ( ( produc4947309494688390418_int_o
% 5.46/5.67 @ ^ [X: int,Y: int] : ( F @ ( product_Pair_int_int @ X @ Y ) ) )
% 5.46/5.67 = F ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_eta
% 5.46/5.67 thf(fact_4204_case__prod__eta,axiom,
% 5.46/5.67 ! [F: product_prod_int_int > int] :
% 5.46/5.67 ( ( produc8211389475949308722nt_int
% 5.46/5.67 @ ^ [X: int,Y: int] : ( F @ ( product_Pair_int_int @ X @ Y ) ) )
% 5.46/5.67 = F ) ).
% 5.46/5.67
% 5.46/5.67 % case_prod_eta
% 5.46/5.67 thf(fact_4205_cond__case__prod__eta,axiom,
% 5.46/5.67 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.46/5.67 ( ! [X3: nat,Y3: nat] :
% 5.46/5.67 ( ( F @ X3 @ Y3 )
% 5.46/5.67 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.46/5.67 => ( ( produc27273713700761075at_nat @ F )
% 5.46/5.67 = G ) ) ).
% 5.46/5.67
% 5.46/5.67 % cond_case_prod_eta
% 5.46/5.67 thf(fact_4206_cond__case__prod__eta,axiom,
% 5.46/5.67 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.46/5.67 ( ! [X3: nat,Y3: nat] :
% 5.46/5.67 ( ( F @ X3 @ Y3 )
% 5.46/5.67 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.46/5.67 => ( ( produc8739625826339149834_nat_o @ F )
% 5.46/5.67 = G ) ) ).
% 5.46/5.67
% 5.46/5.67 % cond_case_prod_eta
% 5.46/5.67 thf(fact_4207_cond__case__prod__eta,axiom,
% 5.46/5.67 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.46/5.67 ( ! [X3: int,Y3: int] :
% 5.46/5.67 ( ( F @ X3 @ Y3 )
% 5.46/5.67 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.46/5.67 => ( ( produc4245557441103728435nt_int @ F )
% 5.46/5.67 = G ) ) ).
% 5.46/5.67
% 5.46/5.67 % cond_case_prod_eta
% 5.46/5.67 thf(fact_4208_cond__case__prod__eta,axiom,
% 5.46/5.67 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.46/5.67 ( ! [X3: int,Y3: int] :
% 5.46/5.67 ( ( F @ X3 @ Y3 )
% 5.46/5.67 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.46/5.67 => ( ( produc4947309494688390418_int_o @ F )
% 5.46/5.67 = G ) ) ).
% 5.46/5.67
% 5.46/5.67 % cond_case_prod_eta
% 5.46/5.67 thf(fact_4209_cond__case__prod__eta,axiom,
% 5.46/5.67 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.46/5.67 ( ! [X3: int,Y3: int] :
% 5.46/5.67 ( ( F @ X3 @ Y3 )
% 5.46/5.67 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.46/5.67 => ( ( produc8211389475949308722nt_int @ F )
% 5.46/5.67 = G ) ) ).
% 5.46/5.67
% 5.46/5.67 % cond_case_prod_eta
% 5.46/5.67 thf(fact_4210_strict__subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: complex,B: complex] :
% 5.46/5.67 ( ( ord_less_set_complex
% 5.46/5.67 @ ( collect_complex
% 5.46/5.67 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 5.46/5.67 @ ( collect_complex
% 5.46/5.67 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 5.46/5.67 = ( ( dvd_dvd_complex @ A @ B )
% 5.46/5.67 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % strict_subset_divisors_dvd
% 5.46/5.67 thf(fact_4211_strict__subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: real,B: real] :
% 5.46/5.67 ( ( ord_less_set_real
% 5.46/5.67 @ ( collect_real
% 5.46/5.67 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 5.46/5.67 @ ( collect_real
% 5.46/5.67 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 5.46/5.67 = ( ( dvd_dvd_real @ A @ B )
% 5.46/5.67 & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % strict_subset_divisors_dvd
% 5.46/5.67 thf(fact_4212_strict__subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( ord_less_set_nat
% 5.46/5.67 @ ( collect_nat
% 5.46/5.67 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.46/5.67 @ ( collect_nat
% 5.46/5.67 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % strict_subset_divisors_dvd
% 5.46/5.67 thf(fact_4213_strict__subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( ord_less_set_int
% 5.46/5.67 @ ( collect_int
% 5.46/5.67 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.46/5.67 @ ( collect_int
% 5.46/5.67 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % strict_subset_divisors_dvd
% 5.46/5.67 thf(fact_4214_strict__subset__divisors__dvd,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( ord_le1307284697595431911nteger
% 5.46/5.67 @ ( collect_Code_integer
% 5.46/5.67 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.46/5.67 @ ( collect_Code_integer
% 5.46/5.67 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % strict_subset_divisors_dvd
% 5.46/5.67 thf(fact_4215_even__signed__take__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_signed_take_bit_iff
% 5.46/5.67 thf(fact_4216_even__signed__take__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.46/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_signed_take_bit_iff
% 5.46/5.67 thf(fact_4217_not__is__unit__0,axiom,
% 5.46/5.67 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.46/5.67
% 5.46/5.67 % not_is_unit_0
% 5.46/5.67 thf(fact_4218_not__is__unit__0,axiom,
% 5.46/5.67 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.46/5.67
% 5.46/5.67 % not_is_unit_0
% 5.46/5.67 thf(fact_4219_not__is__unit__0,axiom,
% 5.46/5.67 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.46/5.67
% 5.46/5.67 % not_is_unit_0
% 5.46/5.67 thf(fact_4220_pinf_I9_J,axiom,
% 5.46/5.67 ! [D2: code_integer,S: code_integer] :
% 5.46/5.67 ? [Z3: code_integer] :
% 5.46/5.67 ! [X4: code_integer] :
% 5.46/5.67 ( ( ord_le6747313008572928689nteger @ Z3 @ X4 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(9)
% 5.46/5.67 thf(fact_4221_pinf_I9_J,axiom,
% 5.46/5.67 ! [D2: real,S: real] :
% 5.46/5.67 ? [Z3: real] :
% 5.46/5.67 ! [X4: real] :
% 5.46/5.67 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.67 => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(9)
% 5.46/5.67 thf(fact_4222_pinf_I9_J,axiom,
% 5.46/5.67 ! [D2: rat,S: rat] :
% 5.46/5.67 ? [Z3: rat] :
% 5.46/5.67 ! [X4: rat] :
% 5.46/5.67 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.67 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(9)
% 5.46/5.67 thf(fact_4223_pinf_I9_J,axiom,
% 5.46/5.67 ! [D2: nat,S: nat] :
% 5.46/5.67 ? [Z3: nat] :
% 5.46/5.67 ! [X4: nat] :
% 5.46/5.67 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(9)
% 5.46/5.67 thf(fact_4224_pinf_I9_J,axiom,
% 5.46/5.67 ! [D2: int,S: int] :
% 5.46/5.67 ? [Z3: int] :
% 5.46/5.67 ! [X4: int] :
% 5.46/5.67 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.67 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(9)
% 5.46/5.67 thf(fact_4225_pinf_I10_J,axiom,
% 5.46/5.67 ! [D2: code_integer,S: code_integer] :
% 5.46/5.67 ? [Z3: code_integer] :
% 5.46/5.67 ! [X4: code_integer] :
% 5.46/5.67 ( ( ord_le6747313008572928689nteger @ Z3 @ X4 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(10)
% 5.46/5.67 thf(fact_4226_pinf_I10_J,axiom,
% 5.46/5.67 ! [D2: real,S: real] :
% 5.46/5.67 ? [Z3: real] :
% 5.46/5.67 ! [X4: real] :
% 5.46/5.67 ( ( ord_less_real @ Z3 @ X4 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(10)
% 5.46/5.67 thf(fact_4227_pinf_I10_J,axiom,
% 5.46/5.67 ! [D2: rat,S: rat] :
% 5.46/5.67 ? [Z3: rat] :
% 5.46/5.67 ! [X4: rat] :
% 5.46/5.67 ( ( ord_less_rat @ Z3 @ X4 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(10)
% 5.46/5.67 thf(fact_4228_pinf_I10_J,axiom,
% 5.46/5.67 ! [D2: nat,S: nat] :
% 5.46/5.67 ? [Z3: nat] :
% 5.46/5.67 ! [X4: nat] :
% 5.46/5.67 ( ( ord_less_nat @ Z3 @ X4 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(10)
% 5.46/5.67 thf(fact_4229_pinf_I10_J,axiom,
% 5.46/5.67 ! [D2: int,S: int] :
% 5.46/5.67 ? [Z3: int] :
% 5.46/5.67 ! [X4: int] :
% 5.46/5.67 ( ( ord_less_int @ Z3 @ X4 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pinf(10)
% 5.46/5.67 thf(fact_4230_minf_I9_J,axiom,
% 5.46/5.67 ! [D2: code_integer,S: code_integer] :
% 5.46/5.67 ? [Z3: code_integer] :
% 5.46/5.67 ! [X4: code_integer] :
% 5.46/5.67 ( ( ord_le6747313008572928689nteger @ X4 @ Z3 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(9)
% 5.46/5.67 thf(fact_4231_minf_I9_J,axiom,
% 5.46/5.67 ! [D2: real,S: real] :
% 5.46/5.67 ? [Z3: real] :
% 5.46/5.67 ! [X4: real] :
% 5.46/5.67 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.67 => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(9)
% 5.46/5.67 thf(fact_4232_minf_I9_J,axiom,
% 5.46/5.67 ! [D2: rat,S: rat] :
% 5.46/5.67 ? [Z3: rat] :
% 5.46/5.67 ! [X4: rat] :
% 5.46/5.67 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.67 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(9)
% 5.46/5.67 thf(fact_4233_minf_I9_J,axiom,
% 5.46/5.67 ! [D2: nat,S: nat] :
% 5.46/5.67 ? [Z3: nat] :
% 5.46/5.67 ! [X4: nat] :
% 5.46/5.67 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(9)
% 5.46/5.67 thf(fact_4234_minf_I9_J,axiom,
% 5.46/5.67 ! [D2: int,S: int] :
% 5.46/5.67 ? [Z3: int] :
% 5.46/5.67 ! [X4: int] :
% 5.46/5.67 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.67 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ S ) )
% 5.46/5.67 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(9)
% 5.46/5.67 thf(fact_4235_minf_I10_J,axiom,
% 5.46/5.67 ! [D2: code_integer,S: code_integer] :
% 5.46/5.67 ? [Z3: code_integer] :
% 5.46/5.67 ! [X4: code_integer] :
% 5.46/5.67 ( ( ord_le6747313008572928689nteger @ X4 @ Z3 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(10)
% 5.46/5.67 thf(fact_4236_minf_I10_J,axiom,
% 5.46/5.67 ! [D2: real,S: real] :
% 5.46/5.67 ? [Z3: real] :
% 5.46/5.67 ! [X4: real] :
% 5.46/5.67 ( ( ord_less_real @ X4 @ Z3 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(10)
% 5.46/5.67 thf(fact_4237_minf_I10_J,axiom,
% 5.46/5.67 ! [D2: rat,S: rat] :
% 5.46/5.67 ? [Z3: rat] :
% 5.46/5.67 ! [X4: rat] :
% 5.46/5.67 ( ( ord_less_rat @ X4 @ Z3 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(10)
% 5.46/5.67 thf(fact_4238_minf_I10_J,axiom,
% 5.46/5.67 ! [D2: nat,S: nat] :
% 5.46/5.67 ? [Z3: nat] :
% 5.46/5.67 ! [X4: nat] :
% 5.46/5.67 ( ( ord_less_nat @ X4 @ Z3 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(10)
% 5.46/5.67 thf(fact_4239_minf_I10_J,axiom,
% 5.46/5.67 ! [D2: int,S: int] :
% 5.46/5.67 ? [Z3: int] :
% 5.46/5.67 ! [X4: int] :
% 5.46/5.67 ( ( ord_less_int @ X4 @ Z3 )
% 5.46/5.67 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ S ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % minf(10)
% 5.46/5.67 thf(fact_4240_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_4241_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B: complex,A: complex] :
% 5.46/5.67 ( ( dvd_dvd_complex @ B @ A )
% 5.46/5.67 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.46/5.67 = zero_zero_complex )
% 5.46/5.67 = ( A = zero_zero_complex ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_4242_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B: real,A: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ B @ A )
% 5.46/5.67 => ( ( ( divide_divide_real @ A @ B )
% 5.46/5.67 = zero_zero_real )
% 5.46/5.67 = ( A = zero_zero_real ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_4243_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B: rat,A: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ B @ A )
% 5.46/5.67 => ( ( ( divide_divide_rat @ A @ B )
% 5.46/5.67 = zero_zero_rat )
% 5.46/5.67 = ( A = zero_zero_rat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_4244_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ A )
% 5.46/5.67 => ( ( ( divide_divide_nat @ A @ B )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 = ( A = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_4245_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ A )
% 5.46/5.67 => ( ( ( divide_divide_int @ A @ B )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 = ( A = zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_4246_unit__mult__right__cancel,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.46/5.67 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.46/5.67 = ( B = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_mult_right_cancel
% 5.46/5.67 thf(fact_4247_unit__mult__right__cancel,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( ( ( times_times_nat @ B @ A )
% 5.46/5.67 = ( times_times_nat @ C @ A ) )
% 5.46/5.67 = ( B = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_mult_right_cancel
% 5.46/5.67 thf(fact_4248_unit__mult__right__cancel,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( ( ( times_times_int @ B @ A )
% 5.46/5.67 = ( times_times_int @ C @ A ) )
% 5.46/5.67 = ( B = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_mult_right_cancel
% 5.46/5.67 thf(fact_4249_unit__mult__left__cancel,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.46/5.67 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.46/5.67 = ( B = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_mult_left_cancel
% 5.46/5.67 thf(fact_4250_unit__mult__left__cancel,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( ( ( times_times_nat @ A @ B )
% 5.46/5.67 = ( times_times_nat @ A @ C ) )
% 5.46/5.67 = ( B = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_mult_left_cancel
% 5.46/5.67 thf(fact_4251_unit__mult__left__cancel,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( ( ( times_times_int @ A @ B )
% 5.46/5.67 = ( times_times_int @ A @ C ) )
% 5.46/5.67 = ( B = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_mult_left_cancel
% 5.46/5.67 thf(fact_4252_mult__unit__dvd__iff_H,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_unit_dvd_iff'
% 5.46/5.67 thf(fact_4253_mult__unit__dvd__iff_H,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_unit_dvd_iff'
% 5.46/5.67 thf(fact_4254_mult__unit__dvd__iff_H,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_unit_dvd_iff'
% 5.46/5.67 thf(fact_4255_dvd__mult__unit__iff_H,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_unit_iff'
% 5.46/5.67 thf(fact_4256_dvd__mult__unit__iff_H,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_unit_iff'
% 5.46/5.67 thf(fact_4257_dvd__mult__unit__iff_H,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_unit_iff'
% 5.46/5.67 thf(fact_4258_mult__unit__dvd__iff,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_unit_dvd_iff
% 5.46/5.67 thf(fact_4259_mult__unit__dvd__iff,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_unit_dvd_iff
% 5.46/5.67 thf(fact_4260_mult__unit__dvd__iff,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_unit_dvd_iff
% 5.46/5.67 thf(fact_4261_dvd__mult__unit__iff,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_unit_iff
% 5.46/5.67 thf(fact_4262_dvd__mult__unit__iff,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_unit_iff
% 5.46/5.67 thf(fact_4263_dvd__mult__unit__iff,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_unit_iff
% 5.46/5.67 thf(fact_4264_is__unit__mult__iff,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_mult_iff
% 5.46/5.67 thf(fact_4265_is__unit__mult__iff,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.46/5.67 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_mult_iff
% 5.46/5.67 thf(fact_4266_is__unit__mult__iff,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.46/5.67 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_mult_iff
% 5.46/5.67 thf(fact_4267_div__mult__div__if__dvd,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,D2: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ D2 @ C )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D2 ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mult_div_if_dvd
% 5.46/5.67 thf(fact_4268_div__mult__div__if__dvd,axiom,
% 5.46/5.67 ! [B: nat,A: nat,D2: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ A )
% 5.46/5.67 => ( ( dvd_dvd_nat @ D2 @ C )
% 5.46/5.67 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D2 ) )
% 5.46/5.67 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mult_div_if_dvd
% 5.46/5.67 thf(fact_4269_div__mult__div__if__dvd,axiom,
% 5.46/5.67 ! [B: int,A: int,D2: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ A )
% 5.46/5.67 => ( ( dvd_dvd_int @ D2 @ C )
% 5.46/5.67 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D2 ) )
% 5.46/5.67 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mult_div_if_dvd
% 5.46/5.67 thf(fact_4270_dvd__mult__imp__div,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_imp_div
% 5.46/5.67 thf(fact_4271_dvd__mult__imp__div,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_imp_div
% 5.46/5.67 thf(fact_4272_dvd__mult__imp__div,axiom,
% 5.46/5.67 ! [A: int,C: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.46/5.67 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_imp_div
% 5.46/5.67 thf(fact_4273_dvd__div__mult2__eq,axiom,
% 5.46/5.67 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_mult2_eq
% 5.46/5.67 thf(fact_4274_dvd__div__mult2__eq,axiom,
% 5.46/5.67 ! [B: nat,C: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.46/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.46/5.67 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_mult2_eq
% 5.46/5.67 thf(fact_4275_dvd__div__mult2__eq,axiom,
% 5.46/5.67 ! [B: int,C: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.46/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.46/5.67 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_mult2_eq
% 5.46/5.67 thf(fact_4276_div__div__eq__right,axiom,
% 5.46/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.46/5.67 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_div_eq_right
% 5.46/5.67 thf(fact_4277_div__div__eq__right,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ A )
% 5.46/5.67 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.46/5.67 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_div_eq_right
% 5.46/5.67 thf(fact_4278_div__div__eq__right,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ A )
% 5.46/5.67 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.46/5.67 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_div_eq_right
% 5.46/5.67 thf(fact_4279_div__mult__swap,axiom,
% 5.46/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mult_swap
% 5.46/5.67 thf(fact_4280_div__mult__swap,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.46/5.67 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mult_swap
% 5.46/5.67 thf(fact_4281_div__mult__swap,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.46/5.67 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mult_swap
% 5.46/5.67 thf(fact_4282_dvd__div__mult,axiom,
% 5.46/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.46/5.67 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_mult
% 5.46/5.67 thf(fact_4283_dvd__div__mult,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.46/5.67 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_mult
% 5.46/5.67 thf(fact_4284_dvd__div__mult,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.46/5.67 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_mult
% 5.46/5.67 thf(fact_4285_dvd__div__unit__iff,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_unit_iff
% 5.46/5.67 thf(fact_4286_dvd__div__unit__iff,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_unit_iff
% 5.46/5.67 thf(fact_4287_dvd__div__unit__iff,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_unit_iff
% 5.46/5.67 thf(fact_4288_div__unit__dvd__iff,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_unit_dvd_iff
% 5.46/5.67 thf(fact_4289_div__unit__dvd__iff,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_unit_dvd_iff
% 5.46/5.67 thf(fact_4290_div__unit__dvd__iff,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_unit_dvd_iff
% 5.46/5.67 thf(fact_4291_unit__div__cancel,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.46/5.67 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.46/5.67 = ( B = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_cancel
% 5.46/5.67 thf(fact_4292_unit__div__cancel,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ( ( ( divide_divide_nat @ B @ A )
% 5.46/5.67 = ( divide_divide_nat @ C @ A ) )
% 5.46/5.67 = ( B = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_cancel
% 5.46/5.67 thf(fact_4293_unit__div__cancel,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ( ( ( divide_divide_int @ B @ A )
% 5.46/5.67 = ( divide_divide_int @ C @ A ) )
% 5.46/5.67 = ( B = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_cancel
% 5.46/5.67 thf(fact_4294_div__plus__div__distrib__dvd__right,axiom,
% 5.46/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.46/5.67 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_plus_div_distrib_dvd_right
% 5.46/5.67 thf(fact_4295_div__plus__div__distrib__dvd__right,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.46/5.67 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_plus_div_distrib_dvd_right
% 5.46/5.67 thf(fact_4296_div__plus__div__distrib__dvd__right,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.46/5.67 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_plus_div_distrib_dvd_right
% 5.46/5.67 thf(fact_4297_div__plus__div__distrib__dvd__left,axiom,
% 5.46/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.46/5.67 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_plus_div_distrib_dvd_left
% 5.46/5.67 thf(fact_4298_div__plus__div__distrib__dvd__left,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ A )
% 5.46/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.46/5.67 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_plus_div_distrib_dvd_left
% 5.46/5.67 thf(fact_4299_div__plus__div__distrib__dvd__left,axiom,
% 5.46/5.67 ! [C: int,A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ A )
% 5.46/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.46/5.67 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_plus_div_distrib_dvd_left
% 5.46/5.67 thf(fact_4300_div__power,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.67 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.46/5.67 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_power
% 5.46/5.67 thf(fact_4301_div__power,axiom,
% 5.46/5.67 ! [B: nat,A: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ A )
% 5.46/5.67 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.46/5.67 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_power
% 5.46/5.67 thf(fact_4302_div__power,axiom,
% 5.46/5.67 ! [B: int,A: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ A )
% 5.46/5.67 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.46/5.67 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_power
% 5.46/5.67 thf(fact_4303_mod__0__imp__dvd,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( ( modulo_modulo_nat @ A @ B )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_0_imp_dvd
% 5.46/5.67 thf(fact_4304_mod__0__imp__dvd,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_0_imp_dvd
% 5.46/5.67 thf(fact_4305_mod__0__imp__dvd,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_0_imp_dvd
% 5.46/5.67 thf(fact_4306_dvd__eq__mod__eq__0,axiom,
% 5.46/5.67 ( dvd_dvd_nat
% 5.46/5.67 = ( ^ [A3: nat,B2: nat] :
% 5.46/5.67 ( ( modulo_modulo_nat @ B2 @ A3 )
% 5.46/5.67 = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_eq_mod_eq_0
% 5.46/5.67 thf(fact_4307_dvd__eq__mod__eq__0,axiom,
% 5.46/5.67 ( dvd_dvd_int
% 5.46/5.67 = ( ^ [A3: int,B2: int] :
% 5.46/5.67 ( ( modulo_modulo_int @ B2 @ A3 )
% 5.46/5.67 = zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_eq_mod_eq_0
% 5.46/5.67 thf(fact_4308_dvd__eq__mod__eq__0,axiom,
% 5.46/5.67 ( dvd_dvd_Code_integer
% 5.46/5.67 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 5.46/5.67 = zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_eq_mod_eq_0
% 5.46/5.67 thf(fact_4309_mod__eq__0__iff__dvd,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( ( modulo_modulo_nat @ A @ B )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_eq_0_iff_dvd
% 5.46/5.67 thf(fact_4310_mod__eq__0__iff__dvd,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_eq_0_iff_dvd
% 5.46/5.67 thf(fact_4311_mod__eq__0__iff__dvd,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_eq_0_iff_dvd
% 5.46/5.67 thf(fact_4312_dvd__power__le,axiom,
% 5.46/5.67 ! [X2: code_integer,Y2: code_integer,N: nat,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ X2 @ Y2 )
% 5.46/5.67 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y2 @ M ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_le
% 5.46/5.67 thf(fact_4313_dvd__power__le,axiom,
% 5.46/5.67 ! [X2: nat,Y2: nat,N: nat,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ X2 @ Y2 )
% 5.46/5.67 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.67 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y2 @ M ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_le
% 5.46/5.67 thf(fact_4314_dvd__power__le,axiom,
% 5.46/5.67 ! [X2: real,Y2: real,N: nat,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_real @ X2 @ Y2 )
% 5.46/5.67 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.67 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y2 @ M ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_le
% 5.46/5.67 thf(fact_4315_dvd__power__le,axiom,
% 5.46/5.67 ! [X2: complex,Y2: complex,N: nat,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_complex @ X2 @ Y2 )
% 5.46/5.67 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.67 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y2 @ M ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_le
% 5.46/5.67 thf(fact_4316_dvd__power__le,axiom,
% 5.46/5.67 ! [X2: int,Y2: int,N: nat,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ X2 @ Y2 )
% 5.46/5.67 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.67 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y2 @ M ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_le
% 5.46/5.67 thf(fact_4317_power__le__dvd,axiom,
% 5.46/5.67 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 5.46/5.67 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_dvd
% 5.46/5.67 thf(fact_4318_power__le__dvd,axiom,
% 5.46/5.67 ! [A: nat,N: nat,B: nat,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.46/5.67 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_dvd
% 5.46/5.67 thf(fact_4319_power__le__dvd,axiom,
% 5.46/5.67 ! [A: real,N: nat,B: real,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.46/5.67 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_dvd
% 5.46/5.67 thf(fact_4320_power__le__dvd,axiom,
% 5.46/5.67 ! [A: complex,N: nat,B: complex,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.46/5.67 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_dvd
% 5.46/5.67 thf(fact_4321_power__le__dvd,axiom,
% 5.46/5.67 ! [A: int,N: nat,B: int,M: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.46/5.67 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_dvd
% 5.46/5.67 thf(fact_4322_le__imp__power__dvd,axiom,
% 5.46/5.67 ! [M: nat,N: nat,A: code_integer] :
% 5.46/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_imp_power_dvd
% 5.46/5.67 thf(fact_4323_le__imp__power__dvd,axiom,
% 5.46/5.67 ! [M: nat,N: nat,A: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_imp_power_dvd
% 5.46/5.67 thf(fact_4324_le__imp__power__dvd,axiom,
% 5.46/5.67 ! [M: nat,N: nat,A: real] :
% 5.46/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_imp_power_dvd
% 5.46/5.67 thf(fact_4325_le__imp__power__dvd,axiom,
% 5.46/5.67 ! [M: nat,N: nat,A: complex] :
% 5.46/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_imp_power_dvd
% 5.46/5.67 thf(fact_4326_le__imp__power__dvd,axiom,
% 5.46/5.67 ! [M: nat,N: nat,A: int] :
% 5.46/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_imp_power_dvd
% 5.46/5.67 thf(fact_4327_mod__eq__dvd__iff,axiom,
% 5.46/5.67 ! [A: int,C: int,B: int] :
% 5.46/5.67 ( ( ( modulo_modulo_int @ A @ C )
% 5.46/5.67 = ( modulo_modulo_int @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_eq_dvd_iff
% 5.46/5.67 thf(fact_4328_mod__eq__dvd__iff,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.46/5.67 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.46/5.67 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_eq_dvd_iff
% 5.46/5.67 thf(fact_4329_dvd__minus__mod,axiom,
% 5.46/5.67 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_minus_mod
% 5.46/5.67 thf(fact_4330_dvd__minus__mod,axiom,
% 5.46/5.67 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_minus_mod
% 5.46/5.67 thf(fact_4331_dvd__minus__mod,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_minus_mod
% 5.46/5.67 thf(fact_4332_nat__dvd__not__less,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.67 => ( ( ord_less_nat @ M @ N )
% 5.46/5.67 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_dvd_not_less
% 5.46/5.67 thf(fact_4333_dvd__pos__nat,axiom,
% 5.46/5.67 ! [N: nat,M: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( dvd_dvd_nat @ M @ N )
% 5.46/5.67 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_pos_nat
% 5.46/5.67 thf(fact_4334_dvd__minus__self,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.67 = ( ( ord_less_nat @ N @ M )
% 5.46/5.67 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_minus_self
% 5.46/5.67 thf(fact_4335_dvd__diffD,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.67 => ( ( dvd_dvd_nat @ K @ N )
% 5.46/5.67 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.67 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diffD
% 5.46/5.67 thf(fact_4336_dvd__diffD1,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.67 => ( ( dvd_dvd_nat @ K @ M )
% 5.46/5.67 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.67 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diffD1
% 5.46/5.67 thf(fact_4337_less__eq__dvd__minus,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 => ( ( dvd_dvd_nat @ M @ N )
% 5.46/5.67 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % less_eq_dvd_minus
% 5.46/5.67 thf(fact_4338_zdvd__not__zless,axiom,
% 5.46/5.67 ! [M: int,N: int] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ M )
% 5.46/5.67 => ( ( ord_less_int @ M @ N )
% 5.46/5.67 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdvd_not_zless
% 5.46/5.67 thf(fact_4339_bezout__lemma__nat,axiom,
% 5.46/5.67 ! [D2: nat,A: nat,B: nat,X2: nat,Y2: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ D2 @ A )
% 5.46/5.67 => ( ( dvd_dvd_nat @ D2 @ B )
% 5.46/5.67 => ( ( ( ( times_times_nat @ A @ X2 )
% 5.46/5.67 = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D2 ) )
% 5.46/5.67 | ( ( times_times_nat @ B @ X2 )
% 5.46/5.67 = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D2 ) ) )
% 5.46/5.67 => ? [X3: nat,Y3: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ D2 @ A )
% 5.46/5.67 & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A @ B ) )
% 5.46/5.67 & ( ( ( times_times_nat @ A @ X3 )
% 5.46/5.67 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D2 ) )
% 5.46/5.67 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 5.46/5.67 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D2 ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % bezout_lemma_nat
% 5.46/5.67 thf(fact_4340_bezout__add__nat,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ? [D3: nat,X3: nat,Y3: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ D3 @ A )
% 5.46/5.67 & ( dvd_dvd_nat @ D3 @ B )
% 5.46/5.67 & ( ( ( times_times_nat @ A @ X3 )
% 5.46/5.67 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 5.46/5.67 | ( ( times_times_nat @ B @ X3 )
% 5.46/5.67 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % bezout_add_nat
% 5.46/5.67 thf(fact_4341_bezout1__nat,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ? [D3: nat,X3: nat,Y3: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ D3 @ A )
% 5.46/5.67 & ( dvd_dvd_nat @ D3 @ B )
% 5.46/5.67 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.46/5.67 = D3 )
% 5.46/5.67 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.46/5.67 = D3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % bezout1_nat
% 5.46/5.67 thf(fact_4342_div2__even__ext__nat,axiom,
% 5.46/5.67 ! [X2: nat,Y2: nat] :
% 5.46/5.67 ( ( ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide_divide_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.67 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 )
% 5.46/5.67 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y2 ) )
% 5.46/5.67 => ( X2 = Y2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div2_even_ext_nat
% 5.46/5.67 thf(fact_4343_unit__dvdE,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ! [C2: code_integer] :
% 5.46/5.67 ( B
% 5.46/5.67 != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_dvdE
% 5.46/5.67 thf(fact_4344_unit__dvdE,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ~ ( ( A != zero_zero_nat )
% 5.46/5.67 => ! [C2: nat] :
% 5.46/5.67 ( B
% 5.46/5.67 != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_dvdE
% 5.46/5.67 thf(fact_4345_unit__dvdE,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ~ ( ( A != zero_zero_int )
% 5.46/5.67 => ! [C2: int] :
% 5.46/5.67 ( B
% 5.46/5.67 != ( times_times_int @ A @ C2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_dvdE
% 5.46/5.67 thf(fact_4346_unity__coeff__ex,axiom,
% 5.46/5.67 ! [P: code_integer > $o,L2: code_integer] :
% 5.46/5.67 ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X ) ) )
% 5.46/5.67 = ( ? [X: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 5.46/5.67 & ( P @ X ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unity_coeff_ex
% 5.46/5.67 thf(fact_4347_unity__coeff__ex,axiom,
% 5.46/5.67 ! [P: complex > $o,L2: complex] :
% 5.46/5.67 ( ( ? [X: complex] : ( P @ ( times_times_complex @ L2 @ X ) ) )
% 5.46/5.67 = ( ? [X: complex] :
% 5.46/5.67 ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X @ zero_zero_complex ) )
% 5.46/5.67 & ( P @ X ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unity_coeff_ex
% 5.46/5.67 thf(fact_4348_unity__coeff__ex,axiom,
% 5.46/5.67 ! [P: real > $o,L2: real] :
% 5.46/5.67 ( ( ? [X: real] : ( P @ ( times_times_real @ L2 @ X ) ) )
% 5.46/5.67 = ( ? [X: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X @ zero_zero_real ) )
% 5.46/5.67 & ( P @ X ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unity_coeff_ex
% 5.46/5.67 thf(fact_4349_unity__coeff__ex,axiom,
% 5.46/5.67 ! [P: rat > $o,L2: rat] :
% 5.46/5.67 ( ( ? [X: rat] : ( P @ ( times_times_rat @ L2 @ X ) ) )
% 5.46/5.67 = ( ? [X: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 5.46/5.67 & ( P @ X ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unity_coeff_ex
% 5.46/5.67 thf(fact_4350_unity__coeff__ex,axiom,
% 5.46/5.67 ! [P: nat > $o,L2: nat] :
% 5.46/5.67 ( ( ? [X: nat] : ( P @ ( times_times_nat @ L2 @ X ) ) )
% 5.46/5.67 = ( ? [X: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 5.46/5.67 & ( P @ X ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unity_coeff_ex
% 5.46/5.67 thf(fact_4351_unity__coeff__ex,axiom,
% 5.46/5.67 ! [P: int > $o,L2: int] :
% 5.46/5.67 ( ( ? [X: int] : ( P @ ( times_times_int @ L2 @ X ) ) )
% 5.46/5.67 = ( ? [X: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X @ zero_zero_int ) )
% 5.46/5.67 & ( P @ X ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unity_coeff_ex
% 5.46/5.67 thf(fact_4352_dvd__div__eq__mult,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.46/5.67 = C )
% 5.46/5.67 = ( B
% 5.46/5.67 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_mult
% 5.46/5.67 thf(fact_4353_dvd__div__eq__mult,axiom,
% 5.46/5.67 ! [A: nat,B: nat,C: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( ( divide_divide_nat @ B @ A )
% 5.46/5.67 = C )
% 5.46/5.67 = ( B
% 5.46/5.67 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_mult
% 5.46/5.67 thf(fact_4354_dvd__div__eq__mult,axiom,
% 5.46/5.67 ! [A: int,B: int,C: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( ( divide_divide_int @ B @ A )
% 5.46/5.67 = C )
% 5.46/5.67 = ( B
% 5.46/5.67 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_mult
% 5.46/5.67 thf(fact_4355_div__dvd__iff__mult,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( B != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_dvd_iff_mult
% 5.46/5.67 thf(fact_4356_div__dvd__iff__mult,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( B != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ A )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_dvd_iff_mult
% 5.46/5.67 thf(fact_4357_div__dvd__iff__mult,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( B != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ A )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.46/5.67 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_dvd_iff_mult
% 5.46/5.67 thf(fact_4358_dvd__div__iff__mult,axiom,
% 5.46/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( C != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_iff_mult
% 5.46/5.67 thf(fact_4359_dvd__div__iff__mult,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( C != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_iff_mult
% 5.46/5.67 thf(fact_4360_dvd__div__iff__mult,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( C != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.46/5.67 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_iff_mult
% 5.46/5.67 thf(fact_4361_dvd__div__div__eq__mult,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( C != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.46/5.67 = ( divide6298287555418463151nteger @ D2 @ C ) )
% 5.46/5.67 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.46/5.67 = ( times_3573771949741848930nteger @ A @ D2 ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_div_eq_mult
% 5.46/5.67 thf(fact_4362_dvd__div__div__eq__mult,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B: nat,D2: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( C != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ D2 )
% 5.46/5.67 => ( ( ( divide_divide_nat @ B @ A )
% 5.46/5.67 = ( divide_divide_nat @ D2 @ C ) )
% 5.46/5.67 = ( ( times_times_nat @ B @ C )
% 5.46/5.67 = ( times_times_nat @ A @ D2 ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_div_eq_mult
% 5.46/5.67 thf(fact_4363_dvd__div__div__eq__mult,axiom,
% 5.46/5.67 ! [A: int,C: int,B: int,D2: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( C != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ B )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ D2 )
% 5.46/5.67 => ( ( ( divide_divide_int @ B @ A )
% 5.46/5.67 = ( divide_divide_int @ D2 @ C ) )
% 5.46/5.67 = ( ( times_times_int @ B @ C )
% 5.46/5.67 = ( times_times_int @ A @ D2 ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_div_eq_mult
% 5.46/5.67 thf(fact_4364_unit__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_eq_0_iff
% 5.46/5.67 thf(fact_4365_unit__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( ( divide_divide_nat @ A @ B )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 = ( A = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_eq_0_iff
% 5.46/5.67 thf(fact_4366_unit__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( ( divide_divide_int @ A @ B )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 = ( A = zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_eq_0_iff
% 5.46/5.67 thf(fact_4367_even__numeral,axiom,
% 5.46/5.67 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_numeral
% 5.46/5.67 thf(fact_4368_even__numeral,axiom,
% 5.46/5.67 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_numeral
% 5.46/5.67 thf(fact_4369_even__numeral,axiom,
% 5.46/5.67 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_numeral
% 5.46/5.67 thf(fact_4370_inf__period_I3_J,axiom,
% 5.46/5.67 ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 5.46/5.67 => ! [X4: code_integer,K4: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ T ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % inf_period(3)
% 5.46/5.67 thf(fact_4371_inf__period_I3_J,axiom,
% 5.46/5.67 ! [D2: real,D4: real,T: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ D2 @ D4 )
% 5.46/5.67 => ! [X4: real,K4: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ T ) )
% 5.46/5.67 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % inf_period(3)
% 5.46/5.67 thf(fact_4372_inf__period_I3_J,axiom,
% 5.46/5.67 ! [D2: rat,D4: rat,T: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ D2 @ D4 )
% 5.46/5.67 => ! [X4: rat,K4: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ T ) )
% 5.46/5.67 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % inf_period(3)
% 5.46/5.67 thf(fact_4373_inf__period_I3_J,axiom,
% 5.46/5.67 ! [D2: int,D4: int,T: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ D2 @ D4 )
% 5.46/5.67 => ! [X4: int,K4: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T ) )
% 5.46/5.67 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % inf_period(3)
% 5.46/5.67 thf(fact_4374_inf__period_I4_J,axiom,
% 5.46/5.67 ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 5.46/5.67 => ! [X4: code_integer,K4: code_integer] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ T ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % inf_period(4)
% 5.46/5.67 thf(fact_4375_inf__period_I4_J,axiom,
% 5.46/5.67 ! [D2: real,D4: real,T: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ D2 @ D4 )
% 5.46/5.67 => ! [X4: real,K4: real] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X4 @ T ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % inf_period(4)
% 5.46/5.67 thf(fact_4376_inf__period_I4_J,axiom,
% 5.46/5.67 ! [D2: rat,D4: rat,T: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ D2 @ D4 )
% 5.46/5.67 => ! [X4: rat,K4: rat] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ T ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % inf_period(4)
% 5.46/5.67 thf(fact_4377_inf__period_I4_J,axiom,
% 5.46/5.67 ! [D2: int,D4: int,T: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ D2 @ D4 )
% 5.46/5.67 => ! [X4: int,K4: int] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T ) ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % inf_period(4)
% 5.46/5.67 thf(fact_4378_is__unit__div__mult2__eq,axiom,
% 5.46/5.67 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult2_eq
% 5.46/5.67 thf(fact_4379_is__unit__div__mult2__eq,axiom,
% 5.46/5.67 ! [B: nat,C: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.46/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.46/5.67 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult2_eq
% 5.46/5.67 thf(fact_4380_is__unit__div__mult2__eq,axiom,
% 5.46/5.67 ! [B: int,C: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.46/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.46/5.67 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult2_eq
% 5.46/5.67 thf(fact_4381_unit__div__mult__swap,axiom,
% 5.46/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_mult_swap
% 5.46/5.67 thf(fact_4382_unit__div__mult__swap,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.46/5.67 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.46/5.67 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_mult_swap
% 5.46/5.67 thf(fact_4383_unit__div__mult__swap,axiom,
% 5.46/5.67 ! [C: int,A: int,B: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.46/5.67 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.46/5.67 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_mult_swap
% 5.46/5.67 thf(fact_4384_unit__div__commute,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.46/5.67 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_commute
% 5.46/5.67 thf(fact_4385_unit__div__commute,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.46/5.67 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_commute
% 5.46/5.67 thf(fact_4386_unit__div__commute,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.46/5.67 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_commute
% 5.46/5.67 thf(fact_4387_div__mult__unit2,axiom,
% 5.46/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mult_unit2
% 5.46/5.67 thf(fact_4388_div__mult__unit2,axiom,
% 5.46/5.67 ! [C: nat,B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ A )
% 5.46/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.46/5.67 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mult_unit2
% 5.46/5.67 thf(fact_4389_div__mult__unit2,axiom,
% 5.46/5.67 ! [C: int,B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ A )
% 5.46/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.46/5.67 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mult_unit2
% 5.46/5.67 thf(fact_4390_unit__eq__div2,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( A
% 5.46/5.67 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.46/5.67 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.46/5.67 = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_eq_div2
% 5.46/5.67 thf(fact_4391_unit__eq__div2,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( A
% 5.46/5.67 = ( divide_divide_nat @ C @ B ) )
% 5.46/5.67 = ( ( times_times_nat @ A @ B )
% 5.46/5.67 = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_eq_div2
% 5.46/5.67 thf(fact_4392_unit__eq__div2,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( A
% 5.46/5.67 = ( divide_divide_int @ C @ B ) )
% 5.46/5.67 = ( ( times_times_int @ A @ B )
% 5.46/5.67 = C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_eq_div2
% 5.46/5.67 thf(fact_4393_unit__eq__div1,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.46/5.67 = C )
% 5.46/5.67 = ( A
% 5.46/5.67 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_eq_div1
% 5.46/5.67 thf(fact_4394_unit__eq__div1,axiom,
% 5.46/5.67 ! [B: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( ( divide_divide_nat @ A @ B )
% 5.46/5.67 = C )
% 5.46/5.67 = ( A
% 5.46/5.67 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_eq_div1
% 5.46/5.67 thf(fact_4395_unit__eq__div1,axiom,
% 5.46/5.67 ! [B: int,A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( ( divide_divide_int @ A @ B )
% 5.46/5.67 = C )
% 5.46/5.67 = ( A
% 5.46/5.67 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_eq_div1
% 5.46/5.67 thf(fact_4396_is__unit__power__iff,axiom,
% 5.46/5.67 ! [A: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_power_iff
% 5.46/5.67 thf(fact_4397_is__unit__power__iff,axiom,
% 5.46/5.67 ! [A: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.46/5.67 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_power_iff
% 5.46/5.67 thf(fact_4398_is__unit__power__iff,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.46/5.67 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_power_iff
% 5.46/5.67 thf(fact_4399_unit__imp__mod__eq__0,axiom,
% 5.46/5.67 ! [B: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( modulo_modulo_nat @ A @ B )
% 5.46/5.67 = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_mod_eq_0
% 5.46/5.67 thf(fact_4400_unit__imp__mod__eq__0,axiom,
% 5.46/5.67 ! [B: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( modulo_modulo_int @ A @ B )
% 5.46/5.67 = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_mod_eq_0
% 5.46/5.67 thf(fact_4401_unit__imp__mod__eq__0,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.46/5.67 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_mod_eq_0
% 5.46/5.67 thf(fact_4402_dvd__imp__le,axiom,
% 5.46/5.67 ! [K: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ K @ N )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_imp_le
% 5.46/5.67 thf(fact_4403_dvd__mult__cancel,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.67 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel
% 5.46/5.67 thf(fact_4404_nat__mult__dvd__cancel1,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.67 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_mult_dvd_cancel1
% 5.46/5.67 thf(fact_4405_bezout__add__strong__nat,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ? [D3: nat,X3: nat,Y3: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ D3 @ A )
% 5.46/5.67 & ( dvd_dvd_nat @ D3 @ B )
% 5.46/5.67 & ( ( times_times_nat @ A @ X3 )
% 5.46/5.67 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % bezout_add_strong_nat
% 5.46/5.67 thf(fact_4406_zdvd__imp__le,axiom,
% 5.46/5.67 ! [Z: int,N: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ Z @ N )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.46/5.67 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdvd_imp_le
% 5.46/5.67 thf(fact_4407_mod__greater__zero__iff__not__dvd,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_greater_zero_iff_not_dvd
% 5.46/5.67 thf(fact_4408_mod__eq__dvd__iff__nat,axiom,
% 5.46/5.67 ! [N: nat,M: nat,Q2: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.67 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.46/5.67 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.46/5.67 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_eq_dvd_iff_nat
% 5.46/5.67 thf(fact_4409_prod__decode__aux_Ocases,axiom,
% 5.46/5.67 ! [X2: product_prod_nat_nat] :
% 5.46/5.67 ~ ! [K3: nat,M4: nat] :
% 5.46/5.67 ( X2
% 5.46/5.67 != ( product_Pair_nat_nat @ K3 @ M4 ) ) ).
% 5.46/5.67
% 5.46/5.67 % prod_decode_aux.cases
% 5.46/5.67 thf(fact_4410_finite__divisors__nat,axiom,
% 5.46/5.67 ! [M: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.67 => ( finite_finite_nat
% 5.46/5.67 @ ( collect_nat
% 5.46/5.67 @ ^ [D: nat] : ( dvd_dvd_nat @ D @ M ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % finite_divisors_nat
% 5.46/5.67 thf(fact_4411_even__zero,axiom,
% 5.46/5.67 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.46/5.67
% 5.46/5.67 % even_zero
% 5.46/5.67 thf(fact_4412_even__zero,axiom,
% 5.46/5.67 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.46/5.67
% 5.46/5.67 % even_zero
% 5.46/5.67 thf(fact_4413_even__zero,axiom,
% 5.46/5.67 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.46/5.67
% 5.46/5.67 % even_zero
% 5.46/5.67 thf(fact_4414_is__unit__div__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_right
% 5.46/5.67 thf(fact_4415_is__unit__div__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.46/5.67 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_right
% 5.46/5.67 thf(fact_4416_is__unit__div__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.46/5.67 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_right
% 5.46/5.67 thf(fact_4417_is__unit__div__mult__cancel__left,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_left
% 5.46/5.67 thf(fact_4418_is__unit__div__mult__cancel__left,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.46/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.46/5.67 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_left
% 5.46/5.67 thf(fact_4419_is__unit__div__mult__cancel__left,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.46/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.46/5.67 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_left
% 5.46/5.67 thf(fact_4420_is__unitE,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ! [B5: code_integer] :
% 5.46/5.67 ( ( B5 != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.46/5.67 = B5 )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 5.46/5.67 = A )
% 5.46/5.67 => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 5.46/5.67 = one_one_Code_integer )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.46/5.67 != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unitE
% 5.46/5.67 thf(fact_4421_is__unitE,axiom,
% 5.46/5.67 ! [A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ~ ( ( A != zero_zero_nat )
% 5.46/5.67 => ! [B5: nat] :
% 5.46/5.67 ( ( B5 != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 5.46/5.67 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.46/5.67 = B5 )
% 5.46/5.67 => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 5.46/5.67 = A )
% 5.46/5.67 => ( ( ( times_times_nat @ A @ B5 )
% 5.46/5.67 = one_one_nat )
% 5.46/5.67 => ( ( divide_divide_nat @ C @ A )
% 5.46/5.67 != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unitE
% 5.46/5.67 thf(fact_4422_is__unitE,axiom,
% 5.46/5.67 ! [A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ~ ( ( A != zero_zero_int )
% 5.46/5.67 => ! [B5: int] :
% 5.46/5.67 ( ( B5 != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 5.46/5.67 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.46/5.67 = B5 )
% 5.46/5.67 => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 5.46/5.67 = A )
% 5.46/5.67 => ( ( ( times_times_int @ A @ B5 )
% 5.46/5.67 = one_one_int )
% 5.46/5.67 => ( ( divide_divide_int @ C @ A )
% 5.46/5.67 != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unitE
% 5.46/5.67 thf(fact_4423_evenE,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ~ ! [B5: code_integer] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % evenE
% 5.46/5.67 thf(fact_4424_evenE,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ~ ! [B5: nat] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % evenE
% 5.46/5.67 thf(fact_4425_evenE,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ~ ! [B5: int] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % evenE
% 5.46/5.67 thf(fact_4426_odd__one,axiom,
% 5.46/5.67 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.46/5.67
% 5.46/5.67 % odd_one
% 5.46/5.67 thf(fact_4427_odd__one,axiom,
% 5.46/5.67 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.46/5.67
% 5.46/5.67 % odd_one
% 5.46/5.67 thf(fact_4428_odd__one,axiom,
% 5.46/5.67 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.46/5.67
% 5.46/5.67 % odd_one
% 5.46/5.67 thf(fact_4429_odd__even__add,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_even_add
% 5.46/5.67 thf(fact_4430_odd__even__add,axiom,
% 5.46/5.67 ! [A: nat,B: nat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.46/5.67 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_even_add
% 5.46/5.67 thf(fact_4431_odd__even__add,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.46/5.67 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_even_add
% 5.46/5.67 thf(fact_4432_bit__eq__rec,axiom,
% 5.46/5.67 ( ( ^ [Y5: code_integer,Z5: code_integer] : ( Y5 = Z5 ) )
% 5.46/5.67 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 5.46/5.67 & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % bit_eq_rec
% 5.46/5.67 thf(fact_4433_bit__eq__rec,axiom,
% 5.46/5.67 ( ( ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 5.46/5.67 = ( ^ [A3: nat,B2: nat] :
% 5.46/5.67 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 5.46/5.67 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 5.46/5.67 & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % bit_eq_rec
% 5.46/5.67 thf(fact_4434_bit__eq__rec,axiom,
% 5.46/5.67 ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.46/5.67 = ( ^ [A3: int,B2: int] :
% 5.46/5.67 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 5.46/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 5.46/5.67 & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % bit_eq_rec
% 5.46/5.67 thf(fact_4435_dvd__power__iff,axiom,
% 5.46/5.67 ! [X2: code_integer,M: nat,N: nat] :
% 5.46/5.67 ( ( X2 != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ M ) @ ( power_8256067586552552935nteger @ X2 @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ X2 @ one_one_Code_integer )
% 5.46/5.67 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_iff
% 5.46/5.67 thf(fact_4436_dvd__power__iff,axiom,
% 5.46/5.67 ! [X2: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( X2 != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( power_power_nat @ X2 @ M ) @ ( power_power_nat @ X2 @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ X2 @ one_one_nat )
% 5.46/5.67 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_iff
% 5.46/5.67 thf(fact_4437_dvd__power__iff,axiom,
% 5.46/5.67 ! [X2: int,M: nat,N: nat] :
% 5.46/5.67 ( ( X2 != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ X2 @ one_one_int )
% 5.46/5.67 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_iff
% 5.46/5.67 thf(fact_4438_odd__numeral,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_numeral
% 5.46/5.67 thf(fact_4439_odd__numeral,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_numeral
% 5.46/5.67 thf(fact_4440_odd__numeral,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_numeral
% 5.46/5.67 thf(fact_4441_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X2: code_integer] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X2 = one_one_Code_integer ) )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ X2 @ ( power_8256067586552552935nteger @ X2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_4442_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X2: rat] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X2 = one_one_rat ) )
% 5.46/5.67 => ( dvd_dvd_rat @ X2 @ ( power_power_rat @ X2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_4443_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X2: nat] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X2 = one_one_nat ) )
% 5.46/5.67 => ( dvd_dvd_nat @ X2 @ ( power_power_nat @ X2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_4444_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X2: real] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X2 = one_one_real ) )
% 5.46/5.67 => ( dvd_dvd_real @ X2 @ ( power_power_real @ X2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_4445_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X2: complex] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X2 = one_one_complex ) )
% 5.46/5.67 => ( dvd_dvd_complex @ X2 @ ( power_power_complex @ X2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_4446_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X2: int] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X2 = one_one_int ) )
% 5.46/5.67 => ( dvd_dvd_int @ X2 @ ( power_power_int @ X2 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_4447_even__even__mod__4__iff,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_even_mod_4_iff
% 5.46/5.67 thf(fact_4448_dvd__mult__cancel2,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.46/5.67 = ( N = one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel2
% 5.46/5.67 thf(fact_4449_dvd__mult__cancel1,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.46/5.67 = ( N = one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel1
% 5.46/5.67 thf(fact_4450_odd__numeral__BitM,axiom,
% 5.46/5.67 ! [W: num] :
% 5.46/5.67 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_numeral_BitM
% 5.46/5.67 thf(fact_4451_odd__numeral__BitM,axiom,
% 5.46/5.67 ! [W: num] :
% 5.46/5.67 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_numeral_BitM
% 5.46/5.67 thf(fact_4452_odd__numeral__BitM,axiom,
% 5.46/5.67 ! [W: num] :
% 5.46/5.67 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_numeral_BitM
% 5.46/5.67 thf(fact_4453_dvd__minus__add,axiom,
% 5.46/5.67 ! [Q2: nat,N: nat,R: nat,M: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.46/5.67 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 5.46/5.67 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 5.46/5.67 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_minus_add
% 5.46/5.67 thf(fact_4454_power__dvd__imp__le,axiom,
% 5.46/5.67 ! [I: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.46/5.67 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.46/5.67 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_dvd_imp_le
% 5.46/5.67 thf(fact_4455_mod__nat__eqI,axiom,
% 5.46/5.67 ! [R: nat,N: nat,M: nat] :
% 5.46/5.67 ( ( ord_less_nat @ R @ N )
% 5.46/5.67 => ( ( ord_less_eq_nat @ R @ M )
% 5.46/5.67 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 5.46/5.67 => ( ( modulo_modulo_nat @ M @ N )
% 5.46/5.67 = R ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_nat_eqI
% 5.46/5.67 thf(fact_4456_mod__int__pos__iff,axiom,
% 5.46/5.67 ! [K: int,L2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ L2 @ K )
% 5.46/5.67 | ( ( L2 = zero_zero_int )
% 5.46/5.67 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.46/5.67 | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_int_pos_iff
% 5.46/5.67 thf(fact_4457_aset_I10_J,axiom,
% 5.46/5.67 ! [D2: int,D4: int,A2: set_int,T: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ D2 @ D4 )
% 5.46/5.67 => ! [X4: int] :
% 5.46/5.67 ( ! [Xa3: int] :
% 5.46/5.67 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.67 => ! [Xb3: int] :
% 5.46/5.67 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.67 => ( X4
% 5.46/5.67 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.67 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T ) )
% 5.46/5.67 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % aset(10)
% 5.46/5.67 thf(fact_4458_aset_I9_J,axiom,
% 5.46/5.67 ! [D2: int,D4: int,A2: set_int,T: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ D2 @ D4 )
% 5.46/5.67 => ! [X4: int] :
% 5.46/5.67 ( ! [Xa3: int] :
% 5.46/5.67 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.67 => ! [Xb3: int] :
% 5.46/5.67 ( ( member_int @ Xb3 @ A2 )
% 5.46/5.67 => ( X4
% 5.46/5.67 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.67 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T ) )
% 5.46/5.67 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % aset(9)
% 5.46/5.67 thf(fact_4459_bset_I10_J,axiom,
% 5.46/5.67 ! [D2: int,D4: int,B3: set_int,T: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ D2 @ D4 )
% 5.46/5.67 => ! [X4: int] :
% 5.46/5.67 ( ! [Xa3: int] :
% 5.46/5.67 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.67 => ! [Xb3: int] :
% 5.46/5.67 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.67 => ( X4
% 5.46/5.67 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.67 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T ) )
% 5.46/5.67 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % bset(10)
% 5.46/5.67 thf(fact_4460_bset_I9_J,axiom,
% 5.46/5.67 ! [D2: int,D4: int,B3: set_int,T: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ D2 @ D4 )
% 5.46/5.67 => ! [X4: int] :
% 5.46/5.67 ( ! [Xa3: int] :
% 5.46/5.67 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.67 => ! [Xb3: int] :
% 5.46/5.67 ( ( member_int @ Xb3 @ B3 )
% 5.46/5.67 => ( X4
% 5.46/5.67 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.67 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T ) )
% 5.46/5.67 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % bset(9)
% 5.46/5.67 thf(fact_4461_even__two__times__div__two,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.46/5.67 = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_two_times_div_two
% 5.46/5.67 thf(fact_4462_even__two__times__div__two,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.67 = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_two_times_div_two
% 5.46/5.67 thf(fact_4463_even__two__times__div__two,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.46/5.67 = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_two_times_div_two
% 5.46/5.67 thf(fact_4464_even__iff__mod__2__eq__zero,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_iff_mod_2_eq_zero
% 5.46/5.67 thf(fact_4465_even__iff__mod__2__eq__zero,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_iff_mod_2_eq_zero
% 5.46/5.67 thf(fact_4466_even__iff__mod__2__eq__zero,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_iff_mod_2_eq_zero
% 5.46/5.67 thf(fact_4467_odd__iff__mod__2__eq__one,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.67 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = one_one_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_iff_mod_2_eq_one
% 5.46/5.67 thf(fact_4468_odd__iff__mod__2__eq__one,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.67 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 = one_one_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_iff_mod_2_eq_one
% 5.46/5.67 thf(fact_4469_odd__iff__mod__2__eq__one,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.67 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 = one_one_Code_integer ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_iff_mod_2_eq_one
% 5.46/5.67 thf(fact_4470_power__mono__odd,axiom,
% 5.46/5.67 ! [N: nat,A: real,B: real] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( ord_less_eq_real @ A @ B )
% 5.46/5.67 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_mono_odd
% 5.46/5.67 thf(fact_4471_power__mono__odd,axiom,
% 5.46/5.67 ! [N: nat,A: rat,B: rat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.67 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_mono_odd
% 5.46/5.67 thf(fact_4472_power__mono__odd,axiom,
% 5.46/5.67 ! [N: nat,A: int,B: int] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( ord_less_eq_int @ A @ B )
% 5.46/5.67 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_mono_odd
% 5.46/5.67 thf(fact_4473_odd__pos,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_pos
% 5.46/5.67 thf(fact_4474_dvd__power__iff__le,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.46/5.67 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_iff_le
% 5.46/5.67 thf(fact_4475_signed__take__bit__int__less__exp,axiom,
% 5.46/5.67 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_int_less_exp
% 5.46/5.67 thf(fact_4476_even__unset__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 | ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_unset_bit_iff
% 5.46/5.67 thf(fact_4477_even__unset__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 | ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_unset_bit_iff
% 5.46/5.67 thf(fact_4478_even__unset__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 | ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_unset_bit_iff
% 5.46/5.67 thf(fact_4479_even__set__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 & ( M != zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_set_bit_iff
% 5.46/5.67 thf(fact_4480_even__set__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 & ( M != zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_set_bit_iff
% 5.46/5.67 thf(fact_4481_even__set__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 & ( M != zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_set_bit_iff
% 5.46/5.67 thf(fact_4482_even__flip__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 != ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_flip_bit_iff
% 5.46/5.67 thf(fact_4483_even__flip__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 != ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_flip_bit_iff
% 5.46/5.67 thf(fact_4484_even__flip__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 != ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_flip_bit_iff
% 5.46/5.67 thf(fact_4485_even__diff__iff,axiom,
% 5.46/5.67 ! [K: int,L2: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 5.46/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_diff_iff
% 5.46/5.67 thf(fact_4486_oddE,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ~ ! [B5: code_integer] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % oddE
% 5.46/5.67 thf(fact_4487_oddE,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ~ ! [B5: nat] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % oddE
% 5.46/5.67 thf(fact_4488_oddE,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ~ ! [B5: int] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % oddE
% 5.46/5.67 thf(fact_4489_parity__cases,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 != zero_zero_nat ) )
% 5.46/5.67 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 != one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % parity_cases
% 5.46/5.67 thf(fact_4490_parity__cases,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 != zero_zero_int ) )
% 5.46/5.67 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 != one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % parity_cases
% 5.46/5.67 thf(fact_4491_parity__cases,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 != zero_z3403309356797280102nteger ) )
% 5.46/5.67 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 != one_one_Code_integer ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % parity_cases
% 5.46/5.67 thf(fact_4492_mod2__eq__if,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = zero_zero_nat ) )
% 5.46/5.67 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod2_eq_if
% 5.46/5.67 thf(fact_4493_mod2__eq__if,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 = zero_zero_int ) )
% 5.46/5.67 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 = one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod2_eq_if
% 5.46/5.67 thf(fact_4494_mod2__eq__if,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 = zero_z3403309356797280102nteger ) )
% 5.46/5.67 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.67 = one_one_Code_integer ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod2_eq_if
% 5.46/5.67 thf(fact_4495_zero__le__even__power,axiom,
% 5.46/5.67 ! [N: nat,A: real] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_even_power
% 5.46/5.67 thf(fact_4496_zero__le__even__power,axiom,
% 5.46/5.67 ! [N: nat,A: rat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_even_power
% 5.46/5.67 thf(fact_4497_zero__le__even__power,axiom,
% 5.46/5.67 ! [N: nat,A: int] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_even_power
% 5.46/5.67 thf(fact_4498_zero__le__odd__power,axiom,
% 5.46/5.67 ! [N: nat,A: real] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.46/5.67 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_odd_power
% 5.46/5.67 thf(fact_4499_zero__le__odd__power,axiom,
% 5.46/5.67 ! [N: nat,A: rat] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.46/5.67 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_odd_power
% 5.46/5.67 thf(fact_4500_zero__le__odd__power,axiom,
% 5.46/5.67 ! [N: nat,A: int] :
% 5.46/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.46/5.67 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_odd_power
% 5.46/5.67 thf(fact_4501_zero__le__power__eq,axiom,
% 5.46/5.67 ! [A: real,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_power_eq
% 5.46/5.67 thf(fact_4502_zero__le__power__eq,axiom,
% 5.46/5.67 ! [A: rat,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_power_eq
% 5.46/5.67 thf(fact_4503_zero__le__power__eq,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le_power_eq
% 5.46/5.67 thf(fact_4504_signed__take__bit__int__less__self__iff,axiom,
% 5.46/5.67 ! [N: nat,K: int] :
% 5.46/5.67 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.46/5.67 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_int_less_self_iff
% 5.46/5.67 thf(fact_4505_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.46/5.67 ! [K: int,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.46/5.67 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_int_greater_eq_self_iff
% 5.46/5.67 thf(fact_4506_list__decode_Ocases,axiom,
% 5.46/5.67 ! [X2: nat] :
% 5.46/5.67 ( ( X2 != zero_zero_nat )
% 5.46/5.67 => ~ ! [N3: nat] :
% 5.46/5.67 ( X2
% 5.46/5.67 != ( suc @ N3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % list_decode.cases
% 5.46/5.67 thf(fact_4507_zero__less__power__eq,axiom,
% 5.46/5.67 ! [A: real,N: nat] :
% 5.46/5.67 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.46/5.67 = ( ( N = zero_zero_nat )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A != zero_zero_real ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_power_eq
% 5.46/5.67 thf(fact_4508_zero__less__power__eq,axiom,
% 5.46/5.67 ! [A: rat,N: nat] :
% 5.46/5.67 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.46/5.67 = ( ( N = zero_zero_nat )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A != zero_zero_rat ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_power_eq
% 5.46/5.67 thf(fact_4509_zero__less__power__eq,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.46/5.67 = ( ( N = zero_zero_nat )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A != zero_zero_int ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_power_eq
% 5.46/5.67 thf(fact_4510_signed__take__bit__int__less__eq,axiom,
% 5.46/5.67 ! [N: nat,K: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.46/5.67 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_int_less_eq
% 5.46/5.67 thf(fact_4511_even__mask__div__iff_H,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mask_div_iff'
% 5.46/5.67 thf(fact_4512_even__mask__div__iff_H,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mask_div_iff'
% 5.46/5.67 thf(fact_4513_even__mask__div__iff_H,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mask_div_iff'
% 5.46/5.67 thf(fact_4514_power__le__zero__eq,axiom,
% 5.46/5.67 ! [A: real,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq
% 5.46/5.67 thf(fact_4515_power__le__zero__eq,axiom,
% 5.46/5.67 ! [A: rat,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq
% 5.46/5.67 thf(fact_4516_power__le__zero__eq,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq
% 5.46/5.67 thf(fact_4517_option_Osize__gen_I1_J,axiom,
% 5.46/5.67 ! [X2: product_prod_nat_nat > nat] :
% 5.46/5.67 ( ( size_o8335143837870341156at_nat @ X2 @ none_P5556105721700978146at_nat )
% 5.46/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % option.size_gen(1)
% 5.46/5.67 thf(fact_4518_option_Osize__gen_I1_J,axiom,
% 5.46/5.67 ! [X2: nat > nat] :
% 5.46/5.67 ( ( size_option_nat @ X2 @ none_nat )
% 5.46/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % option.size_gen(1)
% 5.46/5.67 thf(fact_4519_option_Osize__gen_I1_J,axiom,
% 5.46/5.67 ! [X2: num > nat] :
% 5.46/5.67 ( ( size_option_num @ X2 @ none_num )
% 5.46/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % option.size_gen(1)
% 5.46/5.67 thf(fact_4520_even__mod__4__div__2,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.67 = ( suc @ zero_zero_nat ) )
% 5.46/5.67 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mod_4_div_2
% 5.46/5.67 thf(fact_4521_divmod__step__nat__def,axiom,
% 5.46/5.67 ( unique5026877609467782581ep_nat
% 5.46/5.67 = ( ^ [L: num] :
% 5.46/5.67 ( produc2626176000494625587at_nat
% 5.46/5.67 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_step_nat_def
% 5.46/5.67 thf(fact_4522_even__mask__div__iff,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.67 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mask_div_iff
% 5.46/5.67 thf(fact_4523_even__mask__div__iff,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.67 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mask_div_iff
% 5.46/5.67 thf(fact_4524_even__mask__div__iff,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.67 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mask_div_iff
% 5.46/5.67 thf(fact_4525_divmod__step__int__def,axiom,
% 5.46/5.67 ( unique5024387138958732305ep_int
% 5.46/5.67 = ( ^ [L: num] :
% 5.46/5.67 ( produc4245557441103728435nt_int
% 5.46/5.67 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_step_int_def
% 5.46/5.67 thf(fact_4526_odd__mod__4__div__2,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.46/5.67 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % odd_mod_4_div_2
% 5.46/5.67 thf(fact_4527_even__mult__exp__div__exp__iff,axiom,
% 5.46/5.67 ! [A: code_integer,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.67 = ( ( ord_less_nat @ N @ M )
% 5.46/5.67 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 | ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mult_exp_div_exp_iff
% 5.46/5.67 thf(fact_4528_even__mult__exp__div__exp__iff,axiom,
% 5.46/5.67 ! [A: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.67 = ( ( ord_less_nat @ N @ M )
% 5.46/5.67 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 | ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mult_exp_div_exp_iff
% 5.46/5.67 thf(fact_4529_even__mult__exp__div__exp__iff,axiom,
% 5.46/5.67 ! [A: int,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.67 = ( ( ord_less_nat @ N @ M )
% 5.46/5.67 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 | ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.67 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_mult_exp_div_exp_iff
% 5.46/5.67 thf(fact_4530_divmod__step__def,axiom,
% 5.46/5.67 ( unique5026877609467782581ep_nat
% 5.46/5.67 = ( ^ [L: num] :
% 5.46/5.67 ( produc2626176000494625587at_nat
% 5.46/5.67 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_step_def
% 5.46/5.67 thf(fact_4531_divmod__step__def,axiom,
% 5.46/5.67 ( unique5024387138958732305ep_int
% 5.46/5.67 = ( ^ [L: num] :
% 5.46/5.67 ( produc4245557441103728435nt_int
% 5.46/5.67 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_step_def
% 5.46/5.67 thf(fact_4532_divmod__step__def,axiom,
% 5.46/5.67 ( unique4921790084139445826nteger
% 5.46/5.67 = ( ^ [L: num] :
% 5.46/5.67 ( produc6916734918728496179nteger
% 5.46/5.67 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_step_def
% 5.46/5.67 thf(fact_4533_ex__min__if__finite,axiom,
% 5.46/5.67 ! [S2: set_real] :
% 5.46/5.67 ( ( finite_finite_real @ S2 )
% 5.46/5.67 => ( ( S2 != bot_bot_set_real )
% 5.46/5.67 => ? [X3: real] :
% 5.46/5.67 ( ( member_real @ X3 @ S2 )
% 5.46/5.67 & ~ ? [Xa: real] :
% 5.46/5.67 ( ( member_real @ Xa @ S2 )
% 5.46/5.67 & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % ex_min_if_finite
% 5.46/5.67 thf(fact_4534_ex__min__if__finite,axiom,
% 5.46/5.67 ! [S2: set_rat] :
% 5.46/5.67 ( ( finite_finite_rat @ S2 )
% 5.46/5.67 => ( ( S2 != bot_bot_set_rat )
% 5.46/5.67 => ? [X3: rat] :
% 5.46/5.67 ( ( member_rat @ X3 @ S2 )
% 5.46/5.67 & ~ ? [Xa: rat] :
% 5.46/5.67 ( ( member_rat @ Xa @ S2 )
% 5.46/5.67 & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % ex_min_if_finite
% 5.46/5.67 thf(fact_4535_ex__min__if__finite,axiom,
% 5.46/5.67 ! [S2: set_num] :
% 5.46/5.67 ( ( finite_finite_num @ S2 )
% 5.46/5.67 => ( ( S2 != bot_bot_set_num )
% 5.46/5.67 => ? [X3: num] :
% 5.46/5.67 ( ( member_num @ X3 @ S2 )
% 5.46/5.67 & ~ ? [Xa: num] :
% 5.46/5.67 ( ( member_num @ Xa @ S2 )
% 5.46/5.67 & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % ex_min_if_finite
% 5.46/5.67 thf(fact_4536_ex__min__if__finite,axiom,
% 5.46/5.67 ! [S2: set_nat] :
% 5.46/5.67 ( ( finite_finite_nat @ S2 )
% 5.46/5.67 => ( ( S2 != bot_bot_set_nat )
% 5.46/5.67 => ? [X3: nat] :
% 5.46/5.67 ( ( member_nat @ X3 @ S2 )
% 5.46/5.67 & ~ ? [Xa: nat] :
% 5.46/5.67 ( ( member_nat @ Xa @ S2 )
% 5.46/5.67 & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % ex_min_if_finite
% 5.46/5.67 thf(fact_4537_ex__min__if__finite,axiom,
% 5.46/5.67 ! [S2: set_int] :
% 5.46/5.67 ( ( finite_finite_int @ S2 )
% 5.46/5.67 => ( ( S2 != bot_bot_set_int )
% 5.46/5.67 => ? [X3: int] :
% 5.46/5.67 ( ( member_int @ X3 @ S2 )
% 5.46/5.67 & ~ ? [Xa: int] :
% 5.46/5.67 ( ( member_int @ Xa @ S2 )
% 5.46/5.67 & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % ex_min_if_finite
% 5.46/5.67 thf(fact_4538_infinite__growing,axiom,
% 5.46/5.67 ! [X7: set_real] :
% 5.46/5.67 ( ( X7 != bot_bot_set_real )
% 5.46/5.67 => ( ! [X3: real] :
% 5.46/5.67 ( ( member_real @ X3 @ X7 )
% 5.46/5.67 => ? [Xa: real] :
% 5.46/5.67 ( ( member_real @ Xa @ X7 )
% 5.46/5.67 & ( ord_less_real @ X3 @ Xa ) ) )
% 5.46/5.67 => ~ ( finite_finite_real @ X7 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % infinite_growing
% 5.46/5.67 thf(fact_4539_infinite__growing,axiom,
% 5.46/5.67 ! [X7: set_rat] :
% 5.46/5.67 ( ( X7 != bot_bot_set_rat )
% 5.46/5.67 => ( ! [X3: rat] :
% 5.46/5.67 ( ( member_rat @ X3 @ X7 )
% 5.46/5.67 => ? [Xa: rat] :
% 5.46/5.67 ( ( member_rat @ Xa @ X7 )
% 5.46/5.67 & ( ord_less_rat @ X3 @ Xa ) ) )
% 5.46/5.67 => ~ ( finite_finite_rat @ X7 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % infinite_growing
% 5.46/5.67 thf(fact_4540_infinite__growing,axiom,
% 5.46/5.67 ! [X7: set_num] :
% 5.46/5.67 ( ( X7 != bot_bot_set_num )
% 5.46/5.67 => ( ! [X3: num] :
% 5.46/5.67 ( ( member_num @ X3 @ X7 )
% 5.46/5.67 => ? [Xa: num] :
% 5.46/5.67 ( ( member_num @ Xa @ X7 )
% 5.46/5.67 & ( ord_less_num @ X3 @ Xa ) ) )
% 5.46/5.67 => ~ ( finite_finite_num @ X7 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % infinite_growing
% 5.46/5.67 thf(fact_4541_infinite__growing,axiom,
% 5.46/5.67 ! [X7: set_nat] :
% 5.46/5.67 ( ( X7 != bot_bot_set_nat )
% 5.46/5.67 => ( ! [X3: nat] :
% 5.46/5.67 ( ( member_nat @ X3 @ X7 )
% 5.46/5.67 => ? [Xa: nat] :
% 5.46/5.67 ( ( member_nat @ Xa @ X7 )
% 5.46/5.67 & ( ord_less_nat @ X3 @ Xa ) ) )
% 5.46/5.67 => ~ ( finite_finite_nat @ X7 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % infinite_growing
% 5.46/5.67 thf(fact_4542_infinite__growing,axiom,
% 5.46/5.67 ! [X7: set_int] :
% 5.46/5.67 ( ( X7 != bot_bot_set_int )
% 5.46/5.67 => ( ! [X3: int] :
% 5.46/5.67 ( ( member_int @ X3 @ X7 )
% 5.46/5.67 => ? [Xa: int] :
% 5.46/5.67 ( ( member_int @ Xa @ X7 )
% 5.46/5.67 & ( ord_less_int @ X3 @ Xa ) ) )
% 5.46/5.67 => ~ ( finite_finite_int @ X7 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % infinite_growing
% 5.46/5.67 thf(fact_4543_triangle__def,axiom,
% 5.46/5.67 ( nat_triangle
% 5.46/5.67 = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % triangle_def
% 5.46/5.67 thf(fact_4544_vebt__buildup_Oelims,axiom,
% 5.46/5.67 ! [X2: nat,Y2: vEBT_VEBT] :
% 5.46/5.67 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.46/5.67 = Y2 )
% 5.46/5.67 => ( ( ( X2 = zero_zero_nat )
% 5.46/5.67 => ( Y2
% 5.46/5.67 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.46/5.67 => ( ( ( X2
% 5.46/5.67 = ( suc @ zero_zero_nat ) )
% 5.46/5.67 => ( Y2
% 5.46/5.67 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.46/5.67 => ~ ! [Va3: nat] :
% 5.46/5.67 ( ( X2
% 5.46/5.67 = ( suc @ ( suc @ Va3 ) ) )
% 5.46/5.67 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.46/5.67 => ( Y2
% 5.46/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.46/5.67 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.46/5.67 => ( Y2
% 5.46/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % vebt_buildup.elims
% 5.46/5.67 thf(fact_4545_divmod__nat__if,axiom,
% 5.46/5.67 ( divmod_nat
% 5.46/5.67 = ( ^ [M3: nat,N2: nat] :
% 5.46/5.67 ( if_Pro6206227464963214023at_nat
% 5.46/5.67 @ ( ( N2 = zero_zero_nat )
% 5.46/5.67 | ( ord_less_nat @ M3 @ N2 ) )
% 5.46/5.67 @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 5.46/5.67 @ ( produc2626176000494625587at_nat
% 5.46/5.67 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.46/5.67 @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divmod_nat_if
% 5.46/5.67 thf(fact_4546_signed__take__bit__Suc__minus__bit1,axiom,
% 5.46/5.67 ! [N: nat,K: num] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_Suc_minus_bit1
% 5.46/5.67 thf(fact_4547_signed__take__bit__rec,axiom,
% 5.46/5.67 ( bit_ri6519982836138164636nteger
% 5.46/5.67 = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_rec
% 5.46/5.67 thf(fact_4548_signed__take__bit__rec,axiom,
% 5.46/5.67 ( bit_ri631733984087533419it_int
% 5.46/5.67 = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_rec
% 5.46/5.67 thf(fact_4549_signed__take__bit__numeral__bit1,axiom,
% 5.46/5.67 ! [L2: num,K: num] :
% 5.46/5.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % signed_take_bit_numeral_bit1
% 5.46/5.67 thf(fact_4550_flip__bit__0,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.46/5.67 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % flip_bit_0
% 5.46/5.67 thf(fact_4551_flip__bit__0,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.46/5.67 = ( 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 ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % flip_bit_0
% 5.46/5.67 thf(fact_4552_flip__bit__0,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.46/5.67 = ( 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 ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % flip_bit_0
% 5.46/5.67 thf(fact_4553_intind,axiom,
% 5.46/5.67 ! [I: nat,N: nat,P: nat > $o,X2: nat] :
% 5.46/5.67 ( ( ord_less_nat @ I @ N )
% 5.46/5.67 => ( ( P @ X2 )
% 5.46/5.67 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % intind
% 5.46/5.67 thf(fact_4554_intind,axiom,
% 5.46/5.67 ! [I: nat,N: nat,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.46/5.67 ( ( ord_less_nat @ I @ N )
% 5.46/5.67 => ( ( P @ X2 )
% 5.46/5.67 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % intind
% 5.46/5.67 thf(fact_4555_add_Oinverse__inverse,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_inverse
% 5.46/5.67 thf(fact_4556_add_Oinverse__inverse,axiom,
% 5.46/5.67 ! [A: real] :
% 5.46/5.67 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_inverse
% 5.46/5.67 thf(fact_4557_add_Oinverse__inverse,axiom,
% 5.46/5.67 ! [A: complex] :
% 5.46/5.67 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_inverse
% 5.46/5.67 thf(fact_4558_add_Oinverse__inverse,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_inverse
% 5.46/5.67 thf(fact_4559_add_Oinverse__inverse,axiom,
% 5.46/5.67 ! [A: rat] :
% 5.46/5.67 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_inverse
% 5.46/5.67 thf(fact_4560_neg__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: int,B: int] :
% 5.46/5.67 ( ( ( uminus_uminus_int @ A )
% 5.46/5.67 = ( uminus_uminus_int @ B ) )
% 5.46/5.67 = ( A = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_equal_iff_equal
% 5.46/5.67 thf(fact_4561_neg__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: real,B: real] :
% 5.46/5.67 ( ( ( uminus_uminus_real @ A )
% 5.46/5.67 = ( uminus_uminus_real @ B ) )
% 5.46/5.67 = ( A = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_equal_iff_equal
% 5.46/5.67 thf(fact_4562_neg__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: complex,B: complex] :
% 5.46/5.67 ( ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.67 = ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.67 = ( A = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_equal_iff_equal
% 5.46/5.67 thf(fact_4563_neg__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: code_integer,B: code_integer] :
% 5.46/5.67 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.67 = ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.67 = ( A = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_equal_iff_equal
% 5.46/5.67 thf(fact_4564_neg__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: rat,B: rat] :
% 5.46/5.67 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.67 = ( uminus_uminus_rat @ B ) )
% 5.46/5.67 = ( A = B ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_equal_iff_equal
% 5.46/5.67 thf(fact_4565_case__prodI2,axiom,
% 5.46/5.67 ! [P2: produc6271795597528267376eger_o,C: code_integer > $o > $o] :
% 5.46/5.67 ( ! [A5: code_integer,B5: $o] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.46/5.67 => ( C @ A5 @ B5 ) )
% 5.46/5.67 => ( produc7828578312038201481er_o_o @ C @ P2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI2
% 5.46/5.67 thf(fact_4566_case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_num_num,C: num > num > $o] :
% 5.46/5.67 ( ! [A5: num,B5: num] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.46/5.67 => ( C @ A5 @ B5 ) )
% 5.46/5.67 => ( produc5703948589228662326_num_o @ C @ P2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI2
% 5.46/5.67 thf(fact_4567_case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_nat_num,C: nat > num > $o] :
% 5.46/5.67 ( ! [A5: nat,B5: num] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.46/5.67 => ( C @ A5 @ B5 ) )
% 5.46/5.67 => ( produc4927758841916487424_num_o @ C @ P2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI2
% 5.46/5.67 thf(fact_4568_case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_nat_nat,C: nat > nat > $o] :
% 5.46/5.67 ( ! [A5: nat,B5: nat] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 5.46/5.67 => ( C @ A5 @ B5 ) )
% 5.46/5.67 => ( produc6081775807080527818_nat_o @ C @ P2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI2
% 5.46/5.67 thf(fact_4569_case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_int_int,C: int > int > $o] :
% 5.46/5.67 ( ! [A5: int,B5: int] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.46/5.67 => ( C @ A5 @ B5 ) )
% 5.46/5.67 => ( produc4947309494688390418_int_o @ C @ P2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI2
% 5.46/5.67 thf(fact_4570_case__prodI,axiom,
% 5.46/5.67 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.46/5.67 ( ( F @ A @ B )
% 5.46/5.67 => ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI
% 5.46/5.67 thf(fact_4571_case__prodI,axiom,
% 5.46/5.67 ! [F: num > num > $o,A: num,B: num] :
% 5.46/5.67 ( ( F @ A @ B )
% 5.46/5.67 => ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI
% 5.46/5.67 thf(fact_4572_case__prodI,axiom,
% 5.46/5.67 ! [F: nat > num > $o,A: nat,B: num] :
% 5.46/5.67 ( ( F @ A @ B )
% 5.46/5.67 => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI
% 5.46/5.67 thf(fact_4573_case__prodI,axiom,
% 5.46/5.67 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.46/5.67 ( ( F @ A @ B )
% 5.46/5.67 => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI
% 5.46/5.67 thf(fact_4574_case__prodI,axiom,
% 5.46/5.67 ! [F: int > int > $o,A: int,B: int] :
% 5.46/5.67 ( ( F @ A @ B )
% 5.46/5.67 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI
% 5.46/5.67 thf(fact_4575_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: produc6271795597528267376eger_o,Z: complex,C: code_integer > $o > set_complex] :
% 5.46/5.67 ( ! [A5: code_integer,B5: $o] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.46/5.67 => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4576_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: produc6271795597528267376eger_o,Z: real,C: code_integer > $o > set_real] :
% 5.46/5.67 ( ! [A5: code_integer,B5: $o] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.46/5.67 => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4577_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: produc6271795597528267376eger_o,Z: nat,C: code_integer > $o > set_nat] :
% 5.46/5.67 ( ! [A5: code_integer,B5: $o] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.46/5.67 => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4578_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: produc6271795597528267376eger_o,Z: int,C: code_integer > $o > set_int] :
% 5.46/5.67 ( ! [A5: code_integer,B5: $o] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.46/5.67 => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4579_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_num_num,Z: complex,C: num > num > set_complex] :
% 5.46/5.67 ( ! [A5: num,B5: num] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.46/5.67 => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4580_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_num_num,Z: real,C: num > num > set_real] :
% 5.46/5.67 ( ! [A5: num,B5: num] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.46/5.67 => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4581_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_num_num,Z: nat,C: num > num > set_nat] :
% 5.46/5.67 ( ! [A5: num,B5: num] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.46/5.67 => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4582_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_num_num,Z: int,C: num > num > set_int] :
% 5.46/5.67 ( ! [A5: num,B5: num] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.46/5.67 => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4583_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_nat_num,Z: complex,C: nat > num > set_complex] :
% 5.46/5.67 ( ! [A5: nat,B5: num] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.46/5.67 => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4584_mem__case__prodI2,axiom,
% 5.46/5.67 ! [P2: product_prod_nat_num,Z: real,C: nat > num > set_real] :
% 5.46/5.67 ( ! [A5: nat,B5: num] :
% 5.46/5.67 ( ( P2
% 5.46/5.67 = ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.46/5.67 => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 5.46/5.67 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI2
% 5.46/5.67 thf(fact_4585_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: complex,C: code_integer > $o > set_complex,A: code_integer,B: $o] :
% 5.46/5.67 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4586_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: real,C: code_integer > $o > set_real,A: code_integer,B: $o] :
% 5.46/5.67 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4587_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: nat,C: code_integer > $o > set_nat,A: code_integer,B: $o] :
% 5.46/5.67 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4588_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: int,C: code_integer > $o > set_int,A: code_integer,B: $o] :
% 5.46/5.67 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4589_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: complex,C: num > num > set_complex,A: num,B: num] :
% 5.46/5.67 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4590_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: real,C: num > num > set_real,A: num,B: num] :
% 5.46/5.67 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4591_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: nat,C: num > num > set_nat,A: num,B: num] :
% 5.46/5.67 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4592_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: int,C: num > num > set_int,A: num,B: num] :
% 5.46/5.67 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4593_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: complex,C: nat > num > set_complex,A: nat,B: num] :
% 5.46/5.67 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4594_mem__case__prodI,axiom,
% 5.46/5.67 ! [Z: real,C: nat > num > set_real,A: nat,B: num] :
% 5.46/5.67 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.46/5.67 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mem_case_prodI
% 5.46/5.67 thf(fact_4595_case__prodI2_H,axiom,
% 5.46/5.67 ! [P2: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X2: product_prod_nat_nat] :
% 5.46/5.67 ( ! [A5: nat,B5: nat] :
% 5.46/5.67 ( ( ( product_Pair_nat_nat @ A5 @ B5 )
% 5.46/5.67 = P2 )
% 5.46/5.67 => ( C @ A5 @ B5 @ X2 ) )
% 5.46/5.67 => ( produc8739625826339149834_nat_o @ C @ P2 @ X2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % case_prodI2'
% 5.46/5.67 thf(fact_4596_neg__le__iff__le,axiom,
% 5.46/5.67 ! [B: real,A: real] :
% 5.46/5.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.46/5.67 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_le_iff_le
% 5.46/5.67 thf(fact_4597_neg__le__iff__le,axiom,
% 5.46/5.67 ! [B: code_integer,A: code_integer] :
% 5.46/5.67 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.67 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_le_iff_le
% 5.46/5.67 thf(fact_4598_neg__le__iff__le,axiom,
% 5.46/5.67 ! [B: rat,A: rat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.46/5.67 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_le_iff_le
% 5.46/5.67 thf(fact_4599_neg__le__iff__le,axiom,
% 5.46/5.67 ! [B: int,A: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.46/5.67 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_le_iff_le
% 5.46/5.67 thf(fact_4600_add_Oinverse__neutral,axiom,
% 5.46/5.67 ( ( uminus_uminus_int @ zero_zero_int )
% 5.46/5.67 = zero_zero_int ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_neutral
% 5.46/5.67 thf(fact_4601_add_Oinverse__neutral,axiom,
% 5.46/5.67 ( ( uminus_uminus_real @ zero_zero_real )
% 5.46/5.67 = zero_zero_real ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_neutral
% 5.46/5.67 thf(fact_4602_add_Oinverse__neutral,axiom,
% 5.46/5.67 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.46/5.67 = zero_zero_complex ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_neutral
% 5.46/5.67 thf(fact_4603_add_Oinverse__neutral,axiom,
% 5.46/5.67 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.46/5.67 = zero_z3403309356797280102nteger ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_neutral
% 5.46/5.67 thf(fact_4604_add_Oinverse__neutral,axiom,
% 5.46/5.67 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.46/5.67 = zero_zero_rat ) ).
% 5.46/5.67
% 5.46/5.67 % add.inverse_neutral
% 5.46/5.67 thf(fact_4605_neg__0__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( zero_zero_int
% 5.46/5.67 = ( uminus_uminus_int @ A ) )
% 5.46/5.67 = ( zero_zero_int = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_0_equal_iff_equal
% 5.46/5.67 thf(fact_4606_neg__0__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: real] :
% 5.46/5.67 ( ( zero_zero_real
% 5.46/5.67 = ( uminus_uminus_real @ A ) )
% 5.46/5.67 = ( zero_zero_real = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_0_equal_iff_equal
% 5.46/5.67 thf(fact_4607_neg__0__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: complex] :
% 5.46/5.67 ( ( zero_zero_complex
% 5.46/5.67 = ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.67 = ( zero_zero_complex = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_0_equal_iff_equal
% 5.46/5.67 thf(fact_4608_neg__0__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( zero_z3403309356797280102nteger
% 5.46/5.67 = ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.67 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_0_equal_iff_equal
% 5.46/5.67 thf(fact_4609_neg__0__equal__iff__equal,axiom,
% 5.46/5.67 ! [A: rat] :
% 5.46/5.67 ( ( zero_zero_rat
% 5.46/5.67 = ( uminus_uminus_rat @ A ) )
% 5.46/5.67 = ( zero_zero_rat = A ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_0_equal_iff_equal
% 5.46/5.67 thf(fact_4610_neg__equal__0__iff__equal,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( ( uminus_uminus_int @ A )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 = ( A = zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_equal_0_iff_equal
% 5.46/5.68 thf(fact_4611_neg__equal__0__iff__equal,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ( uminus_uminus_real @ A )
% 5.46/5.68 = zero_zero_real )
% 5.46/5.68 = ( A = zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_equal_0_iff_equal
% 5.46/5.68 thf(fact_4612_neg__equal__0__iff__equal,axiom,
% 5.46/5.68 ! [A: complex] :
% 5.46/5.68 ( ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.68 = zero_zero_complex )
% 5.46/5.68 = ( A = zero_zero_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_equal_0_iff_equal
% 5.46/5.68 thf(fact_4613_neg__equal__0__iff__equal,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.68 = zero_z3403309356797280102nteger )
% 5.46/5.68 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_equal_0_iff_equal
% 5.46/5.68 thf(fact_4614_neg__equal__0__iff__equal,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.68 = zero_zero_rat )
% 5.46/5.68 = ( A = zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_equal_0_iff_equal
% 5.46/5.68 thf(fact_4615_equal__neg__zero,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_int @ A ) )
% 5.46/5.68 = ( A = zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % equal_neg_zero
% 5.46/5.68 thf(fact_4616_equal__neg__zero,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_real @ A ) )
% 5.46/5.68 = ( A = zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % equal_neg_zero
% 5.46/5.68 thf(fact_4617_equal__neg__zero,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.68 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % equal_neg_zero
% 5.46/5.68 thf(fact_4618_equal__neg__zero,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_rat @ A ) )
% 5.46/5.68 = ( A = zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % equal_neg_zero
% 5.46/5.68 thf(fact_4619_neg__equal__zero,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ( uminus_uminus_int @ A )
% 5.46/5.68 = A )
% 5.46/5.68 = ( A = zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_equal_zero
% 5.46/5.68 thf(fact_4620_neg__equal__zero,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ( uminus_uminus_real @ A )
% 5.46/5.68 = A )
% 5.46/5.68 = ( A = zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_equal_zero
% 5.46/5.68 thf(fact_4621_neg__equal__zero,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.68 = A )
% 5.46/5.68 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_equal_zero
% 5.46/5.68 thf(fact_4622_neg__equal__zero,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.68 = A )
% 5.46/5.68 = ( A = zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_equal_zero
% 5.46/5.68 thf(fact_4623_neg__less__iff__less,axiom,
% 5.46/5.68 ! [B: int,A: int] :
% 5.46/5.68 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.46/5.68 = ( ord_less_int @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_iff_less
% 5.46/5.68 thf(fact_4624_neg__less__iff__less,axiom,
% 5.46/5.68 ! [B: real,A: real] :
% 5.46/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.46/5.68 = ( ord_less_real @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_iff_less
% 5.46/5.68 thf(fact_4625_neg__less__iff__less,axiom,
% 5.46/5.68 ! [B: code_integer,A: code_integer] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.68 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_iff_less
% 5.46/5.68 thf(fact_4626_neg__less__iff__less,axiom,
% 5.46/5.68 ! [B: rat,A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.46/5.68 = ( ord_less_rat @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_iff_less
% 5.46/5.68 thf(fact_4627_neg__numeral__eq__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( M = N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_eq_iff
% 5.46/5.68 thf(fact_4628_neg__numeral__eq__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.68 = ( M = N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_eq_iff
% 5.46/5.68 thf(fact_4629_neg__numeral__eq__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.68 = ( M = N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_eq_iff
% 5.46/5.68 thf(fact_4630_neg__numeral__eq__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.68 = ( M = N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_eq_iff
% 5.46/5.68 thf(fact_4631_neg__numeral__eq__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.68 = ( M = N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_eq_iff
% 5.46/5.68 thf(fact_4632_mult__minus__left,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_left
% 5.46/5.68 thf(fact_4633_mult__minus__left,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.46/5.68 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_left
% 5.46/5.68 thf(fact_4634_mult__minus__left,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_left
% 5.46/5.68 thf(fact_4635_mult__minus__left,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_left
% 5.46/5.68 thf(fact_4636_mult__minus__left,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.46/5.68 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_left
% 5.46/5.68 thf(fact_4637_minus__mult__minus,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( times_times_int @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_minus
% 5.46/5.68 thf(fact_4638_minus__mult__minus,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( times_times_real @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_minus
% 5.46/5.68 thf(fact_4639_minus__mult__minus,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.68 = ( times_times_complex @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_minus
% 5.46/5.68 thf(fact_4640_minus__mult__minus,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_minus
% 5.46/5.68 thf(fact_4641_minus__mult__minus,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( times_times_rat @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_minus
% 5.46/5.68 thf(fact_4642_mult__minus__right,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_right
% 5.46/5.68 thf(fact_4643_mult__minus__right,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_right
% 5.46/5.68 thf(fact_4644_mult__minus__right,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_right
% 5.46/5.68 thf(fact_4645_mult__minus__right,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_right
% 5.46/5.68 thf(fact_4646_mult__minus__right,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus_right
% 5.46/5.68 thf(fact_4647_add__minus__cancel,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % add_minus_cancel
% 5.46/5.68 thf(fact_4648_add__minus__cancel,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % add_minus_cancel
% 5.46/5.68 thf(fact_4649_add__minus__cancel,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % add_minus_cancel
% 5.46/5.68 thf(fact_4650_add__minus__cancel,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % add_minus_cancel
% 5.46/5.68 thf(fact_4651_add__minus__cancel,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % add_minus_cancel
% 5.46/5.68 thf(fact_4652_minus__add__cancel,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_cancel
% 5.46/5.68 thf(fact_4653_minus__add__cancel,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_cancel
% 5.46/5.68 thf(fact_4654_minus__add__cancel,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_cancel
% 5.46/5.68 thf(fact_4655_minus__add__cancel,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_cancel
% 5.46/5.68 thf(fact_4656_minus__add__cancel,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.46/5.68 = B ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_cancel
% 5.46/5.68 thf(fact_4657_minus__add__distrib,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.46/5.68 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_distrib
% 5.46/5.68 thf(fact_4658_minus__add__distrib,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.46/5.68 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_distrib
% 5.46/5.68 thf(fact_4659_minus__add__distrib,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.46/5.68 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_distrib
% 5.46/5.68 thf(fact_4660_minus__add__distrib,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_distrib
% 5.46/5.68 thf(fact_4661_minus__add__distrib,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.46/5.68 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_add_distrib
% 5.46/5.68 thf(fact_4662_minus__diff__eq,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.46/5.68 = ( minus_minus_int @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_eq
% 5.46/5.68 thf(fact_4663_minus__diff__eq,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.46/5.68 = ( minus_minus_real @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_eq
% 5.46/5.68 thf(fact_4664_minus__diff__eq,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.46/5.68 = ( minus_minus_complex @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_eq
% 5.46/5.68 thf(fact_4665_minus__diff__eq,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.46/5.68 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_eq
% 5.46/5.68 thf(fact_4666_minus__diff__eq,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.46/5.68 = ( minus_minus_rat @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_eq
% 5.46/5.68 thf(fact_4667_div__minus__minus,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( divide_divide_int @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_minus_minus
% 5.46/5.68 thf(fact_4668_div__minus__minus,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_minus_minus
% 5.46/5.68 thf(fact_4669_dvd__minus__iff,axiom,
% 5.46/5.68 ! [X2: int,Y2: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ X2 @ ( uminus_uminus_int @ Y2 ) )
% 5.46/5.68 = ( dvd_dvd_int @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_minus_iff
% 5.46/5.68 thf(fact_4670_dvd__minus__iff,axiom,
% 5.46/5.68 ! [X2: real,Y2: real] :
% 5.46/5.68 ( ( dvd_dvd_real @ X2 @ ( uminus_uminus_real @ Y2 ) )
% 5.46/5.68 = ( dvd_dvd_real @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_minus_iff
% 5.46/5.68 thf(fact_4671_dvd__minus__iff,axiom,
% 5.46/5.68 ! [X2: complex,Y2: complex] :
% 5.46/5.68 ( ( dvd_dvd_complex @ X2 @ ( uminus1482373934393186551omplex @ Y2 ) )
% 5.46/5.68 = ( dvd_dvd_complex @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_minus_iff
% 5.46/5.68 thf(fact_4672_dvd__minus__iff,axiom,
% 5.46/5.68 ! [X2: code_integer,Y2: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ X2 @ ( uminus1351360451143612070nteger @ Y2 ) )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_minus_iff
% 5.46/5.68 thf(fact_4673_dvd__minus__iff,axiom,
% 5.46/5.68 ! [X2: rat,Y2: rat] :
% 5.46/5.68 ( ( dvd_dvd_rat @ X2 @ ( uminus_uminus_rat @ Y2 ) )
% 5.46/5.68 = ( dvd_dvd_rat @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_minus_iff
% 5.46/5.68 thf(fact_4674_minus__dvd__iff,axiom,
% 5.46/5.68 ! [X2: int,Y2: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X2 ) @ Y2 )
% 5.46/5.68 = ( dvd_dvd_int @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_dvd_iff
% 5.46/5.68 thf(fact_4675_minus__dvd__iff,axiom,
% 5.46/5.68 ! [X2: real,Y2: real] :
% 5.46/5.68 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X2 ) @ Y2 )
% 5.46/5.68 = ( dvd_dvd_real @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_dvd_iff
% 5.46/5.68 thf(fact_4676_minus__dvd__iff,axiom,
% 5.46/5.68 ! [X2: complex,Y2: complex] :
% 5.46/5.68 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X2 ) @ Y2 )
% 5.46/5.68 = ( dvd_dvd_complex @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_dvd_iff
% 5.46/5.68 thf(fact_4677_minus__dvd__iff,axiom,
% 5.46/5.68 ! [X2: code_integer,Y2: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X2 ) @ Y2 )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_dvd_iff
% 5.46/5.68 thf(fact_4678_minus__dvd__iff,axiom,
% 5.46/5.68 ! [X2: rat,Y2: rat] :
% 5.46/5.68 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X2 ) @ Y2 )
% 5.46/5.68 = ( dvd_dvd_rat @ X2 @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_dvd_iff
% 5.46/5.68 thf(fact_4679_mod__minus__minus,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus_minus
% 5.46/5.68 thf(fact_4680_mod__minus__minus,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus_minus
% 5.46/5.68 thf(fact_4681_of__bool__less__eq__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.46/5.68 = ( P
% 5.46/5.68 => Q ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_eq_iff
% 5.46/5.68 thf(fact_4682_of__bool__less__eq__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.46/5.68 = ( P
% 5.46/5.68 => Q ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_eq_iff
% 5.46/5.68 thf(fact_4683_of__bool__less__eq__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.46/5.68 = ( P
% 5.46/5.68 => Q ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_eq_iff
% 5.46/5.68 thf(fact_4684_of__bool__less__eq__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.46/5.68 = ( P
% 5.46/5.68 => Q ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_eq_iff
% 5.46/5.68 thf(fact_4685_of__bool__eq_I1_J,axiom,
% 5.46/5.68 ( ( zero_n1201886186963655149omplex @ $false )
% 5.46/5.68 = zero_zero_complex ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(1)
% 5.46/5.68 thf(fact_4686_of__bool__eq_I1_J,axiom,
% 5.46/5.68 ( ( zero_n3304061248610475627l_real @ $false )
% 5.46/5.68 = zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(1)
% 5.46/5.68 thf(fact_4687_of__bool__eq_I1_J,axiom,
% 5.46/5.68 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.46/5.68 = zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(1)
% 5.46/5.68 thf(fact_4688_of__bool__eq_I1_J,axiom,
% 5.46/5.68 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.46/5.68 = zero_zero_nat ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(1)
% 5.46/5.68 thf(fact_4689_of__bool__eq_I1_J,axiom,
% 5.46/5.68 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.46/5.68 = zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(1)
% 5.46/5.68 thf(fact_4690_of__bool__eq_I1_J,axiom,
% 5.46/5.68 ( ( zero_n356916108424825756nteger @ $false )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(1)
% 5.46/5.68 thf(fact_4691_of__bool__eq__0__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.46/5.68 = zero_zero_complex )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_0_iff
% 5.46/5.68 thf(fact_4692_of__bool__eq__0__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.46/5.68 = zero_zero_real )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_0_iff
% 5.46/5.68 thf(fact_4693_of__bool__eq__0__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.46/5.68 = zero_zero_rat )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_0_iff
% 5.46/5.68 thf(fact_4694_of__bool__eq__0__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.46/5.68 = zero_zero_nat )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_0_iff
% 5.46/5.68 thf(fact_4695_of__bool__eq__0__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.46/5.68 = zero_zero_int )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_0_iff
% 5.46/5.68 thf(fact_4696_of__bool__eq__0__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n356916108424825756nteger @ P )
% 5.46/5.68 = zero_z3403309356797280102nteger )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_0_iff
% 5.46/5.68 thf(fact_4697_real__add__minus__iff,axiom,
% 5.46/5.68 ! [X2: real,A: real] :
% 5.46/5.68 ( ( ( plus_plus_real @ X2 @ ( uminus_uminus_real @ A ) )
% 5.46/5.68 = zero_zero_real )
% 5.46/5.68 = ( X2 = A ) ) ).
% 5.46/5.68
% 5.46/5.68 % real_add_minus_iff
% 5.46/5.68 thf(fact_4698_of__bool__less__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.46/5.68 = ( ~ P
% 5.46/5.68 & Q ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_iff
% 5.46/5.68 thf(fact_4699_of__bool__less__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.46/5.68 = ( ~ P
% 5.46/5.68 & Q ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_iff
% 5.46/5.68 thf(fact_4700_of__bool__less__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.46/5.68 = ( ~ P
% 5.46/5.68 & Q ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_iff
% 5.46/5.68 thf(fact_4701_of__bool__less__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.46/5.68 = ( ~ P
% 5.46/5.68 & Q ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_iff
% 5.46/5.68 thf(fact_4702_of__bool__less__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.46/5.68 = ( ~ P
% 5.46/5.68 & Q ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_iff
% 5.46/5.68 thf(fact_4703_of__bool__eq_I2_J,axiom,
% 5.46/5.68 ( ( zero_n1201886186963655149omplex @ $true )
% 5.46/5.68 = one_one_complex ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(2)
% 5.46/5.68 thf(fact_4704_of__bool__eq_I2_J,axiom,
% 5.46/5.68 ( ( zero_n3304061248610475627l_real @ $true )
% 5.46/5.68 = one_one_real ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(2)
% 5.46/5.68 thf(fact_4705_of__bool__eq_I2_J,axiom,
% 5.46/5.68 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.46/5.68 = one_one_rat ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(2)
% 5.46/5.68 thf(fact_4706_of__bool__eq_I2_J,axiom,
% 5.46/5.68 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.46/5.68 = one_one_nat ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(2)
% 5.46/5.68 thf(fact_4707_of__bool__eq_I2_J,axiom,
% 5.46/5.68 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.46/5.68 = one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(2)
% 5.46/5.68 thf(fact_4708_of__bool__eq_I2_J,axiom,
% 5.46/5.68 ( ( zero_n356916108424825756nteger @ $true )
% 5.46/5.68 = one_one_Code_integer ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq(2)
% 5.46/5.68 thf(fact_4709_of__bool__eq__1__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.46/5.68 = one_one_complex )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_1_iff
% 5.46/5.68 thf(fact_4710_of__bool__eq__1__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.46/5.68 = one_one_real )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_1_iff
% 5.46/5.68 thf(fact_4711_of__bool__eq__1__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.46/5.68 = one_one_rat )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_1_iff
% 5.46/5.68 thf(fact_4712_of__bool__eq__1__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.46/5.68 = one_one_nat )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_1_iff
% 5.46/5.68 thf(fact_4713_of__bool__eq__1__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.46/5.68 = one_one_int )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_1_iff
% 5.46/5.68 thf(fact_4714_of__bool__eq__1__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ( zero_n356916108424825756nteger @ P )
% 5.46/5.68 = one_one_Code_integer )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_1_iff
% 5.46/5.68 thf(fact_4715_length__replicate,axiom,
% 5.46/5.68 ! [N: nat,X2: vEBT_VEBT] :
% 5.46/5.68 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.46/5.68 = N ) ).
% 5.46/5.68
% 5.46/5.68 % length_replicate
% 5.46/5.68 thf(fact_4716_length__replicate,axiom,
% 5.46/5.68 ! [N: nat,X2: $o] :
% 5.46/5.68 ( ( size_size_list_o @ ( replicate_o @ N @ X2 ) )
% 5.46/5.68 = N ) ).
% 5.46/5.68
% 5.46/5.68 % length_replicate
% 5.46/5.68 thf(fact_4717_length__replicate,axiom,
% 5.46/5.68 ! [N: nat,X2: nat] :
% 5.46/5.68 ( ( size_size_list_nat @ ( replicate_nat @ N @ X2 ) )
% 5.46/5.68 = N ) ).
% 5.46/5.68
% 5.46/5.68 % length_replicate
% 5.46/5.68 thf(fact_4718_length__replicate,axiom,
% 5.46/5.68 ! [N: nat,X2: int] :
% 5.46/5.68 ( ( size_size_list_int @ ( replicate_int @ N @ X2 ) )
% 5.46/5.68 = N ) ).
% 5.46/5.68
% 5.46/5.68 % length_replicate
% 5.46/5.68 thf(fact_4719_of__bool__or__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( zero_n2687167440665602831ol_nat
% 5.46/5.68 @ ( P
% 5.46/5.68 | Q ) )
% 5.46/5.68 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_or_iff
% 5.46/5.68 thf(fact_4720_of__bool__or__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( zero_n2684676970156552555ol_int
% 5.46/5.68 @ ( P
% 5.46/5.68 | Q ) )
% 5.46/5.68 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_or_iff
% 5.46/5.68 thf(fact_4721_of__bool__or__iff,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( zero_n356916108424825756nteger
% 5.46/5.68 @ ( P
% 5.46/5.68 | Q ) )
% 5.46/5.68 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_or_iff
% 5.46/5.68 thf(fact_4722_neg__less__eq__nonneg,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.46/5.68 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_eq_nonneg
% 5.46/5.68 thf(fact_4723_neg__less__eq__nonneg,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.46/5.68 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_eq_nonneg
% 5.46/5.68 thf(fact_4724_neg__less__eq__nonneg,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.46/5.68 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_eq_nonneg
% 5.46/5.68 thf(fact_4725_neg__less__eq__nonneg,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.46/5.68 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_eq_nonneg
% 5.46/5.68 thf(fact_4726_less__eq__neg__nonpos,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.46/5.68 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_eq_neg_nonpos
% 5.46/5.68 thf(fact_4727_less__eq__neg__nonpos,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.68 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_eq_neg_nonpos
% 5.46/5.68 thf(fact_4728_less__eq__neg__nonpos,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.46/5.68 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_eq_neg_nonpos
% 5.46/5.68 thf(fact_4729_less__eq__neg__nonpos,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.46/5.68 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_eq_neg_nonpos
% 5.46/5.68 thf(fact_4730_neg__le__0__iff__le,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.46/5.68 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_le_0_iff_le
% 5.46/5.68 thf(fact_4731_neg__le__0__iff__le,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.46/5.68 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_le_0_iff_le
% 5.46/5.68 thf(fact_4732_neg__le__0__iff__le,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.46/5.68 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_le_0_iff_le
% 5.46/5.68 thf(fact_4733_neg__le__0__iff__le,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.46/5.68 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_le_0_iff_le
% 5.46/5.68 thf(fact_4734_neg__0__le__iff__le,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.68 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_0_le_iff_le
% 5.46/5.68 thf(fact_4735_neg__0__le__iff__le,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.68 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_0_le_iff_le
% 5.46/5.68 thf(fact_4736_neg__0__le__iff__le,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.68 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_0_le_iff_le
% 5.46/5.68 thf(fact_4737_neg__0__le__iff__le,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.68 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_0_le_iff_le
% 5.46/5.68 thf(fact_4738_less__neg__neg,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.46/5.68 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_neg_neg
% 5.46/5.68 thf(fact_4739_less__neg__neg,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.46/5.68 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_neg_neg
% 5.46/5.68 thf(fact_4740_less__neg__neg,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.68 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_neg_neg
% 5.46/5.68 thf(fact_4741_less__neg__neg,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.46/5.68 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_neg_neg
% 5.46/5.68 thf(fact_4742_neg__less__pos,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.46/5.68 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_pos
% 5.46/5.68 thf(fact_4743_neg__less__pos,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.46/5.68 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_pos
% 5.46/5.68 thf(fact_4744_neg__less__pos,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.46/5.68 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_pos
% 5.46/5.68 thf(fact_4745_neg__less__pos,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.46/5.68 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_pos
% 5.46/5.68 thf(fact_4746_neg__0__less__iff__less,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.68 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_0_less_iff_less
% 5.46/5.68 thf(fact_4747_neg__0__less__iff__less,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.68 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_0_less_iff_less
% 5.46/5.68 thf(fact_4748_neg__0__less__iff__less,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.68 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_0_less_iff_less
% 5.46/5.68 thf(fact_4749_neg__0__less__iff__less,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.68 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_0_less_iff_less
% 5.46/5.68 thf(fact_4750_neg__less__0__iff__less,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.46/5.68 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_0_iff_less
% 5.46/5.68 thf(fact_4751_neg__less__0__iff__less,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.46/5.68 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_0_iff_less
% 5.46/5.68 thf(fact_4752_neg__less__0__iff__less,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.46/5.68 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_0_iff_less
% 5.46/5.68 thf(fact_4753_neg__less__0__iff__less,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.46/5.68 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_0_iff_less
% 5.46/5.68 thf(fact_4754_add_Oright__inverse,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.46/5.68 = zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % add.right_inverse
% 5.46/5.68 thf(fact_4755_add_Oright__inverse,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.46/5.68 = zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % add.right_inverse
% 5.46/5.68 thf(fact_4756_add_Oright__inverse,axiom,
% 5.46/5.68 ! [A: complex] :
% 5.46/5.68 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.68 = zero_zero_complex ) ).
% 5.46/5.68
% 5.46/5.68 % add.right_inverse
% 5.46/5.68 thf(fact_4757_add_Oright__inverse,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % add.right_inverse
% 5.46/5.68 thf(fact_4758_add_Oright__inverse,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.46/5.68 = zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % add.right_inverse
% 5.46/5.68 thf(fact_4759_ab__left__minus,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.46/5.68 = zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % ab_left_minus
% 5.46/5.68 thf(fact_4760_ab__left__minus,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.46/5.68 = zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % ab_left_minus
% 5.46/5.68 thf(fact_4761_ab__left__minus,axiom,
% 5.46/5.68 ! [A: complex] :
% 5.46/5.68 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.46/5.68 = zero_zero_complex ) ).
% 5.46/5.68
% 5.46/5.68 % ab_left_minus
% 5.46/5.68 thf(fact_4762_ab__left__minus,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % ab_left_minus
% 5.46/5.68 thf(fact_4763_ab__left__minus,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.46/5.68 = zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % ab_left_minus
% 5.46/5.68 thf(fact_4764_verit__minus__simplify_I3_J,axiom,
% 5.46/5.68 ! [B: int] :
% 5.46/5.68 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.46/5.68 = ( uminus_uminus_int @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_minus_simplify(3)
% 5.46/5.68 thf(fact_4765_verit__minus__simplify_I3_J,axiom,
% 5.46/5.68 ! [B: real] :
% 5.46/5.68 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.46/5.68 = ( uminus_uminus_real @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_minus_simplify(3)
% 5.46/5.68 thf(fact_4766_verit__minus__simplify_I3_J,axiom,
% 5.46/5.68 ! [B: complex] :
% 5.46/5.68 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_minus_simplify(3)
% 5.46/5.68 thf(fact_4767_verit__minus__simplify_I3_J,axiom,
% 5.46/5.68 ! [B: code_integer] :
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_minus_simplify(3)
% 5.46/5.68 thf(fact_4768_verit__minus__simplify_I3_J,axiom,
% 5.46/5.68 ! [B: rat] :
% 5.46/5.68 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.46/5.68 = ( uminus_uminus_rat @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_minus_simplify(3)
% 5.46/5.68 thf(fact_4769_diff__0,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.46/5.68 = ( uminus_uminus_int @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_0
% 5.46/5.68 thf(fact_4770_diff__0,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.46/5.68 = ( uminus_uminus_real @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_0
% 5.46/5.68 thf(fact_4771_diff__0,axiom,
% 5.46/5.68 ! [A: complex] :
% 5.46/5.68 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_0
% 5.46/5.68 thf(fact_4772_diff__0,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_0
% 5.46/5.68 thf(fact_4773_diff__0,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.46/5.68 = ( uminus_uminus_rat @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_0
% 5.46/5.68 thf(fact_4774_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4775_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4776_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4777_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4778_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4779_mult__minus1,axiom,
% 5.46/5.68 ! [Z: int] :
% 5.46/5.68 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.46/5.68 = ( uminus_uminus_int @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1
% 5.46/5.68 thf(fact_4780_mult__minus1,axiom,
% 5.46/5.68 ! [Z: real] :
% 5.46/5.68 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.46/5.68 = ( uminus_uminus_real @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1
% 5.46/5.68 thf(fact_4781_mult__minus1,axiom,
% 5.46/5.68 ! [Z: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1
% 5.46/5.68 thf(fact_4782_mult__minus1,axiom,
% 5.46/5.68 ! [Z: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1
% 5.46/5.68 thf(fact_4783_mult__minus1,axiom,
% 5.46/5.68 ! [Z: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.46/5.68 = ( uminus_uminus_rat @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1
% 5.46/5.68 thf(fact_4784_mult__minus1__right,axiom,
% 5.46/5.68 ! [Z: int] :
% 5.46/5.68 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( uminus_uminus_int @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1_right
% 5.46/5.68 thf(fact_4785_mult__minus1__right,axiom,
% 5.46/5.68 ! [Z: real] :
% 5.46/5.68 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( uminus_uminus_real @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1_right
% 5.46/5.68 thf(fact_4786_mult__minus1__right,axiom,
% 5.46/5.68 ! [Z: complex] :
% 5.46/5.68 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1_right
% 5.46/5.68 thf(fact_4787_mult__minus1__right,axiom,
% 5.46/5.68 ! [Z: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1_right
% 5.46/5.68 thf(fact_4788_mult__minus1__right,axiom,
% 5.46/5.68 ! [Z: rat] :
% 5.46/5.68 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( uminus_uminus_rat @ Z ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_minus1_right
% 5.46/5.68 thf(fact_4789_diff__minus__eq__add,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( plus_plus_int @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_minus_eq_add
% 5.46/5.68 thf(fact_4790_diff__minus__eq__add,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( plus_plus_real @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_minus_eq_add
% 5.46/5.68 thf(fact_4791_diff__minus__eq__add,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.68 = ( plus_plus_complex @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_minus_eq_add
% 5.46/5.68 thf(fact_4792_diff__minus__eq__add,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_minus_eq_add
% 5.46/5.68 thf(fact_4793_diff__minus__eq__add,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( plus_plus_rat @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_minus_eq_add
% 5.46/5.68 thf(fact_4794_uminus__add__conv__diff,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( minus_minus_int @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_add_conv_diff
% 5.46/5.68 thf(fact_4795_uminus__add__conv__diff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.46/5.68 = ( minus_minus_real @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_add_conv_diff
% 5.46/5.68 thf(fact_4796_uminus__add__conv__diff,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.46/5.68 = ( minus_minus_complex @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_add_conv_diff
% 5.46/5.68 thf(fact_4797_uminus__add__conv__diff,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.46/5.68 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_add_conv_diff
% 5.46/5.68 thf(fact_4798_uminus__add__conv__diff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.46/5.68 = ( minus_minus_rat @ B @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_add_conv_diff
% 5.46/5.68 thf(fact_4799_div__minus1__right,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( uminus_uminus_int @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_minus1_right
% 5.46/5.68 thf(fact_4800_div__minus1__right,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_minus1_right
% 5.46/5.68 thf(fact_4801_divide__minus1,axiom,
% 5.46/5.68 ! [X2: real] :
% 5.46/5.68 ( ( divide_divide_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( uminus_uminus_real @ X2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_minus1
% 5.46/5.68 thf(fact_4802_divide__minus1,axiom,
% 5.46/5.68 ! [X2: complex] :
% 5.46/5.68 ( ( divide1717551699836669952omplex @ X2 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ X2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_minus1
% 5.46/5.68 thf(fact_4803_divide__minus1,axiom,
% 5.46/5.68 ! [X2: rat] :
% 5.46/5.68 ( ( divide_divide_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( uminus_uminus_rat @ X2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_minus1
% 5.46/5.68 thf(fact_4804_minus__mod__self1,axiom,
% 5.46/5.68 ! [B: int,A: int] :
% 5.46/5.68 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.46/5.68 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mod_self1
% 5.46/5.68 thf(fact_4805_minus__mod__self1,axiom,
% 5.46/5.68 ! [B: code_integer,A: code_integer] :
% 5.46/5.68 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.46/5.68 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mod_self1
% 5.46/5.68 thf(fact_4806_zero__less__of__bool__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_of_bool_iff
% 5.46/5.68 thf(fact_4807_zero__less__of__bool__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_of_bool_iff
% 5.46/5.68 thf(fact_4808_zero__less__of__bool__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_of_bool_iff
% 5.46/5.68 thf(fact_4809_zero__less__of__bool__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_of_bool_iff
% 5.46/5.68 thf(fact_4810_zero__less__of__bool__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.46/5.68 = P ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_of_bool_iff
% 5.46/5.68 thf(fact_4811_of__bool__less__one__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_one_iff
% 5.46/5.68 thf(fact_4812_of__bool__less__one__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_one_iff
% 5.46/5.68 thf(fact_4813_of__bool__less__one__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_one_iff
% 5.46/5.68 thf(fact_4814_of__bool__less__one__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_one_iff
% 5.46/5.68 thf(fact_4815_of__bool__less__one__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.46/5.68 = ~ P ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_one_iff
% 5.46/5.68 thf(fact_4816_of__bool__not__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.46/5.68 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_not_iff
% 5.46/5.68 thf(fact_4817_of__bool__not__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.46/5.68 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_not_iff
% 5.46/5.68 thf(fact_4818_of__bool__not__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.46/5.68 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_not_iff
% 5.46/5.68 thf(fact_4819_of__bool__not__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.46/5.68 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_not_iff
% 5.46/5.68 thf(fact_4820_of__bool__not__iff,axiom,
% 5.46/5.68 ! [P: $o] :
% 5.46/5.68 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.46/5.68 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_not_iff
% 5.46/5.68 thf(fact_4821_Suc__0__mod__eq,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.68 = ( zero_n2687167440665602831ol_nat
% 5.46/5.68 @ ( N
% 5.46/5.68 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Suc_0_mod_eq
% 5.46/5.68 thf(fact_4822_signed__take__bit__of__minus__1,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_of_minus_1
% 5.46/5.68 thf(fact_4823_signed__take__bit__of__minus__1,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_of_minus_1
% 5.46/5.68 thf(fact_4824_Ball__set__replicate,axiom,
% 5.46/5.68 ! [N: nat,A: int,P: int > $o] :
% 5.46/5.68 ( ( ! [X: int] :
% 5.46/5.68 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.46/5.68 => ( P @ X ) ) )
% 5.46/5.68 = ( ( P @ A )
% 5.46/5.68 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Ball_set_replicate
% 5.46/5.68 thf(fact_4825_Ball__set__replicate,axiom,
% 5.46/5.68 ! [N: nat,A: nat,P: nat > $o] :
% 5.46/5.68 ( ( ! [X: nat] :
% 5.46/5.68 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.46/5.68 => ( P @ X ) ) )
% 5.46/5.68 = ( ( P @ A )
% 5.46/5.68 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Ball_set_replicate
% 5.46/5.68 thf(fact_4826_Ball__set__replicate,axiom,
% 5.46/5.68 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.46/5.68 ( ( ! [X: vEBT_VEBT] :
% 5.46/5.68 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.46/5.68 => ( P @ X ) ) )
% 5.46/5.68 = ( ( P @ A )
% 5.46/5.68 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Ball_set_replicate
% 5.46/5.68 thf(fact_4827_Bex__set__replicate,axiom,
% 5.46/5.68 ! [N: nat,A: int,P: int > $o] :
% 5.46/5.68 ( ( ? [X: int] :
% 5.46/5.68 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.46/5.68 & ( P @ X ) ) )
% 5.46/5.68 = ( ( P @ A )
% 5.46/5.68 & ( N != zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Bex_set_replicate
% 5.46/5.68 thf(fact_4828_Bex__set__replicate,axiom,
% 5.46/5.68 ! [N: nat,A: nat,P: nat > $o] :
% 5.46/5.68 ( ( ? [X: nat] :
% 5.46/5.68 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.46/5.68 & ( P @ X ) ) )
% 5.46/5.68 = ( ( P @ A )
% 5.46/5.68 & ( N != zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Bex_set_replicate
% 5.46/5.68 thf(fact_4829_Bex__set__replicate,axiom,
% 5.46/5.68 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.46/5.68 ( ( ? [X: vEBT_VEBT] :
% 5.46/5.68 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.46/5.68 & ( P @ X ) ) )
% 5.46/5.68 = ( ( P @ A )
% 5.46/5.68 & ( N != zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Bex_set_replicate
% 5.46/5.68 thf(fact_4830_in__set__replicate,axiom,
% 5.46/5.68 ! [X2: product_prod_nat_nat,N: nat,Y2: product_prod_nat_nat] :
% 5.46/5.68 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ Y2 ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 & ( N != zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % in_set_replicate
% 5.46/5.68 thf(fact_4831_in__set__replicate,axiom,
% 5.46/5.68 ! [X2: complex,N: nat,Y2: complex] :
% 5.46/5.68 ( ( member_complex @ X2 @ ( set_complex2 @ ( replicate_complex @ N @ Y2 ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 & ( N != zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % in_set_replicate
% 5.46/5.68 thf(fact_4832_in__set__replicate,axiom,
% 5.46/5.68 ! [X2: real,N: nat,Y2: real] :
% 5.46/5.68 ( ( member_real @ X2 @ ( set_real2 @ ( replicate_real @ N @ Y2 ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 & ( N != zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % in_set_replicate
% 5.46/5.68 thf(fact_4833_in__set__replicate,axiom,
% 5.46/5.68 ! [X2: int,N: nat,Y2: int] :
% 5.46/5.68 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ Y2 ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 & ( N != zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % in_set_replicate
% 5.46/5.68 thf(fact_4834_in__set__replicate,axiom,
% 5.46/5.68 ! [X2: nat,N: nat,Y2: nat] :
% 5.46/5.68 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ Y2 ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 & ( N != zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % in_set_replicate
% 5.46/5.68 thf(fact_4835_in__set__replicate,axiom,
% 5.46/5.68 ! [X2: vEBT_VEBT,N: nat,Y2: vEBT_VEBT] :
% 5.46/5.68 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y2 ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 & ( N != zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % in_set_replicate
% 5.46/5.68 thf(fact_4836_pred__numeral__simps_I1_J,axiom,
% 5.46/5.68 ( ( pred_numeral @ one )
% 5.46/5.68 = zero_zero_nat ) ).
% 5.46/5.68
% 5.46/5.68 % pred_numeral_simps(1)
% 5.46/5.68 thf(fact_4837_eq__numeral__Suc,axiom,
% 5.46/5.68 ! [K: num,N: nat] :
% 5.46/5.68 ( ( ( numeral_numeral_nat @ K )
% 5.46/5.68 = ( suc @ N ) )
% 5.46/5.68 = ( ( pred_numeral @ K )
% 5.46/5.68 = N ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_numeral_Suc
% 5.46/5.68 thf(fact_4838_Suc__eq__numeral,axiom,
% 5.46/5.68 ! [N: nat,K: num] :
% 5.46/5.68 ( ( ( suc @ N )
% 5.46/5.68 = ( numeral_numeral_nat @ K ) )
% 5.46/5.68 = ( N
% 5.46/5.68 = ( pred_numeral @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Suc_eq_numeral
% 5.46/5.68 thf(fact_4839_nth__replicate,axiom,
% 5.46/5.68 ! [I: nat,N: nat,X2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ I @ N )
% 5.46/5.68 => ( ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I )
% 5.46/5.68 = X2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % nth_replicate
% 5.46/5.68 thf(fact_4840_nth__replicate,axiom,
% 5.46/5.68 ! [I: nat,N: nat,X2: vEBT_VEBT] :
% 5.46/5.68 ( ( ord_less_nat @ I @ N )
% 5.46/5.68 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I )
% 5.46/5.68 = X2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % nth_replicate
% 5.46/5.68 thf(fact_4841_dbl__simps_I1_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(1)
% 5.46/5.68 thf(fact_4842_dbl__simps_I1_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(1)
% 5.46/5.68 thf(fact_4843_dbl__simps_I1_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(1)
% 5.46/5.68 thf(fact_4844_dbl__simps_I1_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(1)
% 5.46/5.68 thf(fact_4845_dbl__simps_I1_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(1)
% 5.46/5.68 thf(fact_4846_dbl__inc__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_inc_simps(4)
% 5.46/5.68 thf(fact_4847_dbl__inc__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_inc_simps(4)
% 5.46/5.68 thf(fact_4848_dbl__inc__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_inc_simps(4)
% 5.46/5.68 thf(fact_4849_dbl__inc__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_inc_simps(4)
% 5.46/5.68 thf(fact_4850_dbl__inc__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_inc_simps(4)
% 5.46/5.68 thf(fact_4851_triangle__Suc,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( nat_triangle @ ( suc @ N ) )
% 5.46/5.68 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % triangle_Suc
% 5.46/5.68 thf(fact_4852_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.68 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.46/5.68 = zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(8)
% 5.46/5.68 thf(fact_4853_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.68 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.46/5.68 = zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(8)
% 5.46/5.68 thf(fact_4854_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.68 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.46/5.68 = zero_zero_complex ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(8)
% 5.46/5.68 thf(fact_4855_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(8)
% 5.46/5.68 thf(fact_4856_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.68 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.46/5.68 = zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(8)
% 5.46/5.68 thf(fact_4857_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.68 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(7)
% 5.46/5.68 thf(fact_4858_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.68 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(7)
% 5.46/5.68 thf(fact_4859_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.68 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = zero_zero_complex ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(7)
% 5.46/5.68 thf(fact_4860_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(7)
% 5.46/5.68 thf(fact_4861_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.68 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(7)
% 5.46/5.68 thf(fact_4862_diff__numeral__special_I12_J,axiom,
% 5.46/5.68 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(12)
% 5.46/5.68 thf(fact_4863_diff__numeral__special_I12_J,axiom,
% 5.46/5.68 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(12)
% 5.46/5.68 thf(fact_4864_diff__numeral__special_I12_J,axiom,
% 5.46/5.68 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = zero_zero_complex ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(12)
% 5.46/5.68 thf(fact_4865_diff__numeral__special_I12_J,axiom,
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(12)
% 5.46/5.68 thf(fact_4866_diff__numeral__special_I12_J,axiom,
% 5.46/5.68 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(12)
% 5.46/5.68 thf(fact_4867_neg__one__eq__numeral__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus_uminus_int @ one_one_int )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_eq_numeral_iff
% 5.46/5.68 thf(fact_4868_neg__one__eq__numeral__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus_uminus_real @ one_one_real )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_eq_numeral_iff
% 5.46/5.68 thf(fact_4869_neg__one__eq__numeral__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_eq_numeral_iff
% 5.46/5.68 thf(fact_4870_neg__one__eq__numeral__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_eq_numeral_iff
% 5.46/5.68 thf(fact_4871_neg__one__eq__numeral__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_eq_numeral_iff
% 5.46/5.68 thf(fact_4872_numeral__eq__neg__one__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_eq_neg_one_iff
% 5.46/5.68 thf(fact_4873_numeral__eq__neg__one__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.46/5.68 = ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_eq_neg_one_iff
% 5.46/5.68 thf(fact_4874_numeral__eq__neg__one__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_eq_neg_one_iff
% 5.46/5.68 thf(fact_4875_numeral__eq__neg__one__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_eq_neg_one_iff
% 5.46/5.68 thf(fact_4876_numeral__eq__neg__one__iff,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.46/5.68 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( N = one ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_eq_neg_one_iff
% 5.46/5.68 thf(fact_4877_minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.46/5.68 = one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_mult_self
% 5.46/5.68 thf(fact_4878_minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.46/5.68 = one_one_real ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_mult_self
% 5.46/5.68 thf(fact_4879_minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.46/5.68 = one_one_complex ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_mult_self
% 5.46/5.68 thf(fact_4880_minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.46/5.68 = one_one_Code_integer ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_mult_self
% 5.46/5.68 thf(fact_4881_minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.46/5.68 = one_one_rat ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_mult_self
% 5.46/5.68 thf(fact_4882_left__minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat,A: int] :
% 5.46/5.68 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 5.46/5.68 = A ) ).
% 5.46/5.68
% 5.46/5.68 % left_minus_one_mult_self
% 5.46/5.68 thf(fact_4883_left__minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat,A: real] :
% 5.46/5.68 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 5.46/5.68 = A ) ).
% 5.46/5.68
% 5.46/5.68 % left_minus_one_mult_self
% 5.46/5.68 thf(fact_4884_left__minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat,A: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.46/5.68 = A ) ).
% 5.46/5.68
% 5.46/5.68 % left_minus_one_mult_self
% 5.46/5.68 thf(fact_4885_left__minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat,A: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.46/5.68 = A ) ).
% 5.46/5.68
% 5.46/5.68 % left_minus_one_mult_self
% 5.46/5.68 thf(fact_4886_left__minus__one__mult__self,axiom,
% 5.46/5.68 ! [N: nat,A: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 5.46/5.68 = A ) ).
% 5.46/5.68
% 5.46/5.68 % left_minus_one_mult_self
% 5.46/5.68 thf(fact_4887_mod__minus1__right,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus1_right
% 5.46/5.68 thf(fact_4888_mod__minus1__right,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus1_right
% 5.46/5.68 thf(fact_4889_max__number__of_I4_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.68 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.46/5.68 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.68 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(4)
% 5.46/5.68 thf(fact_4890_max__number__of_I4_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.46/5.68 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.46/5.68 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.46/5.68 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(4)
% 5.46/5.68 thf(fact_4891_max__number__of_I4_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.68 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.46/5.68 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.68 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(4)
% 5.46/5.68 thf(fact_4892_max__number__of_I4_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.68 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.46/5.68 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.68 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(4)
% 5.46/5.68 thf(fact_4893_max__number__of_I3_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.46/5.68 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.46/5.68 = ( numeral_numeral_real @ V ) ) )
% 5.46/5.68 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.46/5.68 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(3)
% 5.46/5.68 thf(fact_4894_max__number__of_I3_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.46/5.68 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.46/5.68 = ( numera6620942414471956472nteger @ V ) ) )
% 5.46/5.68 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.46/5.68 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(3)
% 5.46/5.68 thf(fact_4895_max__number__of_I3_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.46/5.68 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.46/5.68 = ( numeral_numeral_rat @ V ) ) )
% 5.46/5.68 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.46/5.68 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(3)
% 5.46/5.68 thf(fact_4896_max__number__of_I3_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.68 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.68 = ( numeral_numeral_int @ V ) ) )
% 5.46/5.68 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.68 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(3)
% 5.46/5.68 thf(fact_4897_max__number__of_I2_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.68 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.46/5.68 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.68 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.68 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(2)
% 5.46/5.68 thf(fact_4898_max__number__of_I2_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.46/5.68 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.46/5.68 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.46/5.68 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.46/5.68 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(2)
% 5.46/5.68 thf(fact_4899_max__number__of_I2_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.68 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.46/5.68 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.68 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.68 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(2)
% 5.46/5.68 thf(fact_4900_max__number__of_I2_J,axiom,
% 5.46/5.68 ! [U: num,V: num] :
% 5.46/5.68 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.68 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.46/5.68 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.68 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.68 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_number_of(2)
% 5.46/5.68 thf(fact_4901_semiring__norm_I168_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: int] :
% 5.46/5.68 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(168)
% 5.46/5.68 thf(fact_4902_semiring__norm_I168_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: real] :
% 5.46/5.68 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(168)
% 5.46/5.68 thf(fact_4903_semiring__norm_I168_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: complex] :
% 5.46/5.68 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(168)
% 5.46/5.68 thf(fact_4904_semiring__norm_I168_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: code_integer] :
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(168)
% 5.46/5.68 thf(fact_4905_semiring__norm_I168_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: rat] :
% 5.46/5.68 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(168)
% 5.46/5.68 thf(fact_4906_diff__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(2)
% 5.46/5.68 thf(fact_4907_diff__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.68 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(2)
% 5.46/5.68 thf(fact_4908_diff__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.68 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(2)
% 5.46/5.68 thf(fact_4909_diff__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.68 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(2)
% 5.46/5.68 thf(fact_4910_diff__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.68 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(2)
% 5.46/5.68 thf(fact_4911_diff__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(3)
% 5.46/5.68 thf(fact_4912_diff__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(3)
% 5.46/5.68 thf(fact_4913_diff__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(3)
% 5.46/5.68 thf(fact_4914_diff__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(3)
% 5.46/5.68 thf(fact_4915_diff__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_simps(3)
% 5.46/5.68 thf(fact_4916_semiring__norm_I172_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: int] :
% 5.46/5.68 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(172)
% 5.46/5.68 thf(fact_4917_semiring__norm_I172_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: real] :
% 5.46/5.68 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(172)
% 5.46/5.68 thf(fact_4918_semiring__norm_I172_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(172)
% 5.46/5.68 thf(fact_4919_semiring__norm_I172_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(172)
% 5.46/5.68 thf(fact_4920_semiring__norm_I172_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(172)
% 5.46/5.68 thf(fact_4921_semiring__norm_I171_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: int] :
% 5.46/5.68 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(171)
% 5.46/5.68 thf(fact_4922_semiring__norm_I171_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: real] :
% 5.46/5.68 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(171)
% 5.46/5.68 thf(fact_4923_semiring__norm_I171_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(171)
% 5.46/5.68 thf(fact_4924_semiring__norm_I171_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(171)
% 5.46/5.68 thf(fact_4925_semiring__norm_I171_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 5.46/5.68 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(171)
% 5.46/5.68 thf(fact_4926_semiring__norm_I170_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: int] :
% 5.46/5.68 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y2 ) )
% 5.46/5.68 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(170)
% 5.46/5.68 thf(fact_4927_semiring__norm_I170_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: real] :
% 5.46/5.68 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y2 ) )
% 5.46/5.68 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(170)
% 5.46/5.68 thf(fact_4928_semiring__norm_I170_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y2 ) )
% 5.46/5.68 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(170)
% 5.46/5.68 thf(fact_4929_semiring__norm_I170_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y2 ) )
% 5.46/5.68 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(170)
% 5.46/5.68 thf(fact_4930_semiring__norm_I170_J,axiom,
% 5.46/5.68 ! [V: num,W: num,Y2: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y2 ) )
% 5.46/5.68 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % semiring_norm(170)
% 5.46/5.68 thf(fact_4931_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4932_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4933_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4934_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4935_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(3)
% 5.46/5.68 thf(fact_4936_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(2)
% 5.46/5.68 thf(fact_4937_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(2)
% 5.46/5.68 thf(fact_4938_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(2)
% 5.46/5.68 thf(fact_4939_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(2)
% 5.46/5.68 thf(fact_4940_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(2)
% 5.46/5.68 thf(fact_4941_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(1)
% 5.46/5.68 thf(fact_4942_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.68 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(1)
% 5.46/5.68 thf(fact_4943_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.68 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(1)
% 5.46/5.68 thf(fact_4944_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.68 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(1)
% 5.46/5.68 thf(fact_4945_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.68 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_numeral_simps(1)
% 5.46/5.68 thf(fact_4946_less__numeral__Suc,axiom,
% 5.46/5.68 ! [K: num,N: nat] :
% 5.46/5.68 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.68 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_numeral_Suc
% 5.46/5.68 thf(fact_4947_less__Suc__numeral,axiom,
% 5.46/5.68 ! [N: nat,K: num] :
% 5.46/5.68 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.68 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_Suc_numeral
% 5.46/5.68 thf(fact_4948_pred__numeral__simps_I3_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.46/5.68 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pred_numeral_simps(3)
% 5.46/5.68 thf(fact_4949_le__Suc__numeral,axiom,
% 5.46/5.68 ! [N: nat,K: num] :
% 5.46/5.68 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.68 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_Suc_numeral
% 5.46/5.68 thf(fact_4950_le__numeral__Suc,axiom,
% 5.46/5.68 ! [K: num,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.68 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_numeral_Suc
% 5.46/5.68 thf(fact_4951_neg__numeral__le__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.68 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_iff
% 5.46/5.68 thf(fact_4952_neg__numeral__le__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.68 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_iff
% 5.46/5.68 thf(fact_4953_neg__numeral__le__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.68 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_iff
% 5.46/5.68 thf(fact_4954_neg__numeral__le__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_iff
% 5.46/5.68 thf(fact_4955_diff__Suc__numeral,axiom,
% 5.46/5.68 ! [N: nat,K: num] :
% 5.46/5.68 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.68 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_Suc_numeral
% 5.46/5.68 thf(fact_4956_diff__numeral__Suc,axiom,
% 5.46/5.68 ! [K: num,N: nat] :
% 5.46/5.68 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.68 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_Suc
% 5.46/5.68 thf(fact_4957_neg__numeral__less__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( ord_less_num @ N @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_iff
% 5.46/5.68 thf(fact_4958_neg__numeral__less__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.68 = ( ord_less_num @ N @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_iff
% 5.46/5.68 thf(fact_4959_neg__numeral__less__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.68 = ( ord_less_num @ N @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_iff
% 5.46/5.68 thf(fact_4960_neg__numeral__less__iff,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.68 = ( ord_less_num @ N @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_iff
% 5.46/5.68 thf(fact_4961_max__Suc__numeral,axiom,
% 5.46/5.68 ! [N: nat,K: num] :
% 5.46/5.68 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.68 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_Suc_numeral
% 5.46/5.68 thf(fact_4962_max__numeral__Suc,axiom,
% 5.46/5.68 ! [K: num,N: nat] :
% 5.46/5.68 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.68 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % max_numeral_Suc
% 5.46/5.68 thf(fact_4963_pred__numeral__simps_I2_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.46/5.68 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pred_numeral_simps(2)
% 5.46/5.68 thf(fact_4964_not__neg__one__le__neg__numeral__iff,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.46/5.68 = ( M != one ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_neg_one_le_neg_numeral_iff
% 5.46/5.68 thf(fact_4965_not__neg__one__le__neg__numeral__iff,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.46/5.68 = ( M != one ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_neg_one_le_neg_numeral_iff
% 5.46/5.68 thf(fact_4966_not__neg__one__le__neg__numeral__iff,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.46/5.68 = ( M != one ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_neg_one_le_neg_numeral_iff
% 5.46/5.68 thf(fact_4967_not__neg__one__le__neg__numeral__iff,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.46/5.68 = ( M != one ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_neg_one_le_neg_numeral_iff
% 5.46/5.68 thf(fact_4968_neg__numeral__less__neg__one__iff,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( M != one ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_neg_one_iff
% 5.46/5.68 thf(fact_4969_neg__numeral__less__neg__one__iff,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( M != one ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_neg_one_iff
% 5.46/5.68 thf(fact_4970_neg__numeral__less__neg__one__iff,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( M != one ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_neg_one_iff
% 5.46/5.68 thf(fact_4971_neg__numeral__less__neg__one__iff,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( M != one ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_neg_one_iff
% 5.46/5.68 thf(fact_4972_divide__le__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [B: real,W: num,A: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.46/5.68 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_le_eq_numeral1(2)
% 5.46/5.68 thf(fact_4973_divide__le__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [B: rat,W: num,A: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.46/5.68 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_le_eq_numeral1(2)
% 5.46/5.68 thf(fact_4974_le__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [A: real,B: real,W: num] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.46/5.68 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_divide_eq_numeral1(2)
% 5.46/5.68 thf(fact_4975_le__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [A: rat,B: rat,W: num] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.46/5.68 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_divide_eq_numeral1(2)
% 5.46/5.68 thf(fact_4976_divide__eq__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [B: real,W: num,A: real] :
% 5.46/5.68 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.68 != zero_zero_real )
% 5.46/5.68 => ( B
% 5.46/5.68 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.46/5.68 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.68 = zero_zero_real )
% 5.46/5.68 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_eq_numeral1(2)
% 5.46/5.68 thf(fact_4977_divide__eq__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [B: complex,W: num,A: complex] :
% 5.46/5.68 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.68 != zero_zero_complex )
% 5.46/5.68 => ( B
% 5.46/5.68 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.46/5.68 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.68 = zero_zero_complex )
% 5.46/5.68 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_eq_numeral1(2)
% 5.46/5.68 thf(fact_4978_divide__eq__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [B: rat,W: num,A: rat] :
% 5.46/5.68 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.68 != zero_zero_rat )
% 5.46/5.68 => ( B
% 5.46/5.68 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.46/5.68 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.68 = zero_zero_rat )
% 5.46/5.68 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_eq_numeral1(2)
% 5.46/5.68 thf(fact_4979_eq__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [A: real,B: real,W: num] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.46/5.68 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.68 != zero_zero_real )
% 5.46/5.68 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.68 = B ) )
% 5.46/5.68 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.68 = zero_zero_real )
% 5.46/5.68 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_eq_numeral1(2)
% 5.46/5.68 thf(fact_4980_eq__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [A: complex,B: complex,W: num] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.46/5.68 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.68 != zero_zero_complex )
% 5.46/5.68 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.68 = B ) )
% 5.46/5.68 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.68 = zero_zero_complex )
% 5.46/5.68 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_eq_numeral1(2)
% 5.46/5.68 thf(fact_4981_eq__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [A: rat,B: rat,W: num] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.46/5.68 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.68 != zero_zero_rat )
% 5.46/5.68 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.68 = B ) )
% 5.46/5.68 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.68 = zero_zero_rat )
% 5.46/5.68 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_eq_numeral1(2)
% 5.46/5.68 thf(fact_4982_divide__less__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [B: real,W: num,A: real] :
% 5.46/5.68 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.46/5.68 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_less_eq_numeral1(2)
% 5.46/5.68 thf(fact_4983_divide__less__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [B: rat,W: num,A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.46/5.68 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_less_eq_numeral1(2)
% 5.46/5.68 thf(fact_4984_less__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [A: real,B: real,W: num] :
% 5.46/5.68 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.46/5.68 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_divide_eq_numeral1(2)
% 5.46/5.68 thf(fact_4985_less__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.68 ! [A: rat,B: rat,W: num] :
% 5.46/5.68 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.46/5.68 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_divide_eq_numeral1(2)
% 5.46/5.68 thf(fact_4986_power2__minus,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_minus
% 5.46/5.68 thf(fact_4987_power2__minus,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_minus
% 5.46/5.68 thf(fact_4988_power2__minus,axiom,
% 5.46/5.68 ! [A: complex] :
% 5.46/5.68 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_minus
% 5.46/5.68 thf(fact_4989_power2__minus,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_minus
% 5.46/5.68 thf(fact_4990_power2__minus,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_minus
% 5.46/5.68 thf(fact_4991_odd__of__bool__self,axiom,
% 5.46/5.68 ! [P2: $o] :
% 5.46/5.68 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P2 ) ) )
% 5.46/5.68 = P2 ) ).
% 5.46/5.68
% 5.46/5.68 % odd_of_bool_self
% 5.46/5.68 thf(fact_4992_odd__of__bool__self,axiom,
% 5.46/5.68 ! [P2: $o] :
% 5.46/5.68 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P2 ) ) )
% 5.46/5.68 = P2 ) ).
% 5.46/5.68
% 5.46/5.68 % odd_of_bool_self
% 5.46/5.68 thf(fact_4993_odd__of__bool__self,axiom,
% 5.46/5.68 ! [P2: $o] :
% 5.46/5.68 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P2 ) ) )
% 5.46/5.68 = P2 ) ).
% 5.46/5.68
% 5.46/5.68 % odd_of_bool_self
% 5.46/5.68 thf(fact_4994_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.68 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(9)
% 5.46/5.68 thf(fact_4995_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.68 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(9)
% 5.46/5.68 thf(fact_4996_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.68 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(9)
% 5.46/5.68 thf(fact_4997_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(9)
% 5.46/5.68 thf(fact_4998_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.68 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_numeral_special(9)
% 5.46/5.68 thf(fact_4999_diff__numeral__special_I11_J,axiom,
% 5.46/5.68 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(11)
% 5.46/5.68 thf(fact_5000_diff__numeral__special_I11_J,axiom,
% 5.46/5.68 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(11)
% 5.46/5.68 thf(fact_5001_diff__numeral__special_I11_J,axiom,
% 5.46/5.68 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(11)
% 5.46/5.68 thf(fact_5002_diff__numeral__special_I11_J,axiom,
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(11)
% 5.46/5.68 thf(fact_5003_diff__numeral__special_I11_J,axiom,
% 5.46/5.68 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(11)
% 5.46/5.68 thf(fact_5004_diff__numeral__special_I10_J,axiom,
% 5.46/5.68 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(10)
% 5.46/5.68 thf(fact_5005_diff__numeral__special_I10_J,axiom,
% 5.46/5.68 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(10)
% 5.46/5.68 thf(fact_5006_diff__numeral__special_I10_J,axiom,
% 5.46/5.68 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(10)
% 5.46/5.68 thf(fact_5007_diff__numeral__special_I10_J,axiom,
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(10)
% 5.46/5.68 thf(fact_5008_diff__numeral__special_I10_J,axiom,
% 5.46/5.68 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(10)
% 5.46/5.68 thf(fact_5009_minus__1__div__2__eq,axiom,
% 5.46/5.68 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_1_div_2_eq
% 5.46/5.68 thf(fact_5010_minus__1__div__2__eq,axiom,
% 5.46/5.68 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_1_div_2_eq
% 5.46/5.68 thf(fact_5011_minus__1__mod__2__eq,axiom,
% 5.46/5.68 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % minus_1_mod_2_eq
% 5.46/5.68 thf(fact_5012_minus__1__mod__2__eq,axiom,
% 5.46/5.68 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_Code_integer ) ).
% 5.46/5.68
% 5.46/5.68 % minus_1_mod_2_eq
% 5.46/5.68 thf(fact_5013_bits__minus__1__mod__2__eq,axiom,
% 5.46/5.68 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % bits_minus_1_mod_2_eq
% 5.46/5.68 thf(fact_5014_bits__minus__1__mod__2__eq,axiom,
% 5.46/5.68 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_Code_integer ) ).
% 5.46/5.68
% 5.46/5.68 % bits_minus_1_mod_2_eq
% 5.46/5.68 thf(fact_5015_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [A: int,N: nat] :
% 5.46/5.68 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Power.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5016_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [A: real,N: nat] :
% 5.46/5.68 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Power.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5017_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [A: complex,N: nat] :
% 5.46/5.68 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Power.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5018_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [A: code_integer,N: nat] :
% 5.46/5.68 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Power.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5019_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [A: rat,N: nat] :
% 5.46/5.68 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Power.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5020_of__bool__half__eq__0,axiom,
% 5.46/5.68 ! [B: $o] :
% 5.46/5.68 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = zero_zero_nat ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_half_eq_0
% 5.46/5.68 thf(fact_5021_of__bool__half__eq__0,axiom,
% 5.46/5.68 ! [B: $o] :
% 5.46/5.68 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 = zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_half_eq_0
% 5.46/5.68 thf(fact_5022_of__bool__half__eq__0,axiom,
% 5.46/5.68 ! [B: $o] :
% 5.46/5.68 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_half_eq_0
% 5.46/5.68 thf(fact_5023_power__minus__odd,axiom,
% 5.46/5.68 ! [N: nat,A: int] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.68 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_odd
% 5.46/5.68 thf(fact_5024_power__minus__odd,axiom,
% 5.46/5.68 ! [N: nat,A: real] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.68 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_odd
% 5.46/5.68 thf(fact_5025_power__minus__odd,axiom,
% 5.46/5.68 ! [N: nat,A: complex] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_odd
% 5.46/5.68 thf(fact_5026_power__minus__odd,axiom,
% 5.46/5.68 ! [N: nat,A: code_integer] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_odd
% 5.46/5.68 thf(fact_5027_power__minus__odd,axiom,
% 5.46/5.68 ! [N: nat,A: rat] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.68 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_odd
% 5.46/5.68 thf(fact_5028_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [N: nat,A: int] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.68 = ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Parity.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5029_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [N: nat,A: real] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.68 = ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Parity.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5030_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [N: nat,A: complex] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.68 = ( power_power_complex @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Parity.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5031_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [N: nat,A: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.68 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Parity.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5032_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.68 ! [N: nat,A: rat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.68 = ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Parity.ring_1_class.power_minus_even
% 5.46/5.68 thf(fact_5033_diff__numeral__special_I4_J,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(4)
% 5.46/5.68 thf(fact_5034_diff__numeral__special_I4_J,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(4)
% 5.46/5.68 thf(fact_5035_diff__numeral__special_I4_J,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(4)
% 5.46/5.68 thf(fact_5036_diff__numeral__special_I4_J,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(4)
% 5.46/5.68 thf(fact_5037_diff__numeral__special_I4_J,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(4)
% 5.46/5.68 thf(fact_5038_diff__numeral__special_I3_J,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(3)
% 5.46/5.68 thf(fact_5039_diff__numeral__special_I3_J,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.68 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(3)
% 5.46/5.68 thf(fact_5040_diff__numeral__special_I3_J,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.68 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(3)
% 5.46/5.68 thf(fact_5041_diff__numeral__special_I3_J,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.68 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(3)
% 5.46/5.68 thf(fact_5042_diff__numeral__special_I3_J,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.68 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_numeral_special(3)
% 5.46/5.68 thf(fact_5043_dbl__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(4)
% 5.46/5.68 thf(fact_5044_dbl__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(4)
% 5.46/5.68 thf(fact_5045_dbl__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(4)
% 5.46/5.68 thf(fact_5046_dbl__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(4)
% 5.46/5.68 thf(fact_5047_dbl__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_simps(4)
% 5.46/5.68 thf(fact_5048_power__minus1__even,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_even
% 5.46/5.68 thf(fact_5049_power__minus1__even,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = one_one_real ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_even
% 5.46/5.68 thf(fact_5050_power__minus1__even,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = one_one_complex ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_even
% 5.46/5.68 thf(fact_5051_power__minus1__even,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = one_one_Code_integer ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_even
% 5.46/5.68 thf(fact_5052_power__minus1__even,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = one_one_rat ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_even
% 5.46/5.68 thf(fact_5053_neg__one__odd__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_odd_power
% 5.46/5.68 thf(fact_5054_neg__one__odd__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.46/5.68 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_odd_power
% 5.46/5.68 thf(fact_5055_neg__one__odd__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_odd_power
% 5.46/5.68 thf(fact_5056_neg__one__odd__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_odd_power
% 5.46/5.68 thf(fact_5057_neg__one__odd__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.46/5.68 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_odd_power
% 5.46/5.68 thf(fact_5058_neg__one__even__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.46/5.68 = one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_even_power
% 5.46/5.68 thf(fact_5059_neg__one__even__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.46/5.68 = one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_even_power
% 5.46/5.68 thf(fact_5060_neg__one__even__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.46/5.68 = one_one_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_even_power
% 5.46/5.68 thf(fact_5061_neg__one__even__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.46/5.68 = one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_even_power
% 5.46/5.68 thf(fact_5062_neg__one__even__power,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.46/5.68 = one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_even_power
% 5.46/5.68 thf(fact_5063_signed__take__bit__0,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_0
% 5.46/5.68 thf(fact_5064_signed__take__bit__0,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.46/5.68 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_0
% 5.46/5.68 thf(fact_5065_signed__take__bit__Suc__minus__bit0,axiom,
% 5.46/5.68 ! [N: nat,K: num] :
% 5.46/5.68 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.68 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_Suc_minus_bit0
% 5.46/5.68 thf(fact_5066_signed__take__bit__numeral__bit0,axiom,
% 5.46/5.68 ! [L2: num,K: num] :
% 5.46/5.68 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.46/5.68 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_numeral_bit0
% 5.46/5.68 thf(fact_5067_one__div__2__pow__eq,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_div_2_pow_eq
% 5.46/5.68 thf(fact_5068_one__div__2__pow__eq,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_div_2_pow_eq
% 5.46/5.68 thf(fact_5069_one__div__2__pow__eq,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_div_2_pow_eq
% 5.46/5.68 thf(fact_5070_bits__1__div__exp,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % bits_1_div_exp
% 5.46/5.68 thf(fact_5071_bits__1__div__exp,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % bits_1_div_exp
% 5.46/5.68 thf(fact_5072_bits__1__div__exp,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % bits_1_div_exp
% 5.46/5.68 thf(fact_5073_signed__take__bit__numeral__minus__bit0,axiom,
% 5.46/5.68 ! [L2: num,K: num] :
% 5.46/5.68 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.68 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_numeral_minus_bit0
% 5.46/5.68 thf(fact_5074_one__mod__2__pow__eq,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_mod_2_pow_eq
% 5.46/5.68 thf(fact_5075_one__mod__2__pow__eq,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_mod_2_pow_eq
% 5.46/5.68 thf(fact_5076_one__mod__2__pow__eq,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_mod_2_pow_eq
% 5.46/5.68 thf(fact_5077_signed__take__bit__numeral__minus__bit1,axiom,
% 5.46/5.68 ! [L2: num,K: num] :
% 5.46/5.68 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.68 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_numeral_minus_bit1
% 5.46/5.68 thf(fact_5078_dvd__antisym,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ M @ N )
% 5.46/5.68 => ( ( dvd_dvd_nat @ N @ M )
% 5.46/5.68 => ( M = N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_antisym
% 5.46/5.68 thf(fact_5079_signed__take__bit__minus,axiom,
% 5.46/5.68 ! [N: nat,K: int] :
% 5.46/5.68 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 5.46/5.68 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_minus
% 5.46/5.68 thf(fact_5080_of__bool__eq__iff,axiom,
% 5.46/5.68 ! [P2: $o,Q2: $o] :
% 5.46/5.68 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 5.46/5.68 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.46/5.68 = ( P2 = Q2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_iff
% 5.46/5.68 thf(fact_5081_of__bool__eq__iff,axiom,
% 5.46/5.68 ! [P2: $o,Q2: $o] :
% 5.46/5.68 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 5.46/5.68 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.46/5.68 = ( P2 = Q2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_iff
% 5.46/5.68 thf(fact_5082_of__bool__eq__iff,axiom,
% 5.46/5.68 ! [P2: $o,Q2: $o] :
% 5.46/5.68 ( ( ( zero_n356916108424825756nteger @ P2 )
% 5.46/5.68 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.46/5.68 = ( P2 = Q2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_eq_iff
% 5.46/5.68 thf(fact_5083_equation__minus__iff,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % equation_minus_iff
% 5.46/5.68 thf(fact_5084_equation__minus__iff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % equation_minus_iff
% 5.46/5.68 thf(fact_5085_equation__minus__iff,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % equation_minus_iff
% 5.46/5.68 thf(fact_5086_equation__minus__iff,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % equation_minus_iff
% 5.46/5.68 thf(fact_5087_equation__minus__iff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % equation_minus_iff
% 5.46/5.68 thf(fact_5088_minus__equation__iff,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ( uminus_uminus_int @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( uminus_uminus_int @ B )
% 5.46/5.68 = A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_equation_iff
% 5.46/5.68 thf(fact_5089_minus__equation__iff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ( uminus_uminus_real @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( uminus_uminus_real @ B )
% 5.46/5.68 = A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_equation_iff
% 5.46/5.68 thf(fact_5090_minus__equation__iff,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( uminus1482373934393186551omplex @ B )
% 5.46/5.68 = A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_equation_iff
% 5.46/5.68 thf(fact_5091_minus__equation__iff,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( uminus1351360451143612070nteger @ B )
% 5.46/5.68 = A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_equation_iff
% 5.46/5.68 thf(fact_5092_minus__equation__iff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( uminus_uminus_rat @ B )
% 5.46/5.68 = A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_equation_iff
% 5.46/5.68 thf(fact_5093_of__bool__conj,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( zero_n3304061248610475627l_real
% 5.46/5.68 @ ( P
% 5.46/5.68 & Q ) )
% 5.46/5.68 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_conj
% 5.46/5.68 thf(fact_5094_of__bool__conj,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( zero_n2052037380579107095ol_rat
% 5.46/5.68 @ ( P
% 5.46/5.68 & Q ) )
% 5.46/5.68 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_conj
% 5.46/5.68 thf(fact_5095_of__bool__conj,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( zero_n2687167440665602831ol_nat
% 5.46/5.68 @ ( P
% 5.46/5.68 & Q ) )
% 5.46/5.68 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_conj
% 5.46/5.68 thf(fact_5096_of__bool__conj,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( zero_n2684676970156552555ol_int
% 5.46/5.68 @ ( P
% 5.46/5.68 & Q ) )
% 5.46/5.68 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_conj
% 5.46/5.68 thf(fact_5097_of__bool__conj,axiom,
% 5.46/5.68 ! [P: $o,Q: $o] :
% 5.46/5.68 ( ( zero_n356916108424825756nteger
% 5.46/5.68 @ ( P
% 5.46/5.68 & Q ) )
% 5.46/5.68 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_conj
% 5.46/5.68 thf(fact_5098_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: complex,C: code_integer > $o > set_complex,P2: produc6271795597528267376eger_o] :
% 5.46/5.68 ( ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: code_integer,Y3: $o] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5099_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: real,C: code_integer > $o > set_real,P2: produc6271795597528267376eger_o] :
% 5.46/5.68 ( ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: code_integer,Y3: $o] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5100_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: nat,C: code_integer > $o > set_nat,P2: produc6271795597528267376eger_o] :
% 5.46/5.68 ( ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: code_integer,Y3: $o] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5101_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: int,C: code_integer > $o > set_int,P2: produc6271795597528267376eger_o] :
% 5.46/5.68 ( ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: code_integer,Y3: $o] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5102_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: complex,C: num > num > set_complex,P2: product_prod_num_num] :
% 5.46/5.68 ( ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: num,Y3: num] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5103_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: real,C: num > num > set_real,P2: product_prod_num_num] :
% 5.46/5.68 ( ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: num,Y3: num] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5104_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: nat,C: num > num > set_nat,P2: product_prod_num_num] :
% 5.46/5.68 ( ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: num,Y3: num] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5105_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: int,C: num > num > set_int,P2: product_prod_num_num] :
% 5.46/5.68 ( ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: num,Y3: num] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5106_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: complex,C: nat > num > set_complex,P2: product_prod_nat_num] :
% 5.46/5.68 ( ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: nat,Y3: num] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5107_mem__case__prodE,axiom,
% 5.46/5.68 ! [Z: real,C: nat > num > set_real,P2: product_prod_nat_num] :
% 5.46/5.68 ( ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P2 ) )
% 5.46/5.68 => ~ ! [X3: nat,Y3: num] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mem_case_prodE
% 5.46/5.68 thf(fact_5108_le__minus__iff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_iff
% 5.46/5.68 thf(fact_5109_le__minus__iff,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_iff
% 5.46/5.68 thf(fact_5110_le__minus__iff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_iff
% 5.46/5.68 thf(fact_5111_le__minus__iff,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_iff
% 5.46/5.68 thf(fact_5112_minus__le__iff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.46/5.68 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_le_iff
% 5.46/5.68 thf(fact_5113_minus__le__iff,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.46/5.68 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_le_iff
% 5.46/5.68 thf(fact_5114_minus__le__iff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.46/5.68 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_le_iff
% 5.46/5.68 thf(fact_5115_minus__le__iff,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_le_iff
% 5.46/5.68 thf(fact_5116_le__imp__neg__le,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.68 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_imp_neg_le
% 5.46/5.68 thf(fact_5117_le__imp__neg__le,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.46/5.68 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_imp_neg_le
% 5.46/5.68 thf(fact_5118_le__imp__neg__le,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.68 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_imp_neg_le
% 5.46/5.68 thf(fact_5119_le__imp__neg__le,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ B )
% 5.46/5.68 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_imp_neg_le
% 5.46/5.68 thf(fact_5120_verit__negate__coefficient_I2_J,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ord_less_int @ A @ B )
% 5.46/5.68 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_negate_coefficient(2)
% 5.46/5.68 thf(fact_5121_verit__negate__coefficient_I2_J,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ B )
% 5.46/5.68 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_negate_coefficient(2)
% 5.46/5.68 thf(fact_5122_verit__negate__coefficient_I2_J,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.46/5.68 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_negate_coefficient(2)
% 5.46/5.68 thf(fact_5123_verit__negate__coefficient_I2_J,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ B )
% 5.46/5.68 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_negate_coefficient(2)
% 5.46/5.68 thf(fact_5124_minus__less__iff,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_less_iff
% 5.46/5.68 thf(fact_5125_minus__less__iff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.46/5.68 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_less_iff
% 5.46/5.68 thf(fact_5126_minus__less__iff,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.46/5.68 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_less_iff
% 5.46/5.68 thf(fact_5127_minus__less__iff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.46/5.68 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_less_iff
% 5.46/5.68 thf(fact_5128_less__minus__iff,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_iff
% 5.46/5.68 thf(fact_5129_less__minus__iff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_iff
% 5.46/5.68 thf(fact_5130_less__minus__iff,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_iff
% 5.46/5.68 thf(fact_5131_less__minus__iff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_iff
% 5.46/5.68 thf(fact_5132_neg__numeral__neq__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.46/5.68 != ( numeral_numeral_int @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_neq_numeral
% 5.46/5.68 thf(fact_5133_neg__numeral__neq__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.46/5.68 != ( numeral_numeral_real @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_neq_numeral
% 5.46/5.68 thf(fact_5134_neg__numeral__neq__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.46/5.68 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_neq_numeral
% 5.46/5.68 thf(fact_5135_neg__numeral__neq__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.46/5.68 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_neq_numeral
% 5.46/5.68 thf(fact_5136_neg__numeral__neq__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.46/5.68 != ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_neq_numeral
% 5.46/5.68 thf(fact_5137_numeral__neq__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( numeral_numeral_int @ M )
% 5.46/5.68 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_numeral
% 5.46/5.68 thf(fact_5138_numeral__neq__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( numeral_numeral_real @ M )
% 5.46/5.68 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_numeral
% 5.46/5.68 thf(fact_5139_numeral__neq__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( numera6690914467698888265omplex @ M )
% 5.46/5.68 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_numeral
% 5.46/5.68 thf(fact_5140_numeral__neq__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( numera6620942414471956472nteger @ M )
% 5.46/5.68 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_numeral
% 5.46/5.68 thf(fact_5141_numeral__neq__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( numeral_numeral_rat @ M )
% 5.46/5.68 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_numeral
% 5.46/5.68 thf(fact_5142_square__eq__iff,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ( times_times_int @ A @ A )
% 5.46/5.68 = ( times_times_int @ B @ B ) )
% 5.46/5.68 = ( ( A = B )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_iff
% 5.46/5.68 thf(fact_5143_square__eq__iff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ( times_times_real @ A @ A )
% 5.46/5.68 = ( times_times_real @ B @ B ) )
% 5.46/5.68 = ( ( A = B )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_iff
% 5.46/5.68 thf(fact_5144_square__eq__iff,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( ( times_times_complex @ A @ A )
% 5.46/5.68 = ( times_times_complex @ B @ B ) )
% 5.46/5.68 = ( ( A = B )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_iff
% 5.46/5.68 thf(fact_5145_square__eq__iff,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.46/5.68 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.46/5.68 = ( ( A = B )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_iff
% 5.46/5.68 thf(fact_5146_square__eq__iff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ( times_times_rat @ A @ A )
% 5.46/5.68 = ( times_times_rat @ B @ B ) )
% 5.46/5.68 = ( ( A = B )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_iff
% 5.46/5.68 thf(fact_5147_minus__mult__commute,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_commute
% 5.46/5.68 thf(fact_5148_minus__mult__commute,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.46/5.68 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_commute
% 5.46/5.68 thf(fact_5149_minus__mult__commute,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.46/5.68 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_commute
% 5.46/5.68 thf(fact_5150_minus__mult__commute,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.46/5.68 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_commute
% 5.46/5.68 thf(fact_5151_minus__mult__commute,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.46/5.68 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mult_commute
% 5.46/5.68 thf(fact_5152_one__neq__neg__one,axiom,
% 5.46/5.68 ( one_one_int
% 5.46/5.68 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_one
% 5.46/5.68 thf(fact_5153_one__neq__neg__one,axiom,
% 5.46/5.68 ( one_one_real
% 5.46/5.68 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_one
% 5.46/5.68 thf(fact_5154_one__neq__neg__one,axiom,
% 5.46/5.68 ( one_one_complex
% 5.46/5.68 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_one
% 5.46/5.68 thf(fact_5155_one__neq__neg__one,axiom,
% 5.46/5.68 ( one_one_Code_integer
% 5.46/5.68 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_one
% 5.46/5.68 thf(fact_5156_one__neq__neg__one,axiom,
% 5.46/5.68 ( one_one_rat
% 5.46/5.68 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_one
% 5.46/5.68 thf(fact_5157_group__cancel_Oneg1,axiom,
% 5.46/5.68 ! [A2: int,K: int,A: int] :
% 5.46/5.68 ( ( A2
% 5.46/5.68 = ( plus_plus_int @ K @ A ) )
% 5.46/5.68 => ( ( uminus_uminus_int @ A2 )
% 5.46/5.68 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.neg1
% 5.46/5.68 thf(fact_5158_group__cancel_Oneg1,axiom,
% 5.46/5.68 ! [A2: real,K: real,A: real] :
% 5.46/5.68 ( ( A2
% 5.46/5.68 = ( plus_plus_real @ K @ A ) )
% 5.46/5.68 => ( ( uminus_uminus_real @ A2 )
% 5.46/5.68 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.neg1
% 5.46/5.68 thf(fact_5159_group__cancel_Oneg1,axiom,
% 5.46/5.68 ! [A2: complex,K: complex,A: complex] :
% 5.46/5.68 ( ( A2
% 5.46/5.68 = ( plus_plus_complex @ K @ A ) )
% 5.46/5.68 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.46/5.68 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.neg1
% 5.46/5.68 thf(fact_5160_group__cancel_Oneg1,axiom,
% 5.46/5.68 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.46/5.68 ( ( A2
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.46/5.68 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.neg1
% 5.46/5.68 thf(fact_5161_group__cancel_Oneg1,axiom,
% 5.46/5.68 ! [A2: rat,K: rat,A: rat] :
% 5.46/5.68 ( ( A2
% 5.46/5.68 = ( plus_plus_rat @ K @ A ) )
% 5.46/5.68 => ( ( uminus_uminus_rat @ A2 )
% 5.46/5.68 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.neg1
% 5.46/5.68 thf(fact_5162_add_Oinverse__distrib__swap,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.46/5.68 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_distrib_swap
% 5.46/5.68 thf(fact_5163_add_Oinverse__distrib__swap,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.46/5.68 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_distrib_swap
% 5.46/5.68 thf(fact_5164_add_Oinverse__distrib__swap,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.46/5.68 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_distrib_swap
% 5.46/5.68 thf(fact_5165_add_Oinverse__distrib__swap,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_distrib_swap
% 5.46/5.68 thf(fact_5166_add_Oinverse__distrib__swap,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.46/5.68 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_distrib_swap
% 5.46/5.68 thf(fact_5167_is__num__normalize_I8_J,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.46/5.68 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % is_num_normalize(8)
% 5.46/5.68 thf(fact_5168_is__num__normalize_I8_J,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.46/5.68 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % is_num_normalize(8)
% 5.46/5.68 thf(fact_5169_is__num__normalize_I8_J,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.46/5.68 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % is_num_normalize(8)
% 5.46/5.68 thf(fact_5170_is__num__normalize_I8_J,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % is_num_normalize(8)
% 5.46/5.68 thf(fact_5171_is__num__normalize_I8_J,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.46/5.68 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % is_num_normalize(8)
% 5.46/5.68 thf(fact_5172_minus__diff__minus,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_minus
% 5.46/5.68 thf(fact_5173_minus__diff__minus,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_minus
% 5.46/5.68 thf(fact_5174_minus__diff__minus,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_minus
% 5.46/5.68 thf(fact_5175_minus__diff__minus,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_minus
% 5.46/5.68 thf(fact_5176_minus__diff__minus,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_minus
% 5.46/5.68 thf(fact_5177_minus__diff__commute,axiom,
% 5.46/5.68 ! [B: int,A: int] :
% 5.46/5.68 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.46/5.68 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_commute
% 5.46/5.68 thf(fact_5178_minus__diff__commute,axiom,
% 5.46/5.68 ! [B: real,A: real] :
% 5.46/5.68 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.46/5.68 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_commute
% 5.46/5.68 thf(fact_5179_minus__diff__commute,axiom,
% 5.46/5.68 ! [B: complex,A: complex] :
% 5.46/5.68 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.46/5.68 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_commute
% 5.46/5.68 thf(fact_5180_minus__diff__commute,axiom,
% 5.46/5.68 ! [B: code_integer,A: code_integer] :
% 5.46/5.68 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.46/5.68 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_commute
% 5.46/5.68 thf(fact_5181_minus__diff__commute,axiom,
% 5.46/5.68 ! [B: rat,A: rat] :
% 5.46/5.68 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.46/5.68 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_diff_commute
% 5.46/5.68 thf(fact_5182_div__minus__right,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_minus_right
% 5.46/5.68 thf(fact_5183_div__minus__right,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_minus_right
% 5.46/5.68 thf(fact_5184_minus__divide__left,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.68 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_left
% 5.46/5.68 thf(fact_5185_minus__divide__left,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.46/5.68 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_left
% 5.46/5.68 thf(fact_5186_minus__divide__left,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.46/5.68 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_left
% 5.46/5.68 thf(fact_5187_minus__divide__divide,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( divide_divide_real @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_divide
% 5.46/5.68 thf(fact_5188_minus__divide__divide,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.68 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_divide
% 5.46/5.68 thf(fact_5189_minus__divide__divide,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( divide_divide_rat @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_divide
% 5.46/5.68 thf(fact_5190_minus__divide__right,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.68 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_right
% 5.46/5.68 thf(fact_5191_minus__divide__right,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.46/5.68 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_right
% 5.46/5.68 thf(fact_5192_minus__divide__right,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.46/5.68 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_right
% 5.46/5.68 thf(fact_5193_mod__minus__eq,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.46/5.68 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus_eq
% 5.46/5.68 thf(fact_5194_mod__minus__eq,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.46/5.68 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus_eq
% 5.46/5.68 thf(fact_5195_mod__minus__cong,axiom,
% 5.46/5.68 ! [A: int,B: int,A4: int] :
% 5.46/5.68 ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.68 = ( modulo_modulo_int @ A4 @ B ) )
% 5.46/5.68 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus_cong
% 5.46/5.68 thf(fact_5196_mod__minus__cong,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer,A4: code_integer] :
% 5.46/5.68 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.46/5.68 = ( modulo364778990260209775nteger @ A4 @ B ) )
% 5.46/5.68 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.46/5.68 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus_cong
% 5.46/5.68 thf(fact_5197_mod__minus__right,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus_right
% 5.46/5.68 thf(fact_5198_mod__minus__right,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_minus_right
% 5.46/5.68 thf(fact_5199_case__prodE,axiom,
% 5.46/5.68 ! [C: code_integer > $o > $o,P2: produc6271795597528267376eger_o] :
% 5.46/5.68 ( ( produc7828578312038201481er_o_o @ C @ P2 )
% 5.46/5.68 => ~ ! [X3: code_integer,Y3: $o] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodE
% 5.46/5.68 thf(fact_5200_case__prodE,axiom,
% 5.46/5.68 ! [C: num > num > $o,P2: product_prod_num_num] :
% 5.46/5.68 ( ( produc5703948589228662326_num_o @ C @ P2 )
% 5.46/5.68 => ~ ! [X3: num,Y3: num] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodE
% 5.46/5.68 thf(fact_5201_case__prodE,axiom,
% 5.46/5.68 ! [C: nat > num > $o,P2: product_prod_nat_num] :
% 5.46/5.68 ( ( produc4927758841916487424_num_o @ C @ P2 )
% 5.46/5.68 => ~ ! [X3: nat,Y3: num] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodE
% 5.46/5.68 thf(fact_5202_case__prodE,axiom,
% 5.46/5.68 ! [C: nat > nat > $o,P2: product_prod_nat_nat] :
% 5.46/5.68 ( ( produc6081775807080527818_nat_o @ C @ P2 )
% 5.46/5.68 => ~ ! [X3: nat,Y3: nat] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodE
% 5.46/5.68 thf(fact_5203_case__prodE,axiom,
% 5.46/5.68 ! [C: int > int > $o,P2: product_prod_int_int] :
% 5.46/5.68 ( ( produc4947309494688390418_int_o @ C @ P2 )
% 5.46/5.68 => ~ ! [X3: int,Y3: int] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodE
% 5.46/5.68 thf(fact_5204_case__prodD,axiom,
% 5.46/5.68 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.46/5.68 ( ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) )
% 5.46/5.68 => ( F @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodD
% 5.46/5.68 thf(fact_5205_case__prodD,axiom,
% 5.46/5.68 ! [F: num > num > $o,A: num,B: num] :
% 5.46/5.68 ( ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) )
% 5.46/5.68 => ( F @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodD
% 5.46/5.68 thf(fact_5206_case__prodD,axiom,
% 5.46/5.68 ! [F: nat > num > $o,A: nat,B: num] :
% 5.46/5.68 ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 5.46/5.68 => ( F @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodD
% 5.46/5.68 thf(fact_5207_case__prodD,axiom,
% 5.46/5.68 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.46/5.68 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.46/5.68 => ( F @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodD
% 5.46/5.68 thf(fact_5208_case__prodD,axiom,
% 5.46/5.68 ! [F: int > int > $o,A: int,B: int] :
% 5.46/5.68 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.46/5.68 => ( F @ A @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodD
% 5.46/5.68 thf(fact_5209_case__prodE_H,axiom,
% 5.46/5.68 ! [C: nat > nat > product_prod_nat_nat > $o,P2: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.46/5.68 ( ( produc8739625826339149834_nat_o @ C @ P2 @ Z )
% 5.46/5.68 => ~ ! [X3: nat,Y3: nat] :
% 5.46/5.68 ( ( P2
% 5.46/5.68 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.46/5.68 => ~ ( C @ X3 @ Y3 @ Z ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodE'
% 5.46/5.68 thf(fact_5210_case__prodD_H,axiom,
% 5.46/5.68 ! [R2: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.46/5.68 ( ( produc8739625826339149834_nat_o @ R2 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.46/5.68 => ( R2 @ A @ B @ C ) ) ).
% 5.46/5.68
% 5.46/5.68 % case_prodD'
% 5.46/5.68 thf(fact_5211_zero__less__eq__of__bool,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_eq_of_bool
% 5.46/5.68 thf(fact_5212_zero__less__eq__of__bool,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_eq_of_bool
% 5.46/5.68 thf(fact_5213_zero__less__eq__of__bool,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_eq_of_bool
% 5.46/5.68 thf(fact_5214_zero__less__eq__of__bool,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_eq_of_bool
% 5.46/5.68 thf(fact_5215_zero__less__eq__of__bool,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_eq_of_bool
% 5.46/5.68 thf(fact_5216_of__bool__less__eq__one,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_eq_one
% 5.46/5.68 thf(fact_5217_of__bool__less__eq__one,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_eq_one
% 5.46/5.68 thf(fact_5218_of__bool__less__eq__one,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_eq_one
% 5.46/5.68 thf(fact_5219_of__bool__less__eq__one,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_eq_one
% 5.46/5.68 thf(fact_5220_of__bool__less__eq__one,axiom,
% 5.46/5.68 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_less_eq_one
% 5.46/5.68 thf(fact_5221_of__bool__def,axiom,
% 5.46/5.68 ( zero_n1201886186963655149omplex
% 5.46/5.68 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_def
% 5.46/5.68 thf(fact_5222_of__bool__def,axiom,
% 5.46/5.68 ( zero_n3304061248610475627l_real
% 5.46/5.68 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_def
% 5.46/5.68 thf(fact_5223_of__bool__def,axiom,
% 5.46/5.68 ( zero_n2052037380579107095ol_rat
% 5.46/5.68 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_def
% 5.46/5.68 thf(fact_5224_of__bool__def,axiom,
% 5.46/5.68 ( zero_n2687167440665602831ol_nat
% 5.46/5.68 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_def
% 5.46/5.68 thf(fact_5225_of__bool__def,axiom,
% 5.46/5.68 ( zero_n2684676970156552555ol_int
% 5.46/5.68 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_def
% 5.46/5.68 thf(fact_5226_of__bool__def,axiom,
% 5.46/5.68 ( zero_n356916108424825756nteger
% 5.46/5.68 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_def
% 5.46/5.68 thf(fact_5227_split__of__bool,axiom,
% 5.46/5.68 ! [P: complex > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.46/5.68 = ( ( P2
% 5.46/5.68 => ( P @ one_one_complex ) )
% 5.46/5.68 & ( ~ P2
% 5.46/5.68 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool
% 5.46/5.68 thf(fact_5228_split__of__bool,axiom,
% 5.46/5.68 ! [P: real > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.46/5.68 = ( ( P2
% 5.46/5.68 => ( P @ one_one_real ) )
% 5.46/5.68 & ( ~ P2
% 5.46/5.68 => ( P @ zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool
% 5.46/5.68 thf(fact_5229_split__of__bool,axiom,
% 5.46/5.68 ! [P: rat > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.46/5.68 = ( ( P2
% 5.46/5.68 => ( P @ one_one_rat ) )
% 5.46/5.68 & ( ~ P2
% 5.46/5.68 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool
% 5.46/5.68 thf(fact_5230_split__of__bool,axiom,
% 5.46/5.68 ! [P: nat > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.46/5.68 = ( ( P2
% 5.46/5.68 => ( P @ one_one_nat ) )
% 5.46/5.68 & ( ~ P2
% 5.46/5.68 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool
% 5.46/5.68 thf(fact_5231_split__of__bool,axiom,
% 5.46/5.68 ! [P: int > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.46/5.68 = ( ( P2
% 5.46/5.68 => ( P @ one_one_int ) )
% 5.46/5.68 & ( ~ P2
% 5.46/5.68 => ( P @ zero_zero_int ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool
% 5.46/5.68 thf(fact_5232_split__of__bool,axiom,
% 5.46/5.68 ! [P: code_integer > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.46/5.68 = ( ( P2
% 5.46/5.68 => ( P @ one_one_Code_integer ) )
% 5.46/5.68 & ( ~ P2
% 5.46/5.68 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool
% 5.46/5.68 thf(fact_5233_split__of__bool__asm,axiom,
% 5.46/5.68 ! [P: complex > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.46/5.68 = ( ~ ( ( P2
% 5.46/5.68 & ~ ( P @ one_one_complex ) )
% 5.46/5.68 | ( ~ P2
% 5.46/5.68 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool_asm
% 5.46/5.68 thf(fact_5234_split__of__bool__asm,axiom,
% 5.46/5.68 ! [P: real > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.46/5.68 = ( ~ ( ( P2
% 5.46/5.68 & ~ ( P @ one_one_real ) )
% 5.46/5.68 | ( ~ P2
% 5.46/5.68 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool_asm
% 5.46/5.68 thf(fact_5235_split__of__bool__asm,axiom,
% 5.46/5.68 ! [P: rat > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.46/5.68 = ( ~ ( ( P2
% 5.46/5.68 & ~ ( P @ one_one_rat ) )
% 5.46/5.68 | ( ~ P2
% 5.46/5.68 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool_asm
% 5.46/5.68 thf(fact_5236_split__of__bool__asm,axiom,
% 5.46/5.68 ! [P: nat > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.46/5.68 = ( ~ ( ( P2
% 5.46/5.68 & ~ ( P @ one_one_nat ) )
% 5.46/5.68 | ( ~ P2
% 5.46/5.68 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool_asm
% 5.46/5.68 thf(fact_5237_split__of__bool__asm,axiom,
% 5.46/5.68 ! [P: int > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.46/5.68 = ( ~ ( ( P2
% 5.46/5.68 & ~ ( P @ one_one_int ) )
% 5.46/5.68 | ( ~ P2
% 5.46/5.68 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool_asm
% 5.46/5.68 thf(fact_5238_split__of__bool__asm,axiom,
% 5.46/5.68 ! [P: code_integer > $o,P2: $o] :
% 5.46/5.68 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.46/5.68 = ( ~ ( ( P2
% 5.46/5.68 & ~ ( P @ one_one_Code_integer ) )
% 5.46/5.68 | ( ~ P2
% 5.46/5.68 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_of_bool_asm
% 5.46/5.68 thf(fact_5239_neg__numeral__le__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_numeral
% 5.46/5.68 thf(fact_5240_neg__numeral__le__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_numeral
% 5.46/5.68 thf(fact_5241_neg__numeral__le__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_numeral
% 5.46/5.68 thf(fact_5242_neg__numeral__le__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_numeral
% 5.46/5.68 thf(fact_5243_not__numeral__le__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_neg_numeral
% 5.46/5.68 thf(fact_5244_not__numeral__le__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_neg_numeral
% 5.46/5.68 thf(fact_5245_not__numeral__le__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_neg_numeral
% 5.46/5.68 thf(fact_5246_not__numeral__le__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_neg_numeral
% 5.46/5.68 thf(fact_5247_zero__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( zero_zero_int
% 5.46/5.68 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_numeral
% 5.46/5.68 thf(fact_5248_zero__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( zero_zero_real
% 5.46/5.68 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_numeral
% 5.46/5.68 thf(fact_5249_zero__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( zero_zero_complex
% 5.46/5.68 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_numeral
% 5.46/5.68 thf(fact_5250_zero__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( zero_z3403309356797280102nteger
% 5.46/5.68 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_numeral
% 5.46/5.68 thf(fact_5251_zero__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( zero_zero_rat
% 5.46/5.68 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_numeral
% 5.46/5.68 thf(fact_5252_neg__numeral__less__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_numeral
% 5.46/5.68 thf(fact_5253_neg__numeral__less__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_numeral
% 5.46/5.68 thf(fact_5254_neg__numeral__less__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_numeral
% 5.46/5.68 thf(fact_5255_neg__numeral__less__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_numeral
% 5.46/5.68 thf(fact_5256_not__numeral__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_neg_numeral
% 5.46/5.68 thf(fact_5257_not__numeral__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_neg_numeral
% 5.46/5.68 thf(fact_5258_not__numeral__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_neg_numeral
% 5.46/5.68 thf(fact_5259_not__numeral__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_neg_numeral
% 5.46/5.68 thf(fact_5260_le__minus__one__simps_I4_J,axiom,
% 5.46/5.68 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(4)
% 5.46/5.68 thf(fact_5261_le__minus__one__simps_I4_J,axiom,
% 5.46/5.68 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(4)
% 5.46/5.68 thf(fact_5262_le__minus__one__simps_I4_J,axiom,
% 5.46/5.68 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(4)
% 5.46/5.68 thf(fact_5263_le__minus__one__simps_I4_J,axiom,
% 5.46/5.68 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(4)
% 5.46/5.68 thf(fact_5264_le__minus__one__simps_I2_J,axiom,
% 5.46/5.68 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(2)
% 5.46/5.68 thf(fact_5265_le__minus__one__simps_I2_J,axiom,
% 5.46/5.68 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(2)
% 5.46/5.68 thf(fact_5266_le__minus__one__simps_I2_J,axiom,
% 5.46/5.68 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(2)
% 5.46/5.68 thf(fact_5267_le__minus__one__simps_I2_J,axiom,
% 5.46/5.68 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(2)
% 5.46/5.68 thf(fact_5268_zero__neq__neg__one,axiom,
% 5.46/5.68 ( zero_zero_int
% 5.46/5.68 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_one
% 5.46/5.68 thf(fact_5269_zero__neq__neg__one,axiom,
% 5.46/5.68 ( zero_zero_real
% 5.46/5.68 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_one
% 5.46/5.68 thf(fact_5270_zero__neq__neg__one,axiom,
% 5.46/5.68 ( zero_zero_complex
% 5.46/5.68 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_one
% 5.46/5.68 thf(fact_5271_zero__neq__neg__one,axiom,
% 5.46/5.68 ( zero_z3403309356797280102nteger
% 5.46/5.68 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_one
% 5.46/5.68 thf(fact_5272_zero__neq__neg__one,axiom,
% 5.46/5.68 ( zero_zero_rat
% 5.46/5.68 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_neq_neg_one
% 5.46/5.68 thf(fact_5273_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ( uminus_uminus_int @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( plus_plus_int @ A @ B )
% 5.46/5.68 = zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_eq_iff_add_eq_0
% 5.46/5.68 thf(fact_5274_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ( uminus_uminus_real @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( plus_plus_real @ A @ B )
% 5.46/5.68 = zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_eq_iff_add_eq_0
% 5.46/5.68 thf(fact_5275_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( plus_plus_complex @ A @ B )
% 5.46/5.68 = zero_zero_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_eq_iff_add_eq_0
% 5.46/5.68 thf(fact_5276_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_eq_iff_add_eq_0
% 5.46/5.68 thf(fact_5277_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.68 = B )
% 5.46/5.68 = ( ( plus_plus_rat @ A @ B )
% 5.46/5.68 = zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_eq_iff_add_eq_0
% 5.46/5.68 thf(fact_5278_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( ( plus_plus_int @ A @ B )
% 5.46/5.68 = zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_neg_iff_add_eq_0
% 5.46/5.68 thf(fact_5279_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( ( plus_plus_real @ A @ B )
% 5.46/5.68 = zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_neg_iff_add_eq_0
% 5.46/5.68 thf(fact_5280_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.68 = ( ( plus_plus_complex @ A @ B )
% 5.46/5.68 = zero_zero_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_neg_iff_add_eq_0
% 5.46/5.68 thf(fact_5281_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_neg_iff_add_eq_0
% 5.46/5.68 thf(fact_5282_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( ( plus_plus_rat @ A @ B )
% 5.46/5.68 = zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_neg_iff_add_eq_0
% 5.46/5.68 thf(fact_5283_add_Oinverse__unique,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ( plus_plus_int @ A @ B )
% 5.46/5.68 = zero_zero_int )
% 5.46/5.68 => ( ( uminus_uminus_int @ A )
% 5.46/5.68 = B ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_unique
% 5.46/5.68 thf(fact_5284_add_Oinverse__unique,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ( plus_plus_real @ A @ B )
% 5.46/5.68 = zero_zero_real )
% 5.46/5.68 => ( ( uminus_uminus_real @ A )
% 5.46/5.68 = B ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_unique
% 5.46/5.68 thf(fact_5285_add_Oinverse__unique,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( ( plus_plus_complex @ A @ B )
% 5.46/5.68 = zero_zero_complex )
% 5.46/5.68 => ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.68 = B ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_unique
% 5.46/5.68 thf(fact_5286_add_Oinverse__unique,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.46/5.68 = zero_z3403309356797280102nteger )
% 5.46/5.68 => ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.68 = B ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_unique
% 5.46/5.68 thf(fact_5287_add_Oinverse__unique,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ( plus_plus_rat @ A @ B )
% 5.46/5.68 = zero_zero_rat )
% 5.46/5.68 => ( ( uminus_uminus_rat @ A )
% 5.46/5.68 = B ) ) ).
% 5.46/5.68
% 5.46/5.68 % add.inverse_unique
% 5.46/5.68 thf(fact_5288_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.46/5.68 = zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_left_minus
% 5.46/5.68 thf(fact_5289_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.46/5.68 = zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_left_minus
% 5.46/5.68 thf(fact_5290_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.68 ! [A: complex] :
% 5.46/5.68 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.46/5.68 = zero_zero_complex ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_left_minus
% 5.46/5.68 thf(fact_5291_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_left_minus
% 5.46/5.68 thf(fact_5292_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.46/5.68 = zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_left_minus
% 5.46/5.68 thf(fact_5293_add__eq__0__iff,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ( plus_plus_int @ A @ B )
% 5.46/5.68 = zero_zero_int )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_eq_0_iff
% 5.46/5.68 thf(fact_5294_add__eq__0__iff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ( plus_plus_real @ A @ B )
% 5.46/5.68 = zero_zero_real )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_eq_0_iff
% 5.46/5.68 thf(fact_5295_add__eq__0__iff,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( ( plus_plus_complex @ A @ B )
% 5.46/5.68 = zero_zero_complex )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_eq_0_iff
% 5.46/5.68 thf(fact_5296_add__eq__0__iff,axiom,
% 5.46/5.68 ! [A: code_integer,B: code_integer] :
% 5.46/5.68 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.46/5.68 = zero_z3403309356797280102nteger )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_eq_0_iff
% 5.46/5.68 thf(fact_5297_add__eq__0__iff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ( plus_plus_rat @ A @ B )
% 5.46/5.68 = zero_zero_rat )
% 5.46/5.68 = ( B
% 5.46/5.68 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_eq_0_iff
% 5.46/5.68 thf(fact_5298_less__minus__one__simps_I4_J,axiom,
% 5.46/5.68 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(4)
% 5.46/5.68 thf(fact_5299_less__minus__one__simps_I4_J,axiom,
% 5.46/5.68 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(4)
% 5.46/5.68 thf(fact_5300_less__minus__one__simps_I4_J,axiom,
% 5.46/5.68 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(4)
% 5.46/5.68 thf(fact_5301_less__minus__one__simps_I4_J,axiom,
% 5.46/5.68 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(4)
% 5.46/5.68 thf(fact_5302_less__minus__one__simps_I2_J,axiom,
% 5.46/5.68 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(2)
% 5.46/5.68 thf(fact_5303_less__minus__one__simps_I2_J,axiom,
% 5.46/5.68 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(2)
% 5.46/5.68 thf(fact_5304_less__minus__one__simps_I2_J,axiom,
% 5.46/5.68 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(2)
% 5.46/5.68 thf(fact_5305_less__minus__one__simps_I2_J,axiom,
% 5.46/5.68 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(2)
% 5.46/5.68 thf(fact_5306_numeral__times__minus__swap,axiom,
% 5.46/5.68 ! [W: num,X2: int] :
% 5.46/5.68 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X2 ) )
% 5.46/5.68 = ( times_times_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_times_minus_swap
% 5.46/5.68 thf(fact_5307_numeral__times__minus__swap,axiom,
% 5.46/5.68 ! [W: num,X2: real] :
% 5.46/5.68 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X2 ) )
% 5.46/5.68 = ( times_times_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_times_minus_swap
% 5.46/5.68 thf(fact_5308_numeral__times__minus__swap,axiom,
% 5.46/5.68 ! [W: num,X2: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.46/5.68 = ( times_times_complex @ X2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_times_minus_swap
% 5.46/5.68 thf(fact_5309_numeral__times__minus__swap,axiom,
% 5.46/5.68 ! [W: num,X2: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X2 ) )
% 5.46/5.68 = ( times_3573771949741848930nteger @ X2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_times_minus_swap
% 5.46/5.68 thf(fact_5310_numeral__times__minus__swap,axiom,
% 5.46/5.68 ! [W: num,X2: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X2 ) )
% 5.46/5.68 = ( times_times_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_times_minus_swap
% 5.46/5.68 thf(fact_5311_nonzero__minus__divide__right,axiom,
% 5.46/5.68 ! [B: real,A: real] :
% 5.46/5.68 ( ( B != zero_zero_real )
% 5.46/5.68 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.68 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_minus_divide_right
% 5.46/5.68 thf(fact_5312_nonzero__minus__divide__right,axiom,
% 5.46/5.68 ! [B: complex,A: complex] :
% 5.46/5.68 ( ( B != zero_zero_complex )
% 5.46/5.68 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.46/5.68 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_minus_divide_right
% 5.46/5.68 thf(fact_5313_nonzero__minus__divide__right,axiom,
% 5.46/5.68 ! [B: rat,A: rat] :
% 5.46/5.68 ( ( B != zero_zero_rat )
% 5.46/5.68 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.46/5.68 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_minus_divide_right
% 5.46/5.68 thf(fact_5314_nonzero__minus__divide__divide,axiom,
% 5.46/5.68 ! [B: real,A: real] :
% 5.46/5.68 ( ( B != zero_zero_real )
% 5.46/5.68 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_minus_divide_divide
% 5.46/5.68 thf(fact_5315_nonzero__minus__divide__divide,axiom,
% 5.46/5.68 ! [B: complex,A: complex] :
% 5.46/5.68 ( ( B != zero_zero_complex )
% 5.46/5.68 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.68 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_minus_divide_divide
% 5.46/5.68 thf(fact_5316_nonzero__minus__divide__divide,axiom,
% 5.46/5.68 ! [B: rat,A: rat] :
% 5.46/5.68 ( ( B != zero_zero_rat )
% 5.46/5.68 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_minus_divide_divide
% 5.46/5.68 thf(fact_5317_numeral__neq__neg__one,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( numeral_numeral_int @ N )
% 5.46/5.68 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_one
% 5.46/5.68 thf(fact_5318_numeral__neq__neg__one,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( numeral_numeral_real @ N )
% 5.46/5.68 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_one
% 5.46/5.68 thf(fact_5319_numeral__neq__neg__one,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( numera6690914467698888265omplex @ N )
% 5.46/5.68 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_one
% 5.46/5.68 thf(fact_5320_numeral__neq__neg__one,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( numera6620942414471956472nteger @ N )
% 5.46/5.68 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_one
% 5.46/5.68 thf(fact_5321_numeral__neq__neg__one,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( numeral_numeral_rat @ N )
% 5.46/5.68 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_neq_neg_one
% 5.46/5.68 thf(fact_5322_one__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( one_one_int
% 5.46/5.68 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_numeral
% 5.46/5.68 thf(fact_5323_one__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( one_one_real
% 5.46/5.68 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_numeral
% 5.46/5.68 thf(fact_5324_one__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( one_one_complex
% 5.46/5.68 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_numeral
% 5.46/5.68 thf(fact_5325_one__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( one_one_Code_integer
% 5.46/5.68 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_numeral
% 5.46/5.68 thf(fact_5326_one__neq__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( one_one_rat
% 5.46/5.68 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_neq_neg_numeral
% 5.46/5.68 thf(fact_5327_square__eq__1__iff,axiom,
% 5.46/5.68 ! [X2: int] :
% 5.46/5.68 ( ( ( times_times_int @ X2 @ X2 )
% 5.46/5.68 = one_one_int )
% 5.46/5.68 = ( ( X2 = one_one_int )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_1_iff
% 5.46/5.68 thf(fact_5328_square__eq__1__iff,axiom,
% 5.46/5.68 ! [X2: real] :
% 5.46/5.68 ( ( ( times_times_real @ X2 @ X2 )
% 5.46/5.68 = one_one_real )
% 5.46/5.68 = ( ( X2 = one_one_real )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_1_iff
% 5.46/5.68 thf(fact_5329_square__eq__1__iff,axiom,
% 5.46/5.68 ! [X2: complex] :
% 5.46/5.68 ( ( ( times_times_complex @ X2 @ X2 )
% 5.46/5.68 = one_one_complex )
% 5.46/5.68 = ( ( X2 = one_one_complex )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_1_iff
% 5.46/5.68 thf(fact_5330_square__eq__1__iff,axiom,
% 5.46/5.68 ! [X2: code_integer] :
% 5.46/5.68 ( ( ( times_3573771949741848930nteger @ X2 @ X2 )
% 5.46/5.68 = one_one_Code_integer )
% 5.46/5.68 = ( ( X2 = one_one_Code_integer )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_1_iff
% 5.46/5.68 thf(fact_5331_square__eq__1__iff,axiom,
% 5.46/5.68 ! [X2: rat] :
% 5.46/5.68 ( ( ( times_times_rat @ X2 @ X2 )
% 5.46/5.68 = one_one_rat )
% 5.46/5.68 = ( ( X2 = one_one_rat )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_eq_1_iff
% 5.46/5.68 thf(fact_5332_group__cancel_Osub2,axiom,
% 5.46/5.68 ! [B3: int,K: int,B: int,A: int] :
% 5.46/5.68 ( ( B3
% 5.46/5.68 = ( plus_plus_int @ K @ B ) )
% 5.46/5.68 => ( ( minus_minus_int @ A @ B3 )
% 5.46/5.68 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.sub2
% 5.46/5.68 thf(fact_5333_group__cancel_Osub2,axiom,
% 5.46/5.68 ! [B3: real,K: real,B: real,A: real] :
% 5.46/5.68 ( ( B3
% 5.46/5.68 = ( plus_plus_real @ K @ B ) )
% 5.46/5.68 => ( ( minus_minus_real @ A @ B3 )
% 5.46/5.68 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.sub2
% 5.46/5.68 thf(fact_5334_group__cancel_Osub2,axiom,
% 5.46/5.68 ! [B3: complex,K: complex,B: complex,A: complex] :
% 5.46/5.68 ( ( B3
% 5.46/5.68 = ( plus_plus_complex @ K @ B ) )
% 5.46/5.68 => ( ( minus_minus_complex @ A @ B3 )
% 5.46/5.68 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.sub2
% 5.46/5.68 thf(fact_5335_group__cancel_Osub2,axiom,
% 5.46/5.68 ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.46/5.68 ( ( B3
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.46/5.68 => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.sub2
% 5.46/5.68 thf(fact_5336_group__cancel_Osub2,axiom,
% 5.46/5.68 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.46/5.68 ( ( B3
% 5.46/5.68 = ( plus_plus_rat @ K @ B ) )
% 5.46/5.68 => ( ( minus_minus_rat @ A @ B3 )
% 5.46/5.68 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % group_cancel.sub2
% 5.46/5.68 thf(fact_5337_diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_minus_int
% 5.46/5.68 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_conv_add_uminus
% 5.46/5.68 thf(fact_5338_diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_minus_real
% 5.46/5.68 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_conv_add_uminus
% 5.46/5.68 thf(fact_5339_diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_minus_complex
% 5.46/5.68 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_conv_add_uminus
% 5.46/5.68 thf(fact_5340_diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_8373710615458151222nteger
% 5.46/5.68 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_conv_add_uminus
% 5.46/5.68 thf(fact_5341_diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_minus_rat
% 5.46/5.68 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_conv_add_uminus
% 5.46/5.68 thf(fact_5342_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_minus_int
% 5.46/5.68 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.68 thf(fact_5343_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_minus_real
% 5.46/5.68 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.68 thf(fact_5344_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_minus_complex
% 5.46/5.68 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.68 thf(fact_5345_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_8373710615458151222nteger
% 5.46/5.68 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.68 thf(fact_5346_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.68 ( minus_minus_rat
% 5.46/5.68 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.68 thf(fact_5347_replicate__eqI,axiom,
% 5.46/5.68 ! [Xs2: list_P6011104703257516679at_nat,N: nat,X2: product_prod_nat_nat] :
% 5.46/5.68 ( ( ( size_s5460976970255530739at_nat @ Xs2 )
% 5.46/5.68 = N )
% 5.46/5.68 => ( ! [Y3: product_prod_nat_nat] :
% 5.46/5.68 ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.46/5.68 => ( Y3 = X2 ) )
% 5.46/5.68 => ( Xs2
% 5.46/5.68 = ( replic4235873036481779905at_nat @ N @ X2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_eqI
% 5.46/5.68 thf(fact_5348_replicate__eqI,axiom,
% 5.46/5.68 ! [Xs2: list_complex,N: nat,X2: complex] :
% 5.46/5.68 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.46/5.68 = N )
% 5.46/5.68 => ( ! [Y3: complex] :
% 5.46/5.68 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 5.46/5.68 => ( Y3 = X2 ) )
% 5.46/5.68 => ( Xs2
% 5.46/5.68 = ( replicate_complex @ N @ X2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_eqI
% 5.46/5.68 thf(fact_5349_replicate__eqI,axiom,
% 5.46/5.68 ! [Xs2: list_real,N: nat,X2: real] :
% 5.46/5.68 ( ( ( size_size_list_real @ Xs2 )
% 5.46/5.68 = N )
% 5.46/5.68 => ( ! [Y3: real] :
% 5.46/5.68 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 5.46/5.68 => ( Y3 = X2 ) )
% 5.46/5.68 => ( Xs2
% 5.46/5.68 = ( replicate_real @ N @ X2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_eqI
% 5.46/5.68 thf(fact_5350_replicate__eqI,axiom,
% 5.46/5.68 ! [Xs2: list_VEBT_VEBT,N: nat,X2: vEBT_VEBT] :
% 5.46/5.68 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.46/5.68 = N )
% 5.46/5.68 => ( ! [Y3: vEBT_VEBT] :
% 5.46/5.68 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.46/5.68 => ( Y3 = X2 ) )
% 5.46/5.68 => ( Xs2
% 5.46/5.68 = ( replicate_VEBT_VEBT @ N @ X2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_eqI
% 5.46/5.68 thf(fact_5351_replicate__eqI,axiom,
% 5.46/5.68 ! [Xs2: list_o,N: nat,X2: $o] :
% 5.46/5.68 ( ( ( size_size_list_o @ Xs2 )
% 5.46/5.68 = N )
% 5.46/5.68 => ( ! [Y3: $o] :
% 5.46/5.68 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 5.46/5.68 => ( Y3 = X2 ) )
% 5.46/5.68 => ( Xs2
% 5.46/5.68 = ( replicate_o @ N @ X2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_eqI
% 5.46/5.68 thf(fact_5352_replicate__eqI,axiom,
% 5.46/5.68 ! [Xs2: list_nat,N: nat,X2: nat] :
% 5.46/5.68 ( ( ( size_size_list_nat @ Xs2 )
% 5.46/5.68 = N )
% 5.46/5.68 => ( ! [Y3: nat] :
% 5.46/5.68 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 5.46/5.68 => ( Y3 = X2 ) )
% 5.46/5.68 => ( Xs2
% 5.46/5.68 = ( replicate_nat @ N @ X2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_eqI
% 5.46/5.68 thf(fact_5353_replicate__eqI,axiom,
% 5.46/5.68 ! [Xs2: list_int,N: nat,X2: int] :
% 5.46/5.68 ( ( ( size_size_list_int @ Xs2 )
% 5.46/5.68 = N )
% 5.46/5.68 => ( ! [Y3: int] :
% 5.46/5.68 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 5.46/5.68 => ( Y3 = X2 ) )
% 5.46/5.68 => ( Xs2
% 5.46/5.68 = ( replicate_int @ N @ X2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_eqI
% 5.46/5.68 thf(fact_5354_replicate__length__same,axiom,
% 5.46/5.68 ! [Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.46/5.68 ( ! [X3: vEBT_VEBT] :
% 5.46/5.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.46/5.68 => ( X3 = X2 ) )
% 5.46/5.68 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X2 )
% 5.46/5.68 = Xs2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_length_same
% 5.46/5.68 thf(fact_5355_replicate__length__same,axiom,
% 5.46/5.68 ! [Xs2: list_o,X2: $o] :
% 5.46/5.68 ( ! [X3: $o] :
% 5.46/5.68 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.46/5.68 => ( X3 = X2 ) )
% 5.46/5.68 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X2 )
% 5.46/5.68 = Xs2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_length_same
% 5.46/5.68 thf(fact_5356_replicate__length__same,axiom,
% 5.46/5.68 ! [Xs2: list_nat,X2: nat] :
% 5.46/5.68 ( ! [X3: nat] :
% 5.46/5.68 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.46/5.68 => ( X3 = X2 ) )
% 5.46/5.68 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X2 )
% 5.46/5.68 = Xs2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_length_same
% 5.46/5.68 thf(fact_5357_replicate__length__same,axiom,
% 5.46/5.68 ! [Xs2: list_int,X2: int] :
% 5.46/5.68 ( ! [X3: int] :
% 5.46/5.68 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.46/5.68 => ( X3 = X2 ) )
% 5.46/5.68 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X2 )
% 5.46/5.68 = Xs2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % replicate_length_same
% 5.46/5.68 thf(fact_5358_dvd__div__neg,axiom,
% 5.46/5.68 ! [B: int,A: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ B @ A )
% 5.46/5.68 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_neg
% 5.46/5.68 thf(fact_5359_dvd__div__neg,axiom,
% 5.46/5.68 ! [B: real,A: real] :
% 5.46/5.68 ( ( dvd_dvd_real @ B @ A )
% 5.46/5.68 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_neg
% 5.46/5.68 thf(fact_5360_dvd__div__neg,axiom,
% 5.46/5.68 ! [B: complex,A: complex] :
% 5.46/5.68 ( ( dvd_dvd_complex @ B @ A )
% 5.46/5.68 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_neg
% 5.46/5.68 thf(fact_5361_dvd__div__neg,axiom,
% 5.46/5.68 ! [B: code_integer,A: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.68 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_neg
% 5.46/5.68 thf(fact_5362_dvd__div__neg,axiom,
% 5.46/5.68 ! [B: rat,A: rat] :
% 5.46/5.68 ( ( dvd_dvd_rat @ B @ A )
% 5.46/5.68 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_neg
% 5.46/5.68 thf(fact_5363_dvd__neg__div,axiom,
% 5.46/5.68 ! [B: int,A: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ B @ A )
% 5.46/5.68 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_neg_div
% 5.46/5.68 thf(fact_5364_dvd__neg__div,axiom,
% 5.46/5.68 ! [B: real,A: real] :
% 5.46/5.68 ( ( dvd_dvd_real @ B @ A )
% 5.46/5.68 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.46/5.68 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_neg_div
% 5.46/5.68 thf(fact_5365_dvd__neg__div,axiom,
% 5.46/5.68 ! [B: complex,A: complex] :
% 5.46/5.68 ( ( dvd_dvd_complex @ B @ A )
% 5.46/5.68 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_neg_div
% 5.46/5.68 thf(fact_5366_dvd__neg__div,axiom,
% 5.46/5.68 ! [B: code_integer,A: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.46/5.68 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_neg_div
% 5.46/5.68 thf(fact_5367_dvd__neg__div,axiom,
% 5.46/5.68 ! [B: rat,A: rat] :
% 5.46/5.68 ( ( dvd_dvd_rat @ B @ A )
% 5.46/5.68 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.46/5.68 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_neg_div
% 5.46/5.68 thf(fact_5368_real__minus__mult__self__le,axiom,
% 5.46/5.68 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X2 @ X2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % real_minus_mult_self_le
% 5.46/5.68 thf(fact_5369_minus__int__code_I2_J,axiom,
% 5.46/5.68 ! [L2: int] :
% 5.46/5.68 ( ( minus_minus_int @ zero_zero_int @ L2 )
% 5.46/5.68 = ( uminus_uminus_int @ L2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_int_code(2)
% 5.46/5.68 thf(fact_5370_numeral__eq__Suc,axiom,
% 5.46/5.68 ( numeral_numeral_nat
% 5.46/5.68 = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_eq_Suc
% 5.46/5.68 thf(fact_5371_zmod__zminus1__not__zero,axiom,
% 5.46/5.68 ! [K: int,L2: int] :
% 5.46/5.68 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.46/5.68 != zero_zero_int )
% 5.46/5.68 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.68 != zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % zmod_zminus1_not_zero
% 5.46/5.68 thf(fact_5372_zmod__zminus2__not__zero,axiom,
% 5.46/5.68 ! [K: int,L2: int] :
% 5.46/5.68 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L2 ) )
% 5.46/5.68 != zero_zero_int )
% 5.46/5.68 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.68 != zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % zmod_zminus2_not_zero
% 5.46/5.68 thf(fact_5373_minus__real__def,axiom,
% 5.46/5.68 ( minus_minus_real
% 5.46/5.68 = ( ^ [X: real,Y: real] : ( plus_plus_real @ X @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_real_def
% 5.46/5.68 thf(fact_5374_neg__numeral__le__zero,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_zero
% 5.46/5.68 thf(fact_5375_neg__numeral__le__zero,axiom,
% 5.46/5.68 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_zero
% 5.46/5.68 thf(fact_5376_neg__numeral__le__zero,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_zero
% 5.46/5.68 thf(fact_5377_neg__numeral__le__zero,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_zero
% 5.46/5.68 thf(fact_5378_not__zero__le__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_zero_le_neg_numeral
% 5.46/5.68 thf(fact_5379_not__zero__le__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_zero_le_neg_numeral
% 5.46/5.68 thf(fact_5380_not__zero__le__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_zero_le_neg_numeral
% 5.46/5.68 thf(fact_5381_not__zero__le__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_zero_le_neg_numeral
% 5.46/5.68 thf(fact_5382_not__zero__less__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_zero_less_neg_numeral
% 5.46/5.68 thf(fact_5383_not__zero__less__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_zero_less_neg_numeral
% 5.46/5.68 thf(fact_5384_not__zero__less__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_zero_less_neg_numeral
% 5.46/5.68 thf(fact_5385_not__zero__less__neg__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_zero_less_neg_numeral
% 5.46/5.68 thf(fact_5386_neg__numeral__less__zero,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_zero
% 5.46/5.68 thf(fact_5387_neg__numeral__less__zero,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_zero
% 5.46/5.68 thf(fact_5388_neg__numeral__less__zero,axiom,
% 5.46/5.68 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_zero
% 5.46/5.68 thf(fact_5389_neg__numeral__less__zero,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_zero
% 5.46/5.68 thf(fact_5390_le__minus__one__simps_I3_J,axiom,
% 5.46/5.68 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(3)
% 5.46/5.68 thf(fact_5391_le__minus__one__simps_I3_J,axiom,
% 5.46/5.68 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(3)
% 5.46/5.68 thf(fact_5392_le__minus__one__simps_I3_J,axiom,
% 5.46/5.68 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(3)
% 5.46/5.68 thf(fact_5393_le__minus__one__simps_I3_J,axiom,
% 5.46/5.68 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(3)
% 5.46/5.68 thf(fact_5394_le__minus__one__simps_I1_J,axiom,
% 5.46/5.68 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(1)
% 5.46/5.68 thf(fact_5395_le__minus__one__simps_I1_J,axiom,
% 5.46/5.68 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(1)
% 5.46/5.68 thf(fact_5396_le__minus__one__simps_I1_J,axiom,
% 5.46/5.68 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(1)
% 5.46/5.68 thf(fact_5397_le__minus__one__simps_I1_J,axiom,
% 5.46/5.68 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.46/5.68
% 5.46/5.68 % le_minus_one_simps(1)
% 5.46/5.68 thf(fact_5398_less__minus__one__simps_I1_J,axiom,
% 5.46/5.68 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(1)
% 5.46/5.68 thf(fact_5399_less__minus__one__simps_I1_J,axiom,
% 5.46/5.68 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(1)
% 5.46/5.68 thf(fact_5400_less__minus__one__simps_I1_J,axiom,
% 5.46/5.68 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(1)
% 5.46/5.68 thf(fact_5401_less__minus__one__simps_I1_J,axiom,
% 5.46/5.68 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(1)
% 5.46/5.68 thf(fact_5402_less__minus__one__simps_I3_J,axiom,
% 5.46/5.68 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(3)
% 5.46/5.68 thf(fact_5403_less__minus__one__simps_I3_J,axiom,
% 5.46/5.68 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(3)
% 5.46/5.68 thf(fact_5404_less__minus__one__simps_I3_J,axiom,
% 5.46/5.68 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(3)
% 5.46/5.68 thf(fact_5405_less__minus__one__simps_I3_J,axiom,
% 5.46/5.68 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_one_simps(3)
% 5.46/5.68 thf(fact_5406_neg__numeral__le__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_one
% 5.46/5.68 thf(fact_5407_neg__numeral__le__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_one
% 5.46/5.68 thf(fact_5408_neg__numeral__le__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_one
% 5.46/5.68 thf(fact_5409_neg__numeral__le__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_one
% 5.46/5.68 thf(fact_5410_neg__one__le__numeral,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_le_numeral
% 5.46/5.68 thf(fact_5411_neg__one__le__numeral,axiom,
% 5.46/5.68 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_le_numeral
% 5.46/5.68 thf(fact_5412_neg__one__le__numeral,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_le_numeral
% 5.46/5.68 thf(fact_5413_neg__one__le__numeral,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_le_numeral
% 5.46/5.68 thf(fact_5414_neg__numeral__le__neg__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_neg_one
% 5.46/5.68 thf(fact_5415_neg__numeral__le__neg__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_neg_one
% 5.46/5.68 thf(fact_5416_neg__numeral__le__neg__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_neg_one
% 5.46/5.68 thf(fact_5417_neg__numeral__le__neg__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_le_neg_one
% 5.46/5.68 thf(fact_5418_not__numeral__le__neg__one,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_neg_one
% 5.46/5.68 thf(fact_5419_not__numeral__le__neg__one,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_neg_one
% 5.46/5.68 thf(fact_5420_not__numeral__le__neg__one,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_neg_one
% 5.46/5.68 thf(fact_5421_not__numeral__le__neg__one,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_neg_one
% 5.46/5.68 thf(fact_5422_not__one__le__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_le_neg_numeral
% 5.46/5.68 thf(fact_5423_not__one__le__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_le_neg_numeral
% 5.46/5.68 thf(fact_5424_not__one__le__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_le_neg_numeral
% 5.46/5.68 thf(fact_5425_not__one__le__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_le_neg_numeral
% 5.46/5.68 thf(fact_5426_neg__numeral__less__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_one
% 5.46/5.68 thf(fact_5427_neg__numeral__less__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_one
% 5.46/5.68 thf(fact_5428_neg__numeral__less__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_one
% 5.46/5.68 thf(fact_5429_neg__numeral__less__one,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.46/5.68
% 5.46/5.68 % neg_numeral_less_one
% 5.46/5.68 thf(fact_5430_neg__one__less__numeral,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_less_numeral
% 5.46/5.68 thf(fact_5431_neg__one__less__numeral,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_less_numeral
% 5.46/5.68 thf(fact_5432_neg__one__less__numeral,axiom,
% 5.46/5.68 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_less_numeral
% 5.46/5.68 thf(fact_5433_neg__one__less__numeral,axiom,
% 5.46/5.68 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_less_numeral
% 5.46/5.68 thf(fact_5434_not__numeral__less__neg__one,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_neg_one
% 5.46/5.68 thf(fact_5435_not__numeral__less__neg__one,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_neg_one
% 5.46/5.68 thf(fact_5436_not__numeral__less__neg__one,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_neg_one
% 5.46/5.68 thf(fact_5437_not__numeral__less__neg__one,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_neg_one
% 5.46/5.68 thf(fact_5438_not__one__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_less_neg_numeral
% 5.46/5.68 thf(fact_5439_not__one__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_less_neg_numeral
% 5.46/5.68 thf(fact_5440_not__one__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_less_neg_numeral
% 5.46/5.68 thf(fact_5441_not__one__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_less_neg_numeral
% 5.46/5.68 thf(fact_5442_not__neg__one__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_neg_one_less_neg_numeral
% 5.46/5.68 thf(fact_5443_not__neg__one__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_neg_one_less_neg_numeral
% 5.46/5.68 thf(fact_5444_not__neg__one__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_neg_one_less_neg_numeral
% 5.46/5.68 thf(fact_5445_not__neg__one__less__neg__numeral,axiom,
% 5.46/5.68 ! [M: num] :
% 5.46/5.68 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % not_neg_one_less_neg_numeral
% 5.46/5.68 thf(fact_5446_nonzero__neg__divide__eq__eq2,axiom,
% 5.46/5.68 ! [B: real,C: real,A: real] :
% 5.46/5.68 ( ( B != zero_zero_real )
% 5.46/5.68 => ( ( C
% 5.46/5.68 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.46/5.68 = ( ( times_times_real @ C @ B )
% 5.46/5.68 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_neg_divide_eq_eq2
% 5.46/5.68 thf(fact_5447_nonzero__neg__divide__eq__eq2,axiom,
% 5.46/5.68 ! [B: complex,C: complex,A: complex] :
% 5.46/5.68 ( ( B != zero_zero_complex )
% 5.46/5.68 => ( ( C
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.46/5.68 = ( ( times_times_complex @ C @ B )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_neg_divide_eq_eq2
% 5.46/5.68 thf(fact_5448_nonzero__neg__divide__eq__eq2,axiom,
% 5.46/5.68 ! [B: rat,C: rat,A: rat] :
% 5.46/5.68 ( ( B != zero_zero_rat )
% 5.46/5.68 => ( ( C
% 5.46/5.68 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.46/5.68 = ( ( times_times_rat @ C @ B )
% 5.46/5.68 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_neg_divide_eq_eq2
% 5.46/5.68 thf(fact_5449_nonzero__neg__divide__eq__eq,axiom,
% 5.46/5.68 ! [B: real,A: real,C: real] :
% 5.46/5.68 ( ( B != zero_zero_real )
% 5.46/5.68 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.68 = C )
% 5.46/5.68 = ( ( uminus_uminus_real @ A )
% 5.46/5.68 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_neg_divide_eq_eq
% 5.46/5.68 thf(fact_5450_nonzero__neg__divide__eq__eq,axiom,
% 5.46/5.68 ! [B: complex,A: complex,C: complex] :
% 5.46/5.68 ( ( B != zero_zero_complex )
% 5.46/5.68 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.46/5.68 = C )
% 5.46/5.68 = ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.68 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_neg_divide_eq_eq
% 5.46/5.68 thf(fact_5451_nonzero__neg__divide__eq__eq,axiom,
% 5.46/5.68 ! [B: rat,A: rat,C: rat] :
% 5.46/5.68 ( ( B != zero_zero_rat )
% 5.46/5.68 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.46/5.68 = C )
% 5.46/5.68 = ( ( uminus_uminus_rat @ A )
% 5.46/5.68 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_neg_divide_eq_eq
% 5.46/5.68 thf(fact_5452_minus__divide__eq__eq,axiom,
% 5.46/5.68 ! [B: real,C: real,A: real] :
% 5.46/5.68 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( ( C != zero_zero_real )
% 5.46/5.68 => ( ( uminus_uminus_real @ B )
% 5.46/5.68 = ( times_times_real @ A @ C ) ) )
% 5.46/5.68 & ( ( C = zero_zero_real )
% 5.46/5.68 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_eq_eq
% 5.46/5.68 thf(fact_5453_minus__divide__eq__eq,axiom,
% 5.46/5.68 ! [B: complex,C: complex,A: complex] :
% 5.46/5.68 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( ( C != zero_zero_complex )
% 5.46/5.68 => ( ( uminus1482373934393186551omplex @ B )
% 5.46/5.68 = ( times_times_complex @ A @ C ) ) )
% 5.46/5.68 & ( ( C = zero_zero_complex )
% 5.46/5.68 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_eq_eq
% 5.46/5.68 thf(fact_5454_minus__divide__eq__eq,axiom,
% 5.46/5.68 ! [B: rat,C: rat,A: rat] :
% 5.46/5.68 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( ( C != zero_zero_rat )
% 5.46/5.68 => ( ( uminus_uminus_rat @ B )
% 5.46/5.68 = ( times_times_rat @ A @ C ) ) )
% 5.46/5.68 & ( ( C = zero_zero_rat )
% 5.46/5.68 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_eq_eq
% 5.46/5.68 thf(fact_5455_eq__minus__divide__eq,axiom,
% 5.46/5.68 ! [A: real,B: real,C: real] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.46/5.68 = ( ( ( C != zero_zero_real )
% 5.46/5.68 => ( ( times_times_real @ A @ C )
% 5.46/5.68 = ( uminus_uminus_real @ B ) ) )
% 5.46/5.68 & ( ( C = zero_zero_real )
% 5.46/5.68 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_minus_divide_eq
% 5.46/5.68 thf(fact_5456_eq__minus__divide__eq,axiom,
% 5.46/5.68 ! [A: complex,B: complex,C: complex] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.46/5.68 = ( ( ( C != zero_zero_complex )
% 5.46/5.68 => ( ( times_times_complex @ A @ C )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.46/5.68 & ( ( C = zero_zero_complex )
% 5.46/5.68 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_minus_divide_eq
% 5.46/5.68 thf(fact_5457_eq__minus__divide__eq,axiom,
% 5.46/5.68 ! [A: rat,B: rat,C: rat] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.46/5.68 = ( ( ( C != zero_zero_rat )
% 5.46/5.68 => ( ( times_times_rat @ A @ C )
% 5.46/5.68 = ( uminus_uminus_rat @ B ) ) )
% 5.46/5.68 & ( ( C = zero_zero_rat )
% 5.46/5.68 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_minus_divide_eq
% 5.46/5.68 thf(fact_5458_divide__eq__minus__1__iff,axiom,
% 5.46/5.68 ! [A: real,B: real] :
% 5.46/5.68 ( ( ( divide_divide_real @ A @ B )
% 5.46/5.68 = ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( ( B != zero_zero_real )
% 5.46/5.68 & ( A
% 5.46/5.68 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_minus_1_iff
% 5.46/5.68 thf(fact_5459_divide__eq__minus__1__iff,axiom,
% 5.46/5.68 ! [A: complex,B: complex] :
% 5.46/5.68 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = ( ( B != zero_zero_complex )
% 5.46/5.68 & ( A
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_minus_1_iff
% 5.46/5.68 thf(fact_5460_divide__eq__minus__1__iff,axiom,
% 5.46/5.68 ! [A: rat,B: rat] :
% 5.46/5.68 ( ( ( divide_divide_rat @ A @ B )
% 5.46/5.68 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( ( B != zero_zero_rat )
% 5.46/5.68 & ( A
% 5.46/5.68 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_minus_1_iff
% 5.46/5.68 thf(fact_5461_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.68 ! [B: int] :
% 5.46/5.68 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(2)
% 5.46/5.68 thf(fact_5462_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.68 ! [B: real] :
% 5.46/5.68 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.46/5.68 = ( uminus_uminus_real @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(2)
% 5.46/5.68 thf(fact_5463_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.68 ! [B: complex] :
% 5.46/5.68 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(2)
% 5.46/5.68 thf(fact_5464_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.68 ! [B: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(2)
% 5.46/5.68 thf(fact_5465_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.68 ! [B: rat] :
% 5.46/5.68 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.46/5.68 = ( uminus_uminus_rat @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(2)
% 5.46/5.68 thf(fact_5466_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.68 ! [B: int] :
% 5.46/5.68 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.46/5.68 = ( uminus_uminus_int @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(1)
% 5.46/5.68 thf(fact_5467_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.68 ! [B: real] :
% 5.46/5.68 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.46/5.68 = ( uminus_uminus_real @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(1)
% 5.46/5.68 thf(fact_5468_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.68 ! [B: complex] :
% 5.46/5.68 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(1)
% 5.46/5.68 thf(fact_5469_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.68 ! [B: code_integer] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(1)
% 5.46/5.68 thf(fact_5470_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.68 ! [B: rat] :
% 5.46/5.68 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.46/5.68 = ( uminus_uminus_rat @ B ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_1s_ring_1(1)
% 5.46/5.68 thf(fact_5471_uminus__numeral__One,axiom,
% 5.46/5.68 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_numeral_One
% 5.46/5.68 thf(fact_5472_uminus__numeral__One,axiom,
% 5.46/5.68 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.46/5.68 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_numeral_One
% 5.46/5.68 thf(fact_5473_uminus__numeral__One,axiom,
% 5.46/5.68 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_numeral_One
% 5.46/5.68 thf(fact_5474_uminus__numeral__One,axiom,
% 5.46/5.68 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_numeral_One
% 5.46/5.68 thf(fact_5475_uminus__numeral__One,axiom,
% 5.46/5.68 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.46/5.68 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_numeral_One
% 5.46/5.68 thf(fact_5476_power__minus,axiom,
% 5.46/5.68 ! [A: int,N: nat] :
% 5.46/5.68 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.68 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus
% 5.46/5.68 thf(fact_5477_power__minus,axiom,
% 5.46/5.68 ! [A: real,N: nat] :
% 5.46/5.68 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.68 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus
% 5.46/5.68 thf(fact_5478_power__minus,axiom,
% 5.46/5.68 ! [A: complex,N: nat] :
% 5.46/5.68 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.68 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus
% 5.46/5.68 thf(fact_5479_power__minus,axiom,
% 5.46/5.68 ! [A: code_integer,N: nat] :
% 5.46/5.68 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.68 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus
% 5.46/5.68 thf(fact_5480_power__minus,axiom,
% 5.46/5.68 ! [A: rat,N: nat] :
% 5.46/5.68 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.68 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus
% 5.46/5.68 thf(fact_5481_power__minus__Bit0,axiom,
% 5.46/5.68 ! [X2: int,K: num] :
% 5.46/5.68 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.68 = ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit0
% 5.46/5.68 thf(fact_5482_power__minus__Bit0,axiom,
% 5.46/5.68 ! [X2: real,K: num] :
% 5.46/5.68 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.68 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit0
% 5.46/5.68 thf(fact_5483_power__minus__Bit0,axiom,
% 5.46/5.68 ! [X2: complex,K: num] :
% 5.46/5.68 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.68 = ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit0
% 5.46/5.68 thf(fact_5484_power__minus__Bit0,axiom,
% 5.46/5.68 ! [X2: code_integer,K: num] :
% 5.46/5.68 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.68 = ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit0
% 5.46/5.68 thf(fact_5485_power__minus__Bit0,axiom,
% 5.46/5.68 ! [X2: rat,K: num] :
% 5.46/5.68 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.68 = ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit0
% 5.46/5.68 thf(fact_5486_power__minus__Bit1,axiom,
% 5.46/5.68 ! [X2: int,K: num] :
% 5.46/5.68 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit1
% 5.46/5.68 thf(fact_5487_power__minus__Bit1,axiom,
% 5.46/5.68 ! [X2: real,K: num] :
% 5.46/5.68 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit1
% 5.46/5.68 thf(fact_5488_power__minus__Bit1,axiom,
% 5.46/5.68 ! [X2: complex,K: num] :
% 5.46/5.68 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit1
% 5.46/5.68 thf(fact_5489_power__minus__Bit1,axiom,
% 5.46/5.68 ! [X2: code_integer,K: num] :
% 5.46/5.68 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit1
% 5.46/5.68 thf(fact_5490_power__minus__Bit1,axiom,
% 5.46/5.68 ! [X2: rat,K: num] :
% 5.46/5.68 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus_Bit1
% 5.46/5.68 thf(fact_5491_real__0__less__add__iff,axiom,
% 5.46/5.68 ! [X2: real,Y2: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.46/5.68 = ( ord_less_real @ ( uminus_uminus_real @ X2 ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % real_0_less_add_iff
% 5.46/5.68 thf(fact_5492_real__add__less__0__iff,axiom,
% 5.46/5.68 ! [X2: real,Y2: real] :
% 5.46/5.68 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y2 ) @ zero_zero_real )
% 5.46/5.68 = ( ord_less_real @ Y2 @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % real_add_less_0_iff
% 5.46/5.68 thf(fact_5493_real__add__le__0__iff,axiom,
% 5.46/5.68 ! [X2: real,Y2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ X2 @ Y2 ) @ zero_zero_real )
% 5.46/5.68 = ( ord_less_eq_real @ Y2 @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % real_add_le_0_iff
% 5.46/5.68 thf(fact_5494_real__0__le__add__iff,axiom,
% 5.46/5.68 ! [X2: real,Y2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.46/5.68 = ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ Y2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % real_0_le_add_iff
% 5.46/5.68 thf(fact_5495_zmod__zminus1__eq__if,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.68 = zero_zero_int )
% 5.46/5.68 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = zero_zero_int ) )
% 5.46/5.68 & ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.68 != zero_zero_int )
% 5.46/5.68 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zmod_zminus1_eq_if
% 5.46/5.68 thf(fact_5496_zmod__zminus2__eq__if,axiom,
% 5.46/5.68 ! [A: int,B: int] :
% 5.46/5.68 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.68 = zero_zero_int )
% 5.46/5.68 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = zero_zero_int ) )
% 5.46/5.68 & ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.68 != zero_zero_int )
% 5.46/5.68 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zmod_zminus2_eq_if
% 5.46/5.68 thf(fact_5497_pred__numeral__def,axiom,
% 5.46/5.68 ( pred_numeral
% 5.46/5.68 = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pred_numeral_def
% 5.46/5.68 thf(fact_5498_pos__minus__divide__less__eq,axiom,
% 5.46/5.68 ! [C: real,B: real,A: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.46/5.68 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_minus_divide_less_eq
% 5.46/5.68 thf(fact_5499_pos__minus__divide__less__eq,axiom,
% 5.46/5.68 ! [C: rat,B: rat,A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.46/5.68 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_minus_divide_less_eq
% 5.46/5.68 thf(fact_5500_pos__less__minus__divide__eq,axiom,
% 5.46/5.68 ! [C: real,A: real,B: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.46/5.68 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_less_minus_divide_eq
% 5.46/5.68 thf(fact_5501_pos__less__minus__divide__eq,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.46/5.68 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_less_minus_divide_eq
% 5.46/5.68 thf(fact_5502_neg__minus__divide__less__eq,axiom,
% 5.46/5.68 ! [C: real,B: real,A: real] :
% 5.46/5.68 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.46/5.68 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_minus_divide_less_eq
% 5.46/5.68 thf(fact_5503_neg__minus__divide__less__eq,axiom,
% 5.46/5.68 ! [C: rat,B: rat,A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.46/5.68 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_minus_divide_less_eq
% 5.46/5.68 thf(fact_5504_neg__less__minus__divide__eq,axiom,
% 5.46/5.68 ! [C: real,A: real,B: real] :
% 5.46/5.68 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.46/5.68 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_minus_divide_eq
% 5.46/5.68 thf(fact_5505_neg__less__minus__divide__eq,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.46/5.68 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_less_minus_divide_eq
% 5.46/5.68 thf(fact_5506_minus__divide__less__eq,axiom,
% 5.46/5.68 ! [B: real,C: real,A: real] :
% 5.46/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_less_eq
% 5.46/5.68 thf(fact_5507_minus__divide__less__eq,axiom,
% 5.46/5.68 ! [B: rat,C: rat,A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_less_eq
% 5.46/5.68 thf(fact_5508_less__minus__divide__eq,axiom,
% 5.46/5.68 ! [A: real,B: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_divide_eq
% 5.46/5.68 thf(fact_5509_less__minus__divide__eq,axiom,
% 5.46/5.68 ! [A: rat,B: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_minus_divide_eq
% 5.46/5.68 thf(fact_5510_divide__eq__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [B: real,C: real,W: num] :
% 5.46/5.68 ( ( ( divide_divide_real @ B @ C )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.68 = ( ( ( C != zero_zero_real )
% 5.46/5.68 => ( B
% 5.46/5.68 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ( C = zero_zero_real )
% 5.46/5.68 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.68 = zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_eq_numeral(2)
% 5.46/5.68 thf(fact_5511_divide__eq__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [B: complex,C: complex,W: num] :
% 5.46/5.68 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.68 = ( ( ( C != zero_zero_complex )
% 5.46/5.68 => ( B
% 5.46/5.68 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ( C = zero_zero_complex )
% 5.46/5.68 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.68 = zero_zero_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_eq_numeral(2)
% 5.46/5.68 thf(fact_5512_divide__eq__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [B: rat,C: rat,W: num] :
% 5.46/5.68 ( ( ( divide_divide_rat @ B @ C )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.68 = ( ( ( C != zero_zero_rat )
% 5.46/5.68 => ( B
% 5.46/5.68 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ( C = zero_zero_rat )
% 5.46/5.68 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.68 = zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_eq_numeral(2)
% 5.46/5.68 thf(fact_5513_eq__divide__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [W: num,B: real,C: real] :
% 5.46/5.68 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.68 = ( divide_divide_real @ B @ C ) )
% 5.46/5.68 = ( ( ( C != zero_zero_real )
% 5.46/5.68 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.46/5.68 = B ) )
% 5.46/5.68 & ( ( C = zero_zero_real )
% 5.46/5.68 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.68 = zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_eq_numeral(2)
% 5.46/5.68 thf(fact_5514_eq__divide__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [W: num,B: complex,C: complex] :
% 5.46/5.68 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.68 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.46/5.68 = ( ( ( C != zero_zero_complex )
% 5.46/5.68 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.46/5.68 = B ) )
% 5.46/5.68 & ( ( C = zero_zero_complex )
% 5.46/5.68 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.68 = zero_zero_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_eq_numeral(2)
% 5.46/5.68 thf(fact_5515_eq__divide__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [W: num,B: rat,C: rat] :
% 5.46/5.68 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.68 = ( divide_divide_rat @ B @ C ) )
% 5.46/5.68 = ( ( ( C != zero_zero_rat )
% 5.46/5.68 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.46/5.68 = B ) )
% 5.46/5.68 & ( ( C = zero_zero_rat )
% 5.46/5.68 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.68 = zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_eq_numeral(2)
% 5.46/5.68 thf(fact_5516_add__divide__eq__if__simps_I3_J,axiom,
% 5.46/5.68 ! [Z: real,A: real,B: real] :
% 5.46/5.68 ( ( ( Z = zero_zero_real )
% 5.46/5.68 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.46/5.68 = B ) )
% 5.46/5.68 & ( ( Z != zero_zero_real )
% 5.46/5.68 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.46/5.68 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_divide_eq_if_simps(3)
% 5.46/5.68 thf(fact_5517_add__divide__eq__if__simps_I3_J,axiom,
% 5.46/5.68 ! [Z: complex,A: complex,B: complex] :
% 5.46/5.68 ( ( ( Z = zero_zero_complex )
% 5.46/5.68 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.46/5.68 = B ) )
% 5.46/5.68 & ( ( Z != zero_zero_complex )
% 5.46/5.68 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.46/5.68 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_divide_eq_if_simps(3)
% 5.46/5.68 thf(fact_5518_add__divide__eq__if__simps_I3_J,axiom,
% 5.46/5.68 ! [Z: rat,A: rat,B: rat] :
% 5.46/5.68 ( ( ( Z = zero_zero_rat )
% 5.46/5.68 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.46/5.68 = B ) )
% 5.46/5.68 & ( ( Z != zero_zero_rat )
% 5.46/5.68 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.46/5.68 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_divide_eq_if_simps(3)
% 5.46/5.68 thf(fact_5519_minus__divide__add__eq__iff,axiom,
% 5.46/5.68 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.68 ( ( Z != zero_zero_real )
% 5.46/5.68 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y2 )
% 5.46/5.68 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_add_eq_iff
% 5.46/5.68 thf(fact_5520_minus__divide__add__eq__iff,axiom,
% 5.46/5.68 ! [Z: complex,X2: complex,Y2: complex] :
% 5.46/5.68 ( ( Z != zero_zero_complex )
% 5.46/5.68 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y2 )
% 5.46/5.68 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_add_eq_iff
% 5.46/5.68 thf(fact_5521_minus__divide__add__eq__iff,axiom,
% 5.46/5.68 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.68 ( ( Z != zero_zero_rat )
% 5.46/5.68 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y2 )
% 5.46/5.68 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_add_eq_iff
% 5.46/5.68 thf(fact_5522_minus__divide__diff__eq__iff,axiom,
% 5.46/5.68 ! [Z: real,X2: real,Y2: real] :
% 5.46/5.68 ( ( Z != zero_zero_real )
% 5.46/5.68 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y2 )
% 5.46/5.68 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_diff_eq_iff
% 5.46/5.68 thf(fact_5523_minus__divide__diff__eq__iff,axiom,
% 5.46/5.68 ! [Z: complex,X2: complex,Y2: complex] :
% 5.46/5.68 ( ( Z != zero_zero_complex )
% 5.46/5.68 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y2 )
% 5.46/5.68 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_diff_eq_iff
% 5.46/5.68 thf(fact_5524_minus__divide__diff__eq__iff,axiom,
% 5.46/5.68 ! [Z: rat,X2: rat,Y2: rat] :
% 5.46/5.68 ( ( Z != zero_zero_rat )
% 5.46/5.68 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y2 )
% 5.46/5.68 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_diff_eq_iff
% 5.46/5.68 thf(fact_5525_add__divide__eq__if__simps_I5_J,axiom,
% 5.46/5.68 ! [Z: real,A: real,B: real] :
% 5.46/5.68 ( ( ( Z = zero_zero_real )
% 5.46/5.68 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.46/5.68 = ( uminus_uminus_real @ B ) ) )
% 5.46/5.68 & ( ( Z != zero_zero_real )
% 5.46/5.68 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.46/5.68 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_divide_eq_if_simps(5)
% 5.46/5.68 thf(fact_5526_add__divide__eq__if__simps_I5_J,axiom,
% 5.46/5.68 ! [Z: complex,A: complex,B: complex] :
% 5.46/5.68 ( ( ( Z = zero_zero_complex )
% 5.46/5.68 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.46/5.68 & ( ( Z != zero_zero_complex )
% 5.46/5.68 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.46/5.68 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_divide_eq_if_simps(5)
% 5.46/5.68 thf(fact_5527_add__divide__eq__if__simps_I5_J,axiom,
% 5.46/5.68 ! [Z: rat,A: rat,B: rat] :
% 5.46/5.68 ( ( ( Z = zero_zero_rat )
% 5.46/5.68 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.46/5.68 = ( uminus_uminus_rat @ B ) ) )
% 5.46/5.68 & ( ( Z != zero_zero_rat )
% 5.46/5.68 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.46/5.68 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_divide_eq_if_simps(5)
% 5.46/5.68 thf(fact_5528_add__divide__eq__if__simps_I6_J,axiom,
% 5.46/5.68 ! [Z: real,A: real,B: real] :
% 5.46/5.68 ( ( ( Z = zero_zero_real )
% 5.46/5.68 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.46/5.68 = ( uminus_uminus_real @ B ) ) )
% 5.46/5.68 & ( ( Z != zero_zero_real )
% 5.46/5.68 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.46/5.68 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_divide_eq_if_simps(6)
% 5.46/5.68 thf(fact_5529_add__divide__eq__if__simps_I6_J,axiom,
% 5.46/5.68 ! [Z: complex,A: complex,B: complex] :
% 5.46/5.68 ( ( ( Z = zero_zero_complex )
% 5.46/5.68 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.46/5.68 & ( ( Z != zero_zero_complex )
% 5.46/5.68 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.46/5.68 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_divide_eq_if_simps(6)
% 5.46/5.68 thf(fact_5530_add__divide__eq__if__simps_I6_J,axiom,
% 5.46/5.68 ! [Z: rat,A: rat,B: rat] :
% 5.46/5.68 ( ( ( Z = zero_zero_rat )
% 5.46/5.68 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.46/5.68 = ( uminus_uminus_rat @ B ) ) )
% 5.46/5.68 & ( ( Z != zero_zero_rat )
% 5.46/5.68 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.46/5.68 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_divide_eq_if_simps(6)
% 5.46/5.68 thf(fact_5531_even__minus,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.46/5.68 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % even_minus
% 5.46/5.68 thf(fact_5532_even__minus,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % even_minus
% 5.46/5.68 thf(fact_5533_power2__eq__iff,axiom,
% 5.46/5.68 ! [X2: int,Y2: int] :
% 5.46/5.68 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus_uminus_int @ Y2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_iff
% 5.46/5.68 thf(fact_5534_power2__eq__iff,axiom,
% 5.46/5.68 ! [X2: real,Y2: real] :
% 5.46/5.68 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_iff
% 5.46/5.68 thf(fact_5535_power2__eq__iff,axiom,
% 5.46/5.68 ! [X2: complex,Y2: complex] :
% 5.46/5.68 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus1482373934393186551omplex @ Y2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_iff
% 5.46/5.68 thf(fact_5536_power2__eq__iff,axiom,
% 5.46/5.68 ! [X2: code_integer,Y2: code_integer] :
% 5.46/5.68 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus1351360451143612070nteger @ Y2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_iff
% 5.46/5.68 thf(fact_5537_power2__eq__iff,axiom,
% 5.46/5.68 ! [X2: rat,Y2: rat] :
% 5.46/5.68 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.68 = ( ( X2 = Y2 )
% 5.46/5.68 | ( X2
% 5.46/5.68 = ( uminus_uminus_rat @ Y2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_iff
% 5.46/5.68 thf(fact_5538_uminus__power__if,axiom,
% 5.46/5.68 ! [N: nat,A: int] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.68 = ( power_power_int @ A @ N ) ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.68 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_power_if
% 5.46/5.68 thf(fact_5539_uminus__power__if,axiom,
% 5.46/5.68 ! [N: nat,A: real] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.68 = ( power_power_real @ A @ N ) ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.68 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_power_if
% 5.46/5.68 thf(fact_5540_uminus__power__if,axiom,
% 5.46/5.68 ! [N: nat,A: complex] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.68 = ( power_power_complex @ A @ N ) ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_power_if
% 5.46/5.68 thf(fact_5541_uminus__power__if,axiom,
% 5.46/5.68 ! [N: nat,A: code_integer] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.68 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_power_if
% 5.46/5.68 thf(fact_5542_uminus__power__if,axiom,
% 5.46/5.68 ! [N: nat,A: rat] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.68 = ( power_power_rat @ A @ N ) ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.68 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % uminus_power_if
% 5.46/5.68 thf(fact_5543_verit__less__mono__div__int2,axiom,
% 5.46/5.68 ! [A2: int,B3: int,N: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.46/5.68 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.46/5.68 => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % verit_less_mono_div_int2
% 5.46/5.68 thf(fact_5544_div__eq__minus1,axiom,
% 5.46/5.68 ! [B: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.68 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_eq_minus1
% 5.46/5.68 thf(fact_5545_of__bool__odd__eq__mod__2,axiom,
% 5.46/5.68 ! [A: nat] :
% 5.46/5.68 ( ( zero_n2687167440665602831ol_nat
% 5.46/5.68 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.68 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_odd_eq_mod_2
% 5.46/5.68 thf(fact_5546_of__bool__odd__eq__mod__2,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( zero_n2684676970156552555ol_int
% 5.46/5.68 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.68 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_odd_eq_mod_2
% 5.46/5.68 thf(fact_5547_of__bool__odd__eq__mod__2,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( zero_n356916108424825756nteger
% 5.46/5.68 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.68 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % of_bool_odd_eq_mod_2
% 5.46/5.68 thf(fact_5548_le__minus__divide__eq,axiom,
% 5.46/5.68 ! [A: real,B: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_divide_eq
% 5.46/5.68 thf(fact_5549_le__minus__divide__eq,axiom,
% 5.46/5.68 ! [A: rat,B: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_minus_divide_eq
% 5.46/5.68 thf(fact_5550_minus__divide__le__eq,axiom,
% 5.46/5.68 ! [B: real,C: real,A: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_le_eq
% 5.46/5.68 thf(fact_5551_minus__divide__le__eq,axiom,
% 5.46/5.68 ! [B: rat,C: rat,A: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_divide_le_eq
% 5.46/5.68 thf(fact_5552_neg__le__minus__divide__eq,axiom,
% 5.46/5.68 ! [C: real,A: real,B: real] :
% 5.46/5.68 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.46/5.68 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_le_minus_divide_eq
% 5.46/5.68 thf(fact_5553_neg__le__minus__divide__eq,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.46/5.68 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_le_minus_divide_eq
% 5.46/5.68 thf(fact_5554_neg__minus__divide__le__eq,axiom,
% 5.46/5.68 ! [C: real,B: real,A: real] :
% 5.46/5.68 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.46/5.68 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_minus_divide_le_eq
% 5.46/5.68 thf(fact_5555_neg__minus__divide__le__eq,axiom,
% 5.46/5.68 ! [C: rat,B: rat,A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.46/5.68 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_minus_divide_le_eq
% 5.46/5.68 thf(fact_5556_pos__le__minus__divide__eq,axiom,
% 5.46/5.68 ! [C: real,A: real,B: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.46/5.68 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_le_minus_divide_eq
% 5.46/5.68 thf(fact_5557_pos__le__minus__divide__eq,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.46/5.68 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_le_minus_divide_eq
% 5.46/5.68 thf(fact_5558_pos__minus__divide__le__eq,axiom,
% 5.46/5.68 ! [C: real,B: real,A: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.46/5.68 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_minus_divide_le_eq
% 5.46/5.68 thf(fact_5559_pos__minus__divide__le__eq,axiom,
% 5.46/5.68 ! [C: rat,B: rat,A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.46/5.68 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_minus_divide_le_eq
% 5.46/5.68 thf(fact_5560_divide__less__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [B: real,C: real,W: num] :
% 5.46/5.68 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_less_eq_numeral(2)
% 5.46/5.68 thf(fact_5561_divide__less__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [B: rat,C: rat,W: num] :
% 5.46/5.68 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_less_eq_numeral(2)
% 5.46/5.68 thf(fact_5562_less__divide__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [W: num,B: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_divide_eq_numeral(2)
% 5.46/5.68 thf(fact_5563_less__divide__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [W: num,B: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_divide_eq_numeral(2)
% 5.46/5.68 thf(fact_5564_power2__eq__1__iff,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_int )
% 5.46/5.68 = ( ( A = one_one_int )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_1_iff
% 5.46/5.68 thf(fact_5565_power2__eq__1__iff,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_real )
% 5.46/5.68 = ( ( A = one_one_real )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_1_iff
% 5.46/5.68 thf(fact_5566_power2__eq__1__iff,axiom,
% 5.46/5.68 ! [A: complex] :
% 5.46/5.68 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_complex )
% 5.46/5.68 = ( ( A = one_one_complex )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_1_iff
% 5.46/5.68 thf(fact_5567_power2__eq__1__iff,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_Code_integer )
% 5.46/5.68 = ( ( A = one_one_Code_integer )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_1_iff
% 5.46/5.68 thf(fact_5568_power2__eq__1__iff,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_rat )
% 5.46/5.68 = ( ( A = one_one_rat )
% 5.46/5.68 | ( A
% 5.46/5.68 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power2_eq_1_iff
% 5.46/5.68 thf(fact_5569_minus__one__power__iff,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.46/5.68 = one_one_int ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_power_iff
% 5.46/5.68 thf(fact_5570_minus__one__power__iff,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.46/5.68 = one_one_real ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.46/5.68 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_power_iff
% 5.46/5.68 thf(fact_5571_minus__one__power__iff,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.46/5.68 = one_one_complex ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_power_iff
% 5.46/5.68 thf(fact_5572_minus__one__power__iff,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.46/5.68 = one_one_Code_integer ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_power_iff
% 5.46/5.68 thf(fact_5573_minus__one__power__iff,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.46/5.68 = one_one_rat ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.46/5.68 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_power_iff
% 5.46/5.68 thf(fact_5574_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.68 ! [K: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.68 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.68 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.68 thf(fact_5575_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.68 ! [K: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.68 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.68 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.68 thf(fact_5576_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.68 ! [K: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.68 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.68 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.68 thf(fact_5577_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.68 ! [K: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.68 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.68 thf(fact_5578_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.68 ! [K: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.68 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.68 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.68 thf(fact_5579_realpow__square__minus__le,axiom,
% 5.46/5.68 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % realpow_square_minus_le
% 5.46/5.68 thf(fact_5580_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.46/5.68 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_int_greater_eq_minus_exp
% 5.46/5.68 thf(fact_5581_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.46/5.68 ! [N: nat,K: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.46/5.68 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_int_less_eq_self_iff
% 5.46/5.68 thf(fact_5582_signed__take__bit__int__greater__self__iff,axiom,
% 5.46/5.68 ! [K: int,N: nat] :
% 5.46/5.68 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.46/5.68 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_int_greater_self_iff
% 5.46/5.68 thf(fact_5583_minus__mod__int__eq,axiom,
% 5.46/5.68 ! [L2: int,K: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.46/5.68 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.46/5.68 = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_mod_int_eq
% 5.46/5.68 thf(fact_5584_zmod__minus1,axiom,
% 5.46/5.68 ! [B: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.68 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.46/5.68 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zmod_minus1
% 5.46/5.68 thf(fact_5585_zdiv__zminus1__eq__if,axiom,
% 5.46/5.68 ! [B: int,A: int] :
% 5.46/5.68 ( ( B != zero_zero_int )
% 5.46/5.68 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.68 = zero_zero_int )
% 5.46/5.68 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.46/5.68 & ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.68 != zero_zero_int )
% 5.46/5.68 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.68 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zdiv_zminus1_eq_if
% 5.46/5.68 thf(fact_5586_zdiv__zminus2__eq__if,axiom,
% 5.46/5.68 ! [B: int,A: int] :
% 5.46/5.68 ( ( B != zero_zero_int )
% 5.46/5.68 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.68 = zero_zero_int )
% 5.46/5.68 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.46/5.68 & ( ( ( modulo_modulo_int @ A @ B )
% 5.46/5.68 != zero_zero_int )
% 5.46/5.68 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.46/5.68 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zdiv_zminus2_eq_if
% 5.46/5.68 thf(fact_5587_zminus1__lemma,axiom,
% 5.46/5.68 ! [A: int,B: int,Q2: int,R: int] :
% 5.46/5.68 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.68 => ( ( B != zero_zero_int )
% 5.46/5.68 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zminus1_lemma
% 5.46/5.68 thf(fact_5588_bits__induct,axiom,
% 5.46/5.68 ! [P: nat > $o,A: nat] :
% 5.46/5.68 ( ! [A5: nat] :
% 5.46/5.68 ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = A5 )
% 5.46/5.68 => ( P @ A5 ) )
% 5.46/5.68 => ( ! [A5: nat,B5: $o] :
% 5.46/5.68 ( ( P @ A5 )
% 5.46/5.68 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = A5 )
% 5.46/5.68 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.46/5.68 => ( P @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % bits_induct
% 5.46/5.68 thf(fact_5589_bits__induct,axiom,
% 5.46/5.68 ! [P: int > $o,A: int] :
% 5.46/5.68 ( ! [A5: int] :
% 5.46/5.68 ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 = A5 )
% 5.46/5.68 => ( P @ A5 ) )
% 5.46/5.68 => ( ! [A5: int,B5: $o] :
% 5.46/5.68 ( ( P @ A5 )
% 5.46/5.68 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 = A5 )
% 5.46/5.68 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.46/5.68 => ( P @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % bits_induct
% 5.46/5.68 thf(fact_5590_bits__induct,axiom,
% 5.46/5.68 ! [P: code_integer > $o,A: code_integer] :
% 5.46/5.68 ( ! [A5: code_integer] :
% 5.46/5.68 ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 = A5 )
% 5.46/5.68 => ( P @ A5 ) )
% 5.46/5.68 => ( ! [A5: code_integer,B5: $o] :
% 5.46/5.68 ( ( P @ A5 )
% 5.46/5.68 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 = A5 )
% 5.46/5.68 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.46/5.68 => ( P @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % bits_induct
% 5.46/5.68 thf(fact_5591_divide__le__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [B: real,C: real,W: num] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_le_eq_numeral(2)
% 5.46/5.68 thf(fact_5592_divide__le__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [B: rat,C: rat,W: num] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_le_eq_numeral(2)
% 5.46/5.68 thf(fact_5593_le__divide__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [W: num,B: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_divide_eq_numeral(2)
% 5.46/5.68 thf(fact_5594_le__divide__eq__numeral_I2_J,axiom,
% 5.46/5.68 ! [W: num,B: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_divide_eq_numeral(2)
% 5.46/5.68 thf(fact_5595_square__le__1,axiom,
% 5.46/5.68 ! [X2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_le_1
% 5.46/5.68 thf(fact_5596_square__le__1,axiom,
% 5.46/5.68 ! [X2: code_integer] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X2 )
% 5.46/5.68 => ( ( ord_le3102999989581377725nteger @ X2 @ one_one_Code_integer )
% 5.46/5.68 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_le_1
% 5.46/5.68 thf(fact_5597_square__le__1,axiom,
% 5.46/5.68 ! [X2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ X2 @ one_one_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_le_1
% 5.46/5.68 thf(fact_5598_square__le__1,axiom,
% 5.46/5.68 ! [X2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X2 )
% 5.46/5.68 => ( ( ord_less_eq_int @ X2 @ one_one_int )
% 5.46/5.68 => ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % square_le_1
% 5.46/5.68 thf(fact_5599_minus__power__mult__self,axiom,
% 5.46/5.68 ! [A: int,N: nat] :
% 5.46/5.68 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.46/5.68 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_power_mult_self
% 5.46/5.68 thf(fact_5600_minus__power__mult__self,axiom,
% 5.46/5.68 ! [A: real,N: nat] :
% 5.46/5.68 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.46/5.68 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_power_mult_self
% 5.46/5.68 thf(fact_5601_minus__power__mult__self,axiom,
% 5.46/5.68 ! [A: complex,N: nat] :
% 5.46/5.68 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.46/5.68 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_power_mult_self
% 5.46/5.68 thf(fact_5602_minus__power__mult__self,axiom,
% 5.46/5.68 ! [A: code_integer,N: nat] :
% 5.46/5.68 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.46/5.68 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_power_mult_self
% 5.46/5.68 thf(fact_5603_minus__power__mult__self,axiom,
% 5.46/5.68 ! [A: rat,N: nat] :
% 5.46/5.68 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.46/5.68 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_power_mult_self
% 5.46/5.68 thf(fact_5604_signed__take__bit__int__eq__self,axiom,
% 5.46/5.68 ! [N: nat,K: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.46/5.68 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.46/5.68 = K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_int_eq_self
% 5.46/5.68 thf(fact_5605_signed__take__bit__int__eq__self__iff,axiom,
% 5.46/5.68 ! [N: nat,K: int] :
% 5.46/5.68 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.46/5.68 = K )
% 5.46/5.68 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.46/5.68 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_int_eq_self_iff
% 5.46/5.68 thf(fact_5606_minus__1__div__exp__eq__int,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_1_div_exp_eq_int
% 5.46/5.68 thf(fact_5607_div__pos__neg__trivial,axiom,
% 5.46/5.68 ! [K: int,L2: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.68 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.68 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_pos_neg_trivial
% 5.46/5.68 thf(fact_5608_exp__mod__exp,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % exp_mod_exp
% 5.46/5.68 thf(fact_5609_exp__mod__exp,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % exp_mod_exp
% 5.46/5.68 thf(fact_5610_exp__mod__exp,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % exp_mod_exp
% 5.46/5.68 thf(fact_5611_divmod__nat__def,axiom,
% 5.46/5.68 ( divmod_nat
% 5.46/5.68 = ( ^ [M3: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M3 @ N2 ) @ ( modulo_modulo_nat @ M3 @ N2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divmod_nat_def
% 5.46/5.68 thf(fact_5612_power__minus1__odd,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_odd
% 5.46/5.68 thf(fact_5613_power__minus1__odd,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_odd
% 5.46/5.68 thf(fact_5614_power__minus1__odd,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_odd
% 5.46/5.68 thf(fact_5615_power__minus1__odd,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_odd
% 5.46/5.68 thf(fact_5616_power__minus1__odd,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_minus1_odd
% 5.46/5.68 thf(fact_5617_int__bit__induct,axiom,
% 5.46/5.68 ! [P: int > $o,K: int] :
% 5.46/5.68 ( ( P @ zero_zero_int )
% 5.46/5.68 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 => ( ! [K3: int] :
% 5.46/5.68 ( ( P @ K3 )
% 5.46/5.68 => ( ( K3 != zero_zero_int )
% 5.46/5.68 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.68 => ( ! [K3: int] :
% 5.46/5.68 ( ( P @ K3 )
% 5.46/5.68 => ( ( K3
% 5.46/5.68 != ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.46/5.68 => ( P @ K ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % int_bit_induct
% 5.46/5.68 thf(fact_5618_signed__take__bit__int__greater__eq,axiom,
% 5.46/5.68 ! [K: int,N: nat] :
% 5.46/5.68 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_int_greater_eq
% 5.46/5.68 thf(fact_5619_exp__div__exp__eq,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( times_times_nat
% 5.46/5.68 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.68 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.46/5.68 != zero_zero_nat )
% 5.46/5.68 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.46/5.68 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % exp_div_exp_eq
% 5.46/5.68 thf(fact_5620_exp__div__exp__eq,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( times_times_int
% 5.46/5.68 @ ( zero_n2684676970156552555ol_int
% 5.46/5.68 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.46/5.68 != zero_zero_int )
% 5.46/5.68 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.46/5.68 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % exp_div_exp_eq
% 5.46/5.68 thf(fact_5621_exp__div__exp__eq,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.68 = ( times_3573771949741848930nteger
% 5.46/5.68 @ ( zero_n356916108424825756nteger
% 5.46/5.68 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.46/5.68 != zero_z3403309356797280102nteger )
% 5.46/5.68 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.46/5.68 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % exp_div_exp_eq
% 5.46/5.68 thf(fact_5622_vebt__buildup_Osimps_I3_J,axiom,
% 5.46/5.68 ! [Va: nat] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.68 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.68 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % vebt_buildup.simps(3)
% 5.46/5.68 thf(fact_5623_one__div__minus__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_div_minus_numeral
% 5.46/5.68 thf(fact_5624_minus__one__div__numeral,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_one_div_numeral
% 5.46/5.68 thf(fact_5625_compl__le__compl__iff,axiom,
% 5.46/5.68 ! [X2: set_nat,Y2: set_nat] :
% 5.46/5.68 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ ( uminus5710092332889474511et_nat @ Y2 ) )
% 5.46/5.68 = ( ord_less_eq_set_nat @ Y2 @ X2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % compl_le_compl_iff
% 5.46/5.68 thf(fact_5626_numeral__div__minus__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % numeral_div_minus_numeral
% 5.46/5.68 thf(fact_5627_minus__numeral__div__numeral,axiom,
% 5.46/5.68 ! [M: num,N: num] :
% 5.46/5.68 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % minus_numeral_div_numeral
% 5.46/5.68 thf(fact_5628_dbl__dec__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(4)
% 5.46/5.68 thf(fact_5629_dbl__dec__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.68 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(4)
% 5.46/5.68 thf(fact_5630_dbl__dec__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.68 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(4)
% 5.46/5.68 thf(fact_5631_dbl__dec__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.68 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(4)
% 5.46/5.68 thf(fact_5632_dbl__dec__simps_I4_J,axiom,
% 5.46/5.68 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.68 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(4)
% 5.46/5.68 thf(fact_5633_dbl__dec__simps_I3_J,axiom,
% 5.46/5.68 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.46/5.68 = one_one_complex ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(3)
% 5.46/5.68 thf(fact_5634_dbl__dec__simps_I3_J,axiom,
% 5.46/5.68 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.46/5.68 = one_one_real ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(3)
% 5.46/5.68 thf(fact_5635_dbl__dec__simps_I3_J,axiom,
% 5.46/5.68 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.46/5.68 = one_one_rat ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(3)
% 5.46/5.68 thf(fact_5636_dbl__dec__simps_I3_J,axiom,
% 5.46/5.68 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.46/5.68 = one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(3)
% 5.46/5.68 thf(fact_5637_dbl__dec__simps_I5_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.46/5.68 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(5)
% 5.46/5.68 thf(fact_5638_dbl__dec__simps_I5_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.46/5.68 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_dec_simps(5)
% 5.46/5.68 thf(fact_5639_dbl__dec__simps_I5_J,axiom,
% 5.46/5.68 ! [K: num] :
% 5.46/5.68 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.46/5.68 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(5)
% 5.46/5.69 thf(fact_5640_dbl__dec__simps_I5_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.46/5.69 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(5)
% 5.46/5.69 thf(fact_5641_dbl__dec__simps_I2_J,axiom,
% 5.46/5.69 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.46/5.69 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(2)
% 5.46/5.69 thf(fact_5642_dbl__dec__simps_I2_J,axiom,
% 5.46/5.69 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.46/5.69 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(2)
% 5.46/5.69 thf(fact_5643_dbl__dec__simps_I2_J,axiom,
% 5.46/5.69 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.46/5.69 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(2)
% 5.46/5.69 thf(fact_5644_dbl__dec__simps_I2_J,axiom,
% 5.46/5.69 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.46/5.69 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(2)
% 5.46/5.69 thf(fact_5645_dbl__dec__simps_I2_J,axiom,
% 5.46/5.69 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.46/5.69 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(2)
% 5.46/5.69 thf(fact_5646_Divides_Oadjust__div__eq,axiom,
% 5.46/5.69 ! [Q2: int,R: int] :
% 5.46/5.69 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.46/5.69 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % Divides.adjust_div_eq
% 5.46/5.69 thf(fact_5647_dbl__dec__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.69 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(1)
% 5.46/5.69 thf(fact_5648_dbl__dec__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.46/5.69 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(1)
% 5.46/5.69 thf(fact_5649_dbl__dec__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.46/5.69 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(1)
% 5.46/5.69 thf(fact_5650_dbl__dec__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.46/5.69 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(1)
% 5.46/5.69 thf(fact_5651_dbl__dec__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.46/5.69 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_simps(1)
% 5.46/5.69 thf(fact_5652_dbl__inc__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.69 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_inc_simps(1)
% 5.46/5.69 thf(fact_5653_dbl__inc__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.46/5.69 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_inc_simps(1)
% 5.46/5.69 thf(fact_5654_dbl__inc__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.46/5.69 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_inc_simps(1)
% 5.46/5.69 thf(fact_5655_dbl__inc__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.46/5.69 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_inc_simps(1)
% 5.46/5.69 thf(fact_5656_dbl__inc__simps_I1_J,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.46/5.69 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_inc_simps(1)
% 5.46/5.69 thf(fact_5657_Divides_Oadjust__div__def,axiom,
% 5.46/5.69 ( adjust_div
% 5.46/5.69 = ( produc8211389475949308722nt_int
% 5.46/5.69 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % Divides.adjust_div_def
% 5.46/5.69 thf(fact_5658_dbl__dec__def,axiom,
% 5.46/5.69 ( neg_nu6511756317524482435omplex
% 5.46/5.69 = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_def
% 5.46/5.69 thf(fact_5659_dbl__dec__def,axiom,
% 5.46/5.69 ( neg_nu6075765906172075777c_real
% 5.46/5.69 = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_def
% 5.46/5.69 thf(fact_5660_dbl__dec__def,axiom,
% 5.46/5.69 ( neg_nu3179335615603231917ec_rat
% 5.46/5.69 = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_def
% 5.46/5.69 thf(fact_5661_dbl__dec__def,axiom,
% 5.46/5.69 ( neg_nu3811975205180677377ec_int
% 5.46/5.69 = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dbl_dec_def
% 5.46/5.69 thf(fact_5662_compl__le__swap2,axiom,
% 5.46/5.69 ! [Y2: set_nat,X2: set_nat] :
% 5.46/5.69 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y2 ) @ X2 )
% 5.46/5.69 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % compl_le_swap2
% 5.46/5.69 thf(fact_5663_compl__le__swap1,axiom,
% 5.46/5.69 ! [Y2: set_nat,X2: set_nat] :
% 5.46/5.69 ( ( ord_less_eq_set_nat @ Y2 @ ( uminus5710092332889474511et_nat @ X2 ) )
% 5.46/5.69 => ( ord_less_eq_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % compl_le_swap1
% 5.46/5.69 thf(fact_5664_compl__mono,axiom,
% 5.46/5.69 ! [X2: set_nat,Y2: set_nat] :
% 5.46/5.69 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 5.46/5.69 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y2 ) @ ( uminus5710092332889474511et_nat @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % compl_mono
% 5.46/5.69 thf(fact_5665_diff__shunt__var,axiom,
% 5.46/5.69 ! [X2: set_int,Y2: set_int] :
% 5.46/5.69 ( ( ( minus_minus_set_int @ X2 @ Y2 )
% 5.46/5.69 = bot_bot_set_int )
% 5.46/5.69 = ( ord_less_eq_set_int @ X2 @ Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_shunt_var
% 5.46/5.69 thf(fact_5666_diff__shunt__var,axiom,
% 5.46/5.69 ! [X2: set_real,Y2: set_real] :
% 5.46/5.69 ( ( ( minus_minus_set_real @ X2 @ Y2 )
% 5.46/5.69 = bot_bot_set_real )
% 5.46/5.69 = ( ord_less_eq_set_real @ X2 @ Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_shunt_var
% 5.46/5.69 thf(fact_5667_diff__shunt__var,axiom,
% 5.46/5.69 ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
% 5.46/5.69 ( ( ( minus_1356011639430497352at_nat @ X2 @ Y2 )
% 5.46/5.69 = bot_bo2099793752762293965at_nat )
% 5.46/5.69 = ( ord_le3146513528884898305at_nat @ X2 @ Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_shunt_var
% 5.46/5.69 thf(fact_5668_diff__shunt__var,axiom,
% 5.46/5.69 ! [X2: set_nat,Y2: set_nat] :
% 5.46/5.69 ( ( ( minus_minus_set_nat @ X2 @ Y2 )
% 5.46/5.69 = bot_bot_set_nat )
% 5.46/5.69 = ( ord_less_eq_set_nat @ X2 @ Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_shunt_var
% 5.46/5.69 thf(fact_5669_ln__one__minus__pos__lower__bound,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_one_minus_pos_lower_bound
% 5.46/5.69 thf(fact_5670_of__int__code__if,axiom,
% 5.46/5.69 ( ring_1_of_int_int
% 5.46/5.69 = ( ^ [K2: int] :
% 5.46/5.69 ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 5.46/5.69 @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.46/5.69 @ ( if_int
% 5.46/5.69 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.69 = zero_zero_int )
% 5.46/5.69 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_code_if
% 5.46/5.69 thf(fact_5671_of__int__code__if,axiom,
% 5.46/5.69 ( ring_1_of_int_real
% 5.46/5.69 = ( ^ [K2: int] :
% 5.46/5.69 ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 5.46/5.69 @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 5.46/5.69 @ ( if_real
% 5.46/5.69 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.69 = zero_zero_int )
% 5.46/5.69 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_code_if
% 5.46/5.69 thf(fact_5672_of__int__code__if,axiom,
% 5.46/5.69 ( ring_17405671764205052669omplex
% 5.46/5.69 = ( ^ [K2: int] :
% 5.46/5.69 ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 5.46/5.69 @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 5.46/5.69 @ ( if_complex
% 5.46/5.69 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.69 = zero_zero_int )
% 5.46/5.69 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_code_if
% 5.46/5.69 thf(fact_5673_of__int__code__if,axiom,
% 5.46/5.69 ( ring_18347121197199848620nteger
% 5.46/5.69 = ( ^ [K2: int] :
% 5.46/5.69 ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.46/5.69 @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 5.46/5.69 @ ( if_Code_integer
% 5.46/5.69 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.69 = zero_zero_int )
% 5.46/5.69 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_code_if
% 5.46/5.69 thf(fact_5674_of__int__code__if,axiom,
% 5.46/5.69 ( ring_1_of_int_rat
% 5.46/5.69 = ( ^ [K2: int] :
% 5.46/5.69 ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 5.46/5.69 @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 5.46/5.69 @ ( if_rat
% 5.46/5.69 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.69 = zero_zero_int )
% 5.46/5.69 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_code_if
% 5.46/5.69 thf(fact_5675_vebt__buildup_Opelims,axiom,
% 5.46/5.69 ! [X2: nat,Y2: vEBT_VEBT] :
% 5.46/5.69 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.46/5.69 = Y2 )
% 5.46/5.69 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X2 )
% 5.46/5.69 => ( ( ( X2 = zero_zero_nat )
% 5.46/5.69 => ( ( Y2
% 5.46/5.69 = ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.69 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.46/5.69 => ( ( ( X2
% 5.46/5.69 = ( suc @ zero_zero_nat ) )
% 5.46/5.69 => ( ( Y2
% 5.46/5.69 = ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.69 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.46/5.69 => ~ ! [Va3: nat] :
% 5.46/5.69 ( ( X2
% 5.46/5.69 = ( suc @ ( suc @ Va3 ) ) )
% 5.46/5.69 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.46/5.69 => ( Y2
% 5.46/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.46/5.69 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.46/5.69 => ( Y2
% 5.46/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.46/5.69 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % vebt_buildup.pelims
% 5.46/5.69 thf(fact_5676_int__ge__less__than__def,axiom,
% 5.46/5.69 ( int_ge_less_than
% 5.46/5.69 = ( ^ [D: int] :
% 5.46/5.69 ( collec213857154873943460nt_int
% 5.46/5.69 @ ( produc4947309494688390418_int_o
% 5.46/5.69 @ ^ [Z6: int,Z4: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ D @ Z6 )
% 5.46/5.69 & ( ord_less_int @ Z6 @ Z4 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % int_ge_less_than_def
% 5.46/5.69 thf(fact_5677_int__ge__less__than2__def,axiom,
% 5.46/5.69 ( int_ge_less_than2
% 5.46/5.69 = ( ^ [D: int] :
% 5.46/5.69 ( collec213857154873943460nt_int
% 5.46/5.69 @ ( produc4947309494688390418_int_o
% 5.46/5.69 @ ^ [Z6: int,Z4: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ D @ Z4 )
% 5.46/5.69 & ( ord_less_int @ Z6 @ Z4 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % int_ge_less_than2_def
% 5.46/5.69 thf(fact_5678_of__int__numeral,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.46/5.69 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral
% 5.46/5.69 thf(fact_5679_of__int__numeral,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.46/5.69 = ( numeral_numeral_real @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral
% 5.46/5.69 thf(fact_5680_of__int__numeral,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.46/5.69 = ( numeral_numeral_rat @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral
% 5.46/5.69 thf(fact_5681_of__int__numeral,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.46/5.69 = ( numeral_numeral_int @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral
% 5.46/5.69 thf(fact_5682_of__int__eq__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.46/5.69 = ( numera6690914467698888265omplex @ N ) )
% 5.46/5.69 = ( Z
% 5.46/5.69 = ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_numeral_iff
% 5.46/5.69 thf(fact_5683_of__int__eq__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ( ring_1_of_int_real @ Z )
% 5.46/5.69 = ( numeral_numeral_real @ N ) )
% 5.46/5.69 = ( Z
% 5.46/5.69 = ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_numeral_iff
% 5.46/5.69 thf(fact_5684_of__int__eq__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ( ring_1_of_int_rat @ Z )
% 5.46/5.69 = ( numeral_numeral_rat @ N ) )
% 5.46/5.69 = ( Z
% 5.46/5.69 = ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_numeral_iff
% 5.46/5.69 thf(fact_5685_of__int__eq__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ( ring_1_of_int_int @ Z )
% 5.46/5.69 = ( numeral_numeral_int @ N ) )
% 5.46/5.69 = ( Z
% 5.46/5.69 = ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_numeral_iff
% 5.46/5.69 thf(fact_5686_of__int__le__iff,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_iff
% 5.46/5.69 thf(fact_5687_of__int__le__iff,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_iff
% 5.46/5.69 thf(fact_5688_of__int__le__iff,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_iff
% 5.46/5.69 thf(fact_5689_of__int__less__iff,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.69 = ( ord_less_int @ W @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_iff
% 5.46/5.69 thf(fact_5690_of__int__less__iff,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.69 = ( ord_less_int @ W @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_iff
% 5.46/5.69 thf(fact_5691_of__int__less__iff,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.69 = ( ord_less_int @ W @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_iff
% 5.46/5.69 thf(fact_5692_ln__one,axiom,
% 5.46/5.69 ( ( ln_ln_real @ one_one_real )
% 5.46/5.69 = zero_zero_real ) ).
% 5.46/5.69
% 5.46/5.69 % ln_one
% 5.46/5.69 thf(fact_5693_of__int__1,axiom,
% 5.46/5.69 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.46/5.69 = one_one_complex ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1
% 5.46/5.69 thf(fact_5694_of__int__1,axiom,
% 5.46/5.69 ( ( ring_1_of_int_int @ one_one_int )
% 5.46/5.69 = one_one_int ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1
% 5.46/5.69 thf(fact_5695_of__int__1,axiom,
% 5.46/5.69 ( ( ring_1_of_int_real @ one_one_int )
% 5.46/5.69 = one_one_real ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1
% 5.46/5.69 thf(fact_5696_of__int__1,axiom,
% 5.46/5.69 ( ( ring_1_of_int_rat @ one_one_int )
% 5.46/5.69 = one_one_rat ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1
% 5.46/5.69 thf(fact_5697_of__int__eq__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.46/5.69 = one_one_complex )
% 5.46/5.69 = ( Z = one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_1_iff
% 5.46/5.69 thf(fact_5698_of__int__eq__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ( ring_1_of_int_int @ Z )
% 5.46/5.69 = one_one_int )
% 5.46/5.69 = ( Z = one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_1_iff
% 5.46/5.69 thf(fact_5699_of__int__eq__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ( ring_1_of_int_real @ Z )
% 5.46/5.69 = one_one_real )
% 5.46/5.69 = ( Z = one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_1_iff
% 5.46/5.69 thf(fact_5700_of__int__eq__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ( ring_1_of_int_rat @ Z )
% 5.46/5.69 = one_one_rat )
% 5.46/5.69 = ( Z = one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_1_iff
% 5.46/5.69 thf(fact_5701_of__int__mult,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.46/5.69 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_mult
% 5.46/5.69 thf(fact_5702_of__int__mult,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.46/5.69 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_mult
% 5.46/5.69 thf(fact_5703_of__int__mult,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.46/5.69 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_mult
% 5.46/5.69 thf(fact_5704_of__int__add,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.46/5.69 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_add
% 5.46/5.69 thf(fact_5705_of__int__add,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.46/5.69 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_add
% 5.46/5.69 thf(fact_5706_of__int__add,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.46/5.69 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_add
% 5.46/5.69 thf(fact_5707_of__int__diff,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 5.46/5.69 = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_diff
% 5.46/5.69 thf(fact_5708_of__int__diff,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 5.46/5.69 = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_diff
% 5.46/5.69 thf(fact_5709_of__int__diff,axiom,
% 5.46/5.69 ! [W: int,Z: int] :
% 5.46/5.69 ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 5.46/5.69 = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_diff
% 5.46/5.69 thf(fact_5710_ln__less__cancel__iff,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.69 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) )
% 5.46/5.69 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_less_cancel_iff
% 5.46/5.69 thf(fact_5711_ln__inj__iff,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.69 => ( ( ( ln_ln_real @ X2 )
% 5.46/5.69 = ( ln_ln_real @ Y2 ) )
% 5.46/5.69 = ( X2 = Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_inj_iff
% 5.46/5.69 thf(fact_5712_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ( ring_1_of_int_rat @ X2 )
% 5.46/5.69 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.46/5.69 = ( X2
% 5.46/5.69 = ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5713_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ( ring_1_of_int_real @ X2 )
% 5.46/5.69 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.46/5.69 = ( X2
% 5.46/5.69 = ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5714_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ( ring_17405671764205052669omplex @ X2 )
% 5.46/5.69 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.46/5.69 = ( X2
% 5.46/5.69 = ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5715_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ( ring_1_of_int_int @ X2 )
% 5.46/5.69 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.46/5.69 = ( X2
% 5.46/5.69 = ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5716_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.46/5.69 = ( ring_1_of_int_rat @ X2 ) )
% 5.46/5.69 = ( ( power_power_int @ B @ W )
% 5.46/5.69 = X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5717_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.46/5.69 = ( ring_1_of_int_real @ X2 ) )
% 5.46/5.69 = ( ( power_power_int @ B @ W )
% 5.46/5.69 = X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5718_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.46/5.69 = ( ring_17405671764205052669omplex @ X2 ) )
% 5.46/5.69 = ( ( power_power_int @ B @ W )
% 5.46/5.69 = X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5719_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.46/5.69 = ( ring_1_of_int_int @ X2 ) )
% 5.46/5.69 = ( ( power_power_int @ B @ W )
% 5.46/5.69 = X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5720_of__int__power,axiom,
% 5.46/5.69 ! [Z: int,N: nat] :
% 5.46/5.69 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.46/5.69 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power
% 5.46/5.69 thf(fact_5721_of__int__power,axiom,
% 5.46/5.69 ! [Z: int,N: nat] :
% 5.46/5.69 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.46/5.69 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power
% 5.46/5.69 thf(fact_5722_of__int__power,axiom,
% 5.46/5.69 ! [Z: int,N: nat] :
% 5.46/5.69 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.46/5.69 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power
% 5.46/5.69 thf(fact_5723_of__int__power,axiom,
% 5.46/5.69 ! [Z: int,N: nat] :
% 5.46/5.69 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.46/5.69 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power
% 5.46/5.69 thf(fact_5724_ln__le__cancel__iff,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) )
% 5.46/5.69 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_le_cancel_iff
% 5.46/5.69 thf(fact_5725_ln__less__zero__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.46/5.69 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_less_zero_iff
% 5.46/5.69 thf(fact_5726_ln__gt__zero__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.46/5.69 = ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_gt_zero_iff
% 5.46/5.69 thf(fact_5727_ln__eq__zero__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ( ln_ln_real @ X2 )
% 5.46/5.69 = zero_zero_real )
% 5.46/5.69 = ( X2 = one_one_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_eq_zero_iff
% 5.46/5.69 thf(fact_5728_of__int__0__le__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_0_le_iff
% 5.46/5.69 thf(fact_5729_of__int__0__le__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_0_le_iff
% 5.46/5.69 thf(fact_5730_of__int__0__le__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_0_le_iff
% 5.46/5.69 thf(fact_5731_of__int__le__0__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.46/5.69 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_0_iff
% 5.46/5.69 thf(fact_5732_of__int__le__0__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.46/5.69 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_0_iff
% 5.46/5.69 thf(fact_5733_of__int__le__0__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.46/5.69 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_0_iff
% 5.46/5.69 thf(fact_5734_of__int__less__0__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.46/5.69 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_0_iff
% 5.46/5.69 thf(fact_5735_of__int__less__0__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.46/5.69 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_0_iff
% 5.46/5.69 thf(fact_5736_of__int__less__0__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.46/5.69 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_0_iff
% 5.46/5.69 thf(fact_5737_of__int__0__less__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.69 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_0_less_iff
% 5.46/5.69 thf(fact_5738_of__int__0__less__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.69 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_0_less_iff
% 5.46/5.69 thf(fact_5739_of__int__0__less__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.69 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_0_less_iff
% 5.46/5.69 thf(fact_5740_of__int__le__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_numeral_iff
% 5.46/5.69 thf(fact_5741_of__int__le__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_numeral_iff
% 5.46/5.69 thf(fact_5742_of__int__le__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_numeral_iff
% 5.46/5.69 thf(fact_5743_of__int__numeral__le__iff,axiom,
% 5.46/5.69 ! [N: num,Z: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral_le_iff
% 5.46/5.69 thf(fact_5744_of__int__numeral__le__iff,axiom,
% 5.46/5.69 ! [N: num,Z: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral_le_iff
% 5.46/5.69 thf(fact_5745_of__int__numeral__le__iff,axiom,
% 5.46/5.69 ! [N: num,Z: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral_le_iff
% 5.46/5.69 thf(fact_5746_of__int__numeral__less__iff,axiom,
% 5.46/5.69 ! [N: num,Z: int] :
% 5.46/5.69 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.69 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral_less_iff
% 5.46/5.69 thf(fact_5747_of__int__numeral__less__iff,axiom,
% 5.46/5.69 ! [N: num,Z: int] :
% 5.46/5.69 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.69 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral_less_iff
% 5.46/5.69 thf(fact_5748_of__int__numeral__less__iff,axiom,
% 5.46/5.69 ! [N: num,Z: int] :
% 5.46/5.69 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.69 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_numeral_less_iff
% 5.46/5.69 thf(fact_5749_of__int__less__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.69 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_numeral_iff
% 5.46/5.69 thf(fact_5750_of__int__less__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.69 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_numeral_iff
% 5.46/5.69 thf(fact_5751_of__int__less__numeral__iff,axiom,
% 5.46/5.69 ! [Z: int,N: num] :
% 5.46/5.69 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.69 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_numeral_iff
% 5.46/5.69 thf(fact_5752_of__int__1__le__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1_le_iff
% 5.46/5.69 thf(fact_5753_of__int__1__le__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1_le_iff
% 5.46/5.69 thf(fact_5754_of__int__1__le__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.69 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1_le_iff
% 5.46/5.69 thf(fact_5755_of__int__le__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.46/5.69 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_1_iff
% 5.46/5.69 thf(fact_5756_of__int__le__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.46/5.69 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_1_iff
% 5.46/5.69 thf(fact_5757_of__int__le__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.46/5.69 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_1_iff
% 5.46/5.69 thf(fact_5758_of__int__less__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.46/5.69 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_1_iff
% 5.46/5.69 thf(fact_5759_of__int__less__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.46/5.69 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_1_iff
% 5.46/5.69 thf(fact_5760_of__int__less__1__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.46/5.69 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_1_iff
% 5.46/5.69 thf(fact_5761_of__int__1__less__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.69 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1_less_iff
% 5.46/5.69 thf(fact_5762_of__int__1__less__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.69 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1_less_iff
% 5.46/5.69 thf(fact_5763_of__int__1__less__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.69 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_1_less_iff
% 5.46/5.69 thf(fact_5764_ln__ge__zero__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.46/5.69 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_ge_zero_iff
% 5.46/5.69 thf(fact_5765_ln__le__zero__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.46/5.69 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_le_zero_iff
% 5.46/5.69 thf(fact_5766_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ( ring_17405671764205052669omplex @ Y2 )
% 5.46/5.69 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 5.46/5.69 = ( Y2
% 5.46/5.69 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5767_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ( ring_1_of_int_real @ Y2 )
% 5.46/5.69 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.46/5.69 = ( Y2
% 5.46/5.69 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5768_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ( ring_1_of_int_rat @ Y2 )
% 5.46/5.69 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.46/5.69 = ( Y2
% 5.46/5.69 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5769_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ( ring_1_of_int_int @ Y2 )
% 5.46/5.69 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.46/5.69 = ( Y2
% 5.46/5.69 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5770_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.69 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 5.46/5.69 = ( ring_17405671764205052669omplex @ Y2 ) )
% 5.46/5.69 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.46/5.69 = Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5771_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.69 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 5.46/5.69 = ( ring_1_of_int_real @ Y2 ) )
% 5.46/5.69 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.46/5.69 = Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5772_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.69 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 5.46/5.69 = ( ring_1_of_int_rat @ Y2 ) )
% 5.46/5.69 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.46/5.69 = Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5773_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.69 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.46/5.69 = ( ring_1_of_int_int @ Y2 ) )
% 5.46/5.69 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.46/5.69 = Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5774_of__int__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.46/5.69 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5775_of__int__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.46/5.69 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5776_of__int__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.46/5.69 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5777_of__int__le__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5778_of__int__le__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5779_of__int__le__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5780_of__int__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ord_less_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.46/5.69 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5781_of__int__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.46/5.69 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5782_of__int__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: int,B: int,W: nat] :
% 5.46/5.69 ( ( ord_less_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.46/5.69 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5783_of__int__less__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5784_of__int__less__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5785_of__int__less__of__int__power__cancel__iff,axiom,
% 5.46/5.69 ! [B: int,W: nat,X2: int] :
% 5.46/5.69 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_of_int_power_cancel_iff
% 5.46/5.69 thf(fact_5786_numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5787_numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5788_numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5789_of__int__le__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5790_of__int__le__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5791_of__int__le__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5792_of__int__less__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.46/5.69 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5793_of__int__less__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.46/5.69 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5794_of__int__less__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.46/5.69 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5795_numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5796_numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5797_numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5798_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ( ring_1_of_int_int @ Y2 )
% 5.46/5.69 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.46/5.69 = ( Y2
% 5.46/5.69 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5799_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ( ring_1_of_int_real @ Y2 )
% 5.46/5.69 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.46/5.69 = ( Y2
% 5.46/5.69 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5800_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ( ring_17405671764205052669omplex @ Y2 )
% 5.46/5.69 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N ) )
% 5.46/5.69 = ( Y2
% 5.46/5.69 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5801_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ( ring_18347121197199848620nteger @ Y2 )
% 5.46/5.69 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.46/5.69 = ( Y2
% 5.46/5.69 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5802_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ( ring_1_of_int_rat @ Y2 )
% 5.46/5.69 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.46/5.69 = ( Y2
% 5.46/5.69 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5803_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.69 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.46/5.69 = ( ring_1_of_int_int @ Y2 ) )
% 5.46/5.69 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.46/5.69 = Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5804_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.69 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N )
% 5.46/5.69 = ( ring_1_of_int_real @ Y2 ) )
% 5.46/5.69 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.46/5.69 = Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5805_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.69 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N )
% 5.46/5.69 = ( ring_17405671764205052669omplex @ Y2 ) )
% 5.46/5.69 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.46/5.69 = Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5806_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.69 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N )
% 5.46/5.69 = ( ring_18347121197199848620nteger @ Y2 ) )
% 5.46/5.69 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.46/5.69 = Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5807_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.69 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N )
% 5.46/5.69 = ( ring_1_of_int_rat @ Y2 ) )
% 5.46/5.69 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.46/5.69 = Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.69 thf(fact_5808_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5809_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5810_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5811_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_le_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5812_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5813_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5814_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5815_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_le_of_int_cancel_iff
% 5.46/5.69 thf(fact_5816_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.46/5.69 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5817_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.46/5.69 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5818_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.46/5.69 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5819_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.69 ! [A: int,X2: num,N: nat] :
% 5.46/5.69 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.46/5.69 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_less_neg_numeral_power_cancel_iff
% 5.46/5.69 thf(fact_5820_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5821_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5822_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5823_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.69 ! [X2: num,N: nat,A: int] :
% 5.46/5.69 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.69 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_numeral_power_less_of_int_cancel_iff
% 5.46/5.69 thf(fact_5824_mult__of__int__commute,axiom,
% 5.46/5.69 ! [X2: int,Y2: real] :
% 5.46/5.69 ( ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ Y2 )
% 5.46/5.69 = ( times_times_real @ Y2 @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_of_int_commute
% 5.46/5.69 thf(fact_5825_mult__of__int__commute,axiom,
% 5.46/5.69 ! [X2: int,Y2: rat] :
% 5.46/5.69 ( ( times_times_rat @ ( ring_1_of_int_rat @ X2 ) @ Y2 )
% 5.46/5.69 = ( times_times_rat @ Y2 @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_of_int_commute
% 5.46/5.69 thf(fact_5826_mult__of__int__commute,axiom,
% 5.46/5.69 ! [X2: int,Y2: int] :
% 5.46/5.69 ( ( times_times_int @ ( ring_1_of_int_int @ X2 ) @ Y2 )
% 5.46/5.69 = ( times_times_int @ Y2 @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_of_int_commute
% 5.46/5.69 thf(fact_5827_bot__nat__def,axiom,
% 5.46/5.69 bot_bot_nat = zero_zero_nat ).
% 5.46/5.69
% 5.46/5.69 % bot_nat_def
% 5.46/5.69 thf(fact_5828_bot__enat__def,axiom,
% 5.46/5.69 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.46/5.69
% 5.46/5.69 % bot_enat_def
% 5.46/5.69 thf(fact_5829_ln__less__self,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_less_self
% 5.46/5.69 thf(fact_5830_ln__bound,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_bound
% 5.46/5.69 thf(fact_5831_ln__gt__zero__imp__gt__one,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_gt_zero_imp_gt_one
% 5.46/5.69 thf(fact_5832_ln__less__zero,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.69 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_less_zero
% 5.46/5.69 thf(fact_5833_ln__gt__zero,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_gt_zero
% 5.46/5.69 thf(fact_5834_ln__ge__zero,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_ge_zero
% 5.46/5.69 thf(fact_5835_real__of__int__div4,axiom,
% 5.46/5.69 ! [N: int,X2: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % real_of_int_div4
% 5.46/5.69 thf(fact_5836_real__of__int__div,axiom,
% 5.46/5.69 ! [D2: int,N: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ D2 @ N )
% 5.46/5.69 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D2 ) )
% 5.46/5.69 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % real_of_int_div
% 5.46/5.69 thf(fact_5837_ln__ge__zero__imp__ge__one,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_ge_zero_imp_ge_one
% 5.46/5.69 thf(fact_5838_ln__add__one__self__le__self,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_add_one_self_le_self
% 5.46/5.69 thf(fact_5839_ln__mult,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.69 => ( ( ln_ln_real @ ( times_times_real @ X2 @ Y2 ) )
% 5.46/5.69 = ( plus_plus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_mult
% 5.46/5.69 thf(fact_5840_ln__eq__minus__one,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ( ln_ln_real @ X2 )
% 5.46/5.69 = ( minus_minus_real @ X2 @ one_one_real ) )
% 5.46/5.69 => ( X2 = one_one_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_eq_minus_one
% 5.46/5.69 thf(fact_5841_ln__div,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.69 => ( ( ln_ln_real @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.46/5.69 = ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_div
% 5.46/5.69 thf(fact_5842_of__int__nonneg,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_nonneg
% 5.46/5.69 thf(fact_5843_of__int__nonneg,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_nonneg
% 5.46/5.69 thf(fact_5844_of__int__nonneg,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_nonneg
% 5.46/5.69 thf(fact_5845_of__int__pos,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_pos
% 5.46/5.69 thf(fact_5846_of__int__pos,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_pos
% 5.46/5.69 thf(fact_5847_of__int__pos,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.69 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_pos
% 5.46/5.69 thf(fact_5848_of__int__neg__numeral,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_neg_numeral
% 5.46/5.69 thf(fact_5849_of__int__neg__numeral,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_neg_numeral
% 5.46/5.69 thf(fact_5850_of__int__neg__numeral,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_neg_numeral
% 5.46/5.69 thf(fact_5851_of__int__neg__numeral,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_neg_numeral
% 5.46/5.69 thf(fact_5852_of__int__neg__numeral,axiom,
% 5.46/5.69 ! [K: num] :
% 5.46/5.69 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_neg_numeral
% 5.46/5.69 thf(fact_5853_int__le__real__less,axiom,
% 5.46/5.69 ( ord_less_eq_int
% 5.46/5.69 = ( ^ [N2: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % int_le_real_less
% 5.46/5.69 thf(fact_5854_int__less__real__le,axiom,
% 5.46/5.69 ( ord_less_int
% 5.46/5.69 = ( ^ [N2: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % int_less_real_le
% 5.46/5.69 thf(fact_5855_real__of__int__div__aux,axiom,
% 5.46/5.69 ! [X2: int,D2: int] :
% 5.46/5.69 ( ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ D2 ) )
% 5.46/5.69 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X2 @ D2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X2 @ D2 ) ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % real_of_int_div_aux
% 5.46/5.69 thf(fact_5856_ln__2__less__1,axiom,
% 5.46/5.69 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.46/5.69
% 5.46/5.69 % ln_2_less_1
% 5.46/5.69 thf(fact_5857_ln__le__minus__one,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_le_minus_one
% 5.46/5.69 thf(fact_5858_ln__diff__le,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y2 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X2 @ Y2 ) @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_diff_le
% 5.46/5.69 thf(fact_5859_ln__add__one__self__le__self2,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_add_one_self_le_self2
% 5.46/5.69 thf(fact_5860_real__of__int__div2,axiom,
% 5.46/5.69 ! [N: int,X2: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % real_of_int_div2
% 5.46/5.69 thf(fact_5861_real__of__int__div3,axiom,
% 5.46/5.69 ! [N: int,X2: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) @ one_one_real ) ).
% 5.46/5.69
% 5.46/5.69 % real_of_int_div3
% 5.46/5.69 thf(fact_5862_ln__one__minus__pos__upper__bound,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_one_minus_pos_upper_bound
% 5.46/5.69 thf(fact_5863_even__of__int__iff,axiom,
% 5.46/5.69 ! [K: int] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.46/5.69 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_of_int_iff
% 5.46/5.69 thf(fact_5864_even__of__int__iff,axiom,
% 5.46/5.69 ! [K: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.46/5.69 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_of_int_iff
% 5.46/5.69 thf(fact_5865_ln__one__plus__pos__lower__bound,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ln_one_plus_pos_lower_bound
% 5.46/5.69 thf(fact_5866_artanh__def,axiom,
% 5.46/5.69 ( artanh_real
% 5.46/5.69 = ( ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X ) @ ( minus_minus_real @ one_one_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % artanh_def
% 5.46/5.69 thf(fact_5867_floor__exists1,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ? [X3: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ X2 )
% 5.46/5.69 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.46/5.69 & ! [Y4: int] :
% 5.46/5.69 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X2 )
% 5.46/5.69 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.46/5.69 => ( Y4 = X3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % floor_exists1
% 5.46/5.69 thf(fact_5868_floor__exists1,axiom,
% 5.46/5.69 ! [X2: rat] :
% 5.46/5.69 ? [X3: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X2 )
% 5.46/5.69 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.46/5.69 & ! [Y4: int] :
% 5.46/5.69 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X2 )
% 5.46/5.69 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.46/5.69 => ( Y4 = X3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % floor_exists1
% 5.46/5.69 thf(fact_5869_floor__exists,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ? [Z3: int] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X2 )
% 5.46/5.69 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % floor_exists
% 5.46/5.69 thf(fact_5870_floor__exists,axiom,
% 5.46/5.69 ! [X2: rat] :
% 5.46/5.69 ? [Z3: int] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 )
% 5.46/5.69 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % floor_exists
% 5.46/5.69 thf(fact_5871_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.46/5.69 thf(fact_5872_tanh__ln__real,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( tanh_real @ ( ln_ln_real @ X2 ) )
% 5.46/5.69 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % tanh_ln_real
% 5.46/5.69 thf(fact_5873_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ln_one_plus_x_minus_x_bound
% 5.46/5.69 thf(fact_5874_abs__idempotent,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.46/5.69 = ( abs_abs_real @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_idempotent
% 5.46/5.69 thf(fact_5875_abs__idempotent,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.46/5.69 = ( abs_abs_int @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_idempotent
% 5.46/5.69 thf(fact_5876_abs__idempotent,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.69 = ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_idempotent
% 5.46/5.69 thf(fact_5877_abs__idempotent,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.46/5.69 = ( abs_abs_rat @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_idempotent
% 5.46/5.69 thf(fact_5878_abs__abs,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.46/5.69 = ( abs_abs_real @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_abs
% 5.46/5.69 thf(fact_5879_abs__abs,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.46/5.69 = ( abs_abs_int @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_abs
% 5.46/5.69 thf(fact_5880_abs__abs,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.69 = ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_abs
% 5.46/5.69 thf(fact_5881_abs__abs,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.46/5.69 = ( abs_abs_rat @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_abs
% 5.46/5.69 thf(fact_5882_abs__zero,axiom,
% 5.46/5.69 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.46/5.69 = zero_z3403309356797280102nteger ) ).
% 5.46/5.69
% 5.46/5.69 % abs_zero
% 5.46/5.69 thf(fact_5883_abs__zero,axiom,
% 5.46/5.69 ( ( abs_abs_real @ zero_zero_real )
% 5.46/5.69 = zero_zero_real ) ).
% 5.46/5.69
% 5.46/5.69 % abs_zero
% 5.46/5.69 thf(fact_5884_abs__zero,axiom,
% 5.46/5.69 ( ( abs_abs_rat @ zero_zero_rat )
% 5.46/5.69 = zero_zero_rat ) ).
% 5.46/5.69
% 5.46/5.69 % abs_zero
% 5.46/5.69 thf(fact_5885_abs__zero,axiom,
% 5.46/5.69 ( ( abs_abs_int @ zero_zero_int )
% 5.46/5.69 = zero_zero_int ) ).
% 5.46/5.69
% 5.46/5.69 % abs_zero
% 5.46/5.69 thf(fact_5886_abs__eq__0,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( ( abs_abs_Code_integer @ A )
% 5.46/5.69 = zero_z3403309356797280102nteger )
% 5.46/5.69 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_0
% 5.46/5.69 thf(fact_5887_abs__eq__0,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( ( abs_abs_real @ A )
% 5.46/5.69 = zero_zero_real )
% 5.46/5.69 = ( A = zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_0
% 5.46/5.69 thf(fact_5888_abs__eq__0,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( ( abs_abs_rat @ A )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 = ( A = zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_0
% 5.46/5.69 thf(fact_5889_abs__eq__0,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( ( abs_abs_int @ A )
% 5.46/5.69 = zero_zero_int )
% 5.46/5.69 = ( A = zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_0
% 5.46/5.69 thf(fact_5890_abs__0__eq,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( zero_z3403309356797280102nteger
% 5.46/5.69 = ( abs_abs_Code_integer @ A ) )
% 5.46/5.69 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_0_eq
% 5.46/5.69 thf(fact_5891_abs__0__eq,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( zero_zero_real
% 5.46/5.69 = ( abs_abs_real @ A ) )
% 5.46/5.69 = ( A = zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_0_eq
% 5.46/5.69 thf(fact_5892_abs__0__eq,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( zero_zero_rat
% 5.46/5.69 = ( abs_abs_rat @ A ) )
% 5.46/5.69 = ( A = zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_0_eq
% 5.46/5.69 thf(fact_5893_abs__0__eq,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( zero_zero_int
% 5.46/5.69 = ( abs_abs_int @ A ) )
% 5.46/5.69 = ( A = zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_0_eq
% 5.46/5.69 thf(fact_5894_abs__0,axiom,
% 5.46/5.69 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.46/5.69 = zero_z3403309356797280102nteger ) ).
% 5.46/5.69
% 5.46/5.69 % abs_0
% 5.46/5.69 thf(fact_5895_abs__0,axiom,
% 5.46/5.69 ( ( abs_abs_complex @ zero_zero_complex )
% 5.46/5.69 = zero_zero_complex ) ).
% 5.46/5.69
% 5.46/5.69 % abs_0
% 5.46/5.69 thf(fact_5896_abs__0,axiom,
% 5.46/5.69 ( ( abs_abs_real @ zero_zero_real )
% 5.46/5.69 = zero_zero_real ) ).
% 5.46/5.69
% 5.46/5.69 % abs_0
% 5.46/5.69 thf(fact_5897_abs__0,axiom,
% 5.46/5.69 ( ( abs_abs_rat @ zero_zero_rat )
% 5.46/5.69 = zero_zero_rat ) ).
% 5.46/5.69
% 5.46/5.69 % abs_0
% 5.46/5.69 thf(fact_5898_abs__0,axiom,
% 5.46/5.69 ( ( abs_abs_int @ zero_zero_int )
% 5.46/5.69 = zero_zero_int ) ).
% 5.46/5.69
% 5.46/5.69 % abs_0
% 5.46/5.69 thf(fact_5899_abs__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.69 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_numeral
% 5.46/5.69 thf(fact_5900_abs__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.46/5.69 = ( numeral_numeral_real @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_numeral
% 5.46/5.69 thf(fact_5901_abs__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.46/5.69 = ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_numeral
% 5.46/5.69 thf(fact_5902_abs__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.46/5.69 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_numeral
% 5.46/5.69 thf(fact_5903_abs__mult__self__eq,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.69 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_self_eq
% 5.46/5.69 thf(fact_5904_abs__mult__self__eq,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.46/5.69 = ( times_times_real @ A @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_self_eq
% 5.46/5.69 thf(fact_5905_abs__mult__self__eq,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.46/5.69 = ( times_times_rat @ A @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_self_eq
% 5.46/5.69 thf(fact_5906_abs__mult__self__eq,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.46/5.69 = ( times_times_int @ A @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_self_eq
% 5.46/5.69 thf(fact_5907_abs__1,axiom,
% 5.46/5.69 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.46/5.69 = one_one_Code_integer ) ).
% 5.46/5.69
% 5.46/5.69 % abs_1
% 5.46/5.69 thf(fact_5908_abs__1,axiom,
% 5.46/5.69 ( ( abs_abs_complex @ one_one_complex )
% 5.46/5.69 = one_one_complex ) ).
% 5.46/5.69
% 5.46/5.69 % abs_1
% 5.46/5.69 thf(fact_5909_abs__1,axiom,
% 5.46/5.69 ( ( abs_abs_real @ one_one_real )
% 5.46/5.69 = one_one_real ) ).
% 5.46/5.69
% 5.46/5.69 % abs_1
% 5.46/5.69 thf(fact_5910_abs__1,axiom,
% 5.46/5.69 ( ( abs_abs_rat @ one_one_rat )
% 5.46/5.69 = one_one_rat ) ).
% 5.46/5.69
% 5.46/5.69 % abs_1
% 5.46/5.69 thf(fact_5911_abs__1,axiom,
% 5.46/5.69 ( ( abs_abs_int @ one_one_int )
% 5.46/5.69 = one_one_int ) ).
% 5.46/5.69
% 5.46/5.69 % abs_1
% 5.46/5.69 thf(fact_5912_abs__add__abs,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.46/5.69 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_add_abs
% 5.46/5.69 thf(fact_5913_abs__add__abs,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.46/5.69 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_add_abs
% 5.46/5.69 thf(fact_5914_abs__add__abs,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.46/5.69 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_add_abs
% 5.46/5.69 thf(fact_5915_abs__add__abs,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.46/5.69 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_add_abs
% 5.46/5.69 thf(fact_5916_abs__divide,axiom,
% 5.46/5.69 ! [A: complex,B: complex] :
% 5.46/5.69 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_divide
% 5.46/5.69 thf(fact_5917_abs__divide,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.69 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_divide
% 5.46/5.69 thf(fact_5918_abs__divide,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.46/5.69 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_divide
% 5.46/5.69 thf(fact_5919_abs__minus__cancel,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.69 = ( abs_abs_int @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_cancel
% 5.46/5.69 thf(fact_5920_abs__minus__cancel,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.69 = ( abs_abs_real @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_cancel
% 5.46/5.69 thf(fact_5921_abs__minus__cancel,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.69 = ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_cancel
% 5.46/5.69 thf(fact_5922_abs__minus__cancel,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.69 = ( abs_abs_rat @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_cancel
% 5.46/5.69 thf(fact_5923_abs__minus,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.69 = ( abs_abs_int @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus
% 5.46/5.69 thf(fact_5924_abs__minus,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.69 = ( abs_abs_real @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus
% 5.46/5.69 thf(fact_5925_abs__minus,axiom,
% 5.46/5.69 ! [A: complex] :
% 5.46/5.69 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.69 = ( abs_abs_complex @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus
% 5.46/5.69 thf(fact_5926_abs__minus,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.69 = ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus
% 5.46/5.69 thf(fact_5927_abs__minus,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.69 = ( abs_abs_rat @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus
% 5.46/5.69 thf(fact_5928_dvd__abs__iff,axiom,
% 5.46/5.69 ! [M: real,K: real] :
% 5.46/5.69 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.46/5.69 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % dvd_abs_iff
% 5.46/5.69 thf(fact_5929_dvd__abs__iff,axiom,
% 5.46/5.69 ! [M: int,K: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.46/5.69 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % dvd_abs_iff
% 5.46/5.69 thf(fact_5930_dvd__abs__iff,axiom,
% 5.46/5.69 ! [M: code_integer,K: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.46/5.69 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % dvd_abs_iff
% 5.46/5.69 thf(fact_5931_dvd__abs__iff,axiom,
% 5.46/5.69 ! [M: rat,K: rat] :
% 5.46/5.69 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 5.46/5.69 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % dvd_abs_iff
% 5.46/5.69 thf(fact_5932_abs__dvd__iff,axiom,
% 5.46/5.69 ! [M: real,K: real] :
% 5.46/5.69 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.46/5.69 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_dvd_iff
% 5.46/5.69 thf(fact_5933_abs__dvd__iff,axiom,
% 5.46/5.69 ! [M: int,K: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.46/5.69 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_dvd_iff
% 5.46/5.69 thf(fact_5934_abs__dvd__iff,axiom,
% 5.46/5.69 ! [M: code_integer,K: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.46/5.69 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_dvd_iff
% 5.46/5.69 thf(fact_5935_abs__dvd__iff,axiom,
% 5.46/5.69 ! [M: rat,K: rat] :
% 5.46/5.69 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 5.46/5.69 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_dvd_iff
% 5.46/5.69 thf(fact_5936_abs__bool__eq,axiom,
% 5.46/5.69 ! [P: $o] :
% 5.46/5.69 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.46/5.69 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_bool_eq
% 5.46/5.69 thf(fact_5937_abs__bool__eq,axiom,
% 5.46/5.69 ! [P: $o] :
% 5.46/5.69 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.46/5.69 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_bool_eq
% 5.46/5.69 thf(fact_5938_abs__bool__eq,axiom,
% 5.46/5.69 ! [P: $o] :
% 5.46/5.69 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.46/5.69 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_bool_eq
% 5.46/5.69 thf(fact_5939_abs__bool__eq,axiom,
% 5.46/5.69 ! [P: $o] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.46/5.69 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_bool_eq
% 5.46/5.69 thf(fact_5940_tanh__real__less__iff,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y2 ) )
% 5.46/5.69 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % tanh_real_less_iff
% 5.46/5.69 thf(fact_5941_tanh__real__le__iff,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y2 ) )
% 5.46/5.69 = ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % tanh_real_le_iff
% 5.46/5.69 thf(fact_5942_abs__le__zero__iff,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.46/5.69 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_zero_iff
% 5.46/5.69 thf(fact_5943_abs__le__zero__iff,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.46/5.69 = ( A = zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_zero_iff
% 5.46/5.69 thf(fact_5944_abs__le__zero__iff,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.46/5.69 = ( A = zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_zero_iff
% 5.46/5.69 thf(fact_5945_abs__le__zero__iff,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.46/5.69 = ( A = zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_zero_iff
% 5.46/5.69 thf(fact_5946_abs__le__self__iff,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.46/5.69 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_self_iff
% 5.46/5.69 thf(fact_5947_abs__le__self__iff,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.46/5.69 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_self_iff
% 5.46/5.69 thf(fact_5948_abs__le__self__iff,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.46/5.69 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_self_iff
% 5.46/5.69 thf(fact_5949_abs__le__self__iff,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.46/5.69 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_self_iff
% 5.46/5.69 thf(fact_5950_abs__of__nonneg,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.69 => ( ( abs_abs_Code_integer @ A )
% 5.46/5.69 = A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_nonneg
% 5.46/5.69 thf(fact_5951_abs__of__nonneg,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( abs_abs_real @ A )
% 5.46/5.69 = A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_nonneg
% 5.46/5.69 thf(fact_5952_abs__of__nonneg,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( abs_abs_rat @ A )
% 5.46/5.69 = A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_nonneg
% 5.46/5.69 thf(fact_5953_abs__of__nonneg,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( abs_abs_int @ A )
% 5.46/5.69 = A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_nonneg
% 5.46/5.69 thf(fact_5954_zero__less__abs__iff,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.69 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_abs_iff
% 5.46/5.69 thf(fact_5955_zero__less__abs__iff,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.46/5.69 = ( A != zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_abs_iff
% 5.46/5.69 thf(fact_5956_zero__less__abs__iff,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.46/5.69 = ( A != zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_abs_iff
% 5.46/5.69 thf(fact_5957_zero__less__abs__iff,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.46/5.69 = ( A != zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_abs_iff
% 5.46/5.69 thf(fact_5958_abs__neg__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.69 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_neg_numeral
% 5.46/5.69 thf(fact_5959_abs__neg__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.69 = ( numeral_numeral_real @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_neg_numeral
% 5.46/5.69 thf(fact_5960_abs__neg__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.69 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_neg_numeral
% 5.46/5.69 thf(fact_5961_abs__neg__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.69 = ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_neg_numeral
% 5.46/5.69 thf(fact_5962_abs__neg__one,axiom,
% 5.46/5.69 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.69 = one_one_int ) ).
% 5.46/5.69
% 5.46/5.69 % abs_neg_one
% 5.46/5.69 thf(fact_5963_abs__neg__one,axiom,
% 5.46/5.69 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.69 = one_one_real ) ).
% 5.46/5.69
% 5.46/5.69 % abs_neg_one
% 5.46/5.69 thf(fact_5964_abs__neg__one,axiom,
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.69 = one_one_Code_integer ) ).
% 5.46/5.69
% 5.46/5.69 % abs_neg_one
% 5.46/5.69 thf(fact_5965_abs__neg__one,axiom,
% 5.46/5.69 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.69 = one_one_rat ) ).
% 5.46/5.69
% 5.46/5.69 % abs_neg_one
% 5.46/5.69 thf(fact_5966_abs__power__minus,axiom,
% 5.46/5.69 ! [A: int,N: nat] :
% 5.46/5.69 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.46/5.69 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_power_minus
% 5.46/5.69 thf(fact_5967_abs__power__minus,axiom,
% 5.46/5.69 ! [A: real,N: nat] :
% 5.46/5.69 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.46/5.69 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_power_minus
% 5.46/5.69 thf(fact_5968_abs__power__minus,axiom,
% 5.46/5.69 ! [A: code_integer,N: nat] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.46/5.69 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_power_minus
% 5.46/5.69 thf(fact_5969_abs__power__minus,axiom,
% 5.46/5.69 ! [A: rat,N: nat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.46/5.69 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_power_minus
% 5.46/5.69 thf(fact_5970_tanh__real__pos__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X2 ) )
% 5.46/5.69 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % tanh_real_pos_iff
% 5.46/5.69 thf(fact_5971_tanh__real__neg__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( tanh_real @ X2 ) @ zero_zero_real )
% 5.46/5.69 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % tanh_real_neg_iff
% 5.46/5.69 thf(fact_5972_tanh__real__nonneg__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X2 ) )
% 5.46/5.69 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % tanh_real_nonneg_iff
% 5.46/5.69 thf(fact_5973_tanh__real__nonpos__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( tanh_real @ X2 ) @ zero_zero_real )
% 5.46/5.69 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % tanh_real_nonpos_iff
% 5.46/5.69 thf(fact_5974_divide__le__0__abs__iff,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.46/5.69 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.69 | ( B = zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_le_0_abs_iff
% 5.46/5.69 thf(fact_5975_divide__le__0__abs__iff,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.46/5.69 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.69 | ( B = zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_le_0_abs_iff
% 5.46/5.69 thf(fact_5976_zero__le__divide__abs__iff,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.46/5.69 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 | ( B = zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_divide_abs_iff
% 5.46/5.69 thf(fact_5977_zero__le__divide__abs__iff,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.46/5.69 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 | ( B = zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_divide_abs_iff
% 5.46/5.69 thf(fact_5978_abs__of__nonpos,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.69 => ( ( abs_abs_real @ A )
% 5.46/5.69 = ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_nonpos
% 5.46/5.69 thf(fact_5979_abs__of__nonpos,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.46/5.69 => ( ( abs_abs_Code_integer @ A )
% 5.46/5.69 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_nonpos
% 5.46/5.69 thf(fact_5980_abs__of__nonpos,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.69 => ( ( abs_abs_rat @ A )
% 5.46/5.69 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_nonpos
% 5.46/5.69 thf(fact_5981_abs__of__nonpos,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.69 => ( ( abs_abs_int @ A )
% 5.46/5.69 = ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_nonpos
% 5.46/5.69 thf(fact_5982_artanh__minus__real,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.69 => ( ( artanh_real @ ( uminus_uminus_real @ X2 ) )
% 5.46/5.69 = ( uminus_uminus_real @ ( artanh_real @ X2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % artanh_minus_real
% 5.46/5.69 thf(fact_5983_zero__less__power__abs__iff,axiom,
% 5.46/5.69 ! [A: code_integer,N: nat] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.46/5.69 = ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.69 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_power_abs_iff
% 5.46/5.69 thf(fact_5984_zero__less__power__abs__iff,axiom,
% 5.46/5.69 ! [A: real,N: nat] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.46/5.69 = ( ( A != zero_zero_real )
% 5.46/5.69 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_power_abs_iff
% 5.46/5.69 thf(fact_5985_zero__less__power__abs__iff,axiom,
% 5.46/5.69 ! [A: rat,N: nat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.46/5.69 = ( ( A != zero_zero_rat )
% 5.46/5.69 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_power_abs_iff
% 5.46/5.69 thf(fact_5986_zero__less__power__abs__iff,axiom,
% 5.46/5.69 ! [A: int,N: nat] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.46/5.69 = ( ( A != zero_zero_int )
% 5.46/5.69 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_power_abs_iff
% 5.46/5.69 thf(fact_5987_power2__abs,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power2_abs
% 5.46/5.69 thf(fact_5988_power2__abs,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power2_abs
% 5.46/5.69 thf(fact_5989_power2__abs,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power2_abs
% 5.46/5.69 thf(fact_5990_power2__abs,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power2_abs
% 5.46/5.69 thf(fact_5991_abs__power2,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_power2
% 5.46/5.69 thf(fact_5992_abs__power2,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_power2
% 5.46/5.69 thf(fact_5993_abs__power2,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_power2
% 5.46/5.69 thf(fact_5994_abs__power2,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_power2
% 5.46/5.69 thf(fact_5995_power__even__abs__numeral,axiom,
% 5.46/5.69 ! [W: num,A: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.69 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.69 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_even_abs_numeral
% 5.46/5.69 thf(fact_5996_power__even__abs__numeral,axiom,
% 5.46/5.69 ! [W: num,A: rat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.69 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.69 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_even_abs_numeral
% 5.46/5.69 thf(fact_5997_power__even__abs__numeral,axiom,
% 5.46/5.69 ! [W: num,A: real] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.69 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.69 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_even_abs_numeral
% 5.46/5.69 thf(fact_5998_power__even__abs__numeral,axiom,
% 5.46/5.69 ! [W: num,A: int] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.69 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.69 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_even_abs_numeral
% 5.46/5.69 thf(fact_5999_abs__ge__self,axiom,
% 5.46/5.69 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_self
% 5.46/5.69 thf(fact_6000_abs__ge__self,axiom,
% 5.46/5.69 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_self
% 5.46/5.69 thf(fact_6001_abs__ge__self,axiom,
% 5.46/5.69 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_self
% 5.46/5.69 thf(fact_6002_abs__ge__self,axiom,
% 5.46/5.69 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_self
% 5.46/5.69 thf(fact_6003_abs__le__D1,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.46/5.69 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_D1
% 5.46/5.69 thf(fact_6004_abs__le__D1,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.46/5.69 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_D1
% 5.46/5.69 thf(fact_6005_abs__le__D1,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_D1
% 5.46/5.69 thf(fact_6006_abs__le__D1,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.46/5.69 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_D1
% 5.46/5.69 thf(fact_6007_abs__eq__0__iff,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( ( abs_abs_Code_integer @ A )
% 5.46/5.69 = zero_z3403309356797280102nteger )
% 5.46/5.69 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_0_iff
% 5.46/5.69 thf(fact_6008_abs__eq__0__iff,axiom,
% 5.46/5.69 ! [A: complex] :
% 5.46/5.69 ( ( ( abs_abs_complex @ A )
% 5.46/5.69 = zero_zero_complex )
% 5.46/5.69 = ( A = zero_zero_complex ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_0_iff
% 5.46/5.69 thf(fact_6009_abs__eq__0__iff,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( ( abs_abs_real @ A )
% 5.46/5.69 = zero_zero_real )
% 5.46/5.69 = ( A = zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_0_iff
% 5.46/5.69 thf(fact_6010_abs__eq__0__iff,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( ( abs_abs_rat @ A )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 = ( A = zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_0_iff
% 5.46/5.69 thf(fact_6011_abs__eq__0__iff,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( ( abs_abs_int @ A )
% 5.46/5.69 = zero_zero_int )
% 5.46/5.69 = ( A = zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_0_iff
% 5.46/5.69 thf(fact_6012_abs__mult,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.46/5.69 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult
% 5.46/5.69 thf(fact_6013_abs__mult,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.46/5.69 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult
% 5.46/5.69 thf(fact_6014_abs__mult,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.46/5.69 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult
% 5.46/5.69 thf(fact_6015_abs__mult,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.46/5.69 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult
% 5.46/5.69 thf(fact_6016_abs__one,axiom,
% 5.46/5.69 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.46/5.69 = one_one_Code_integer ) ).
% 5.46/5.69
% 5.46/5.69 % abs_one
% 5.46/5.69 thf(fact_6017_abs__one,axiom,
% 5.46/5.69 ( ( abs_abs_real @ one_one_real )
% 5.46/5.69 = one_one_real ) ).
% 5.46/5.69
% 5.46/5.69 % abs_one
% 5.46/5.69 thf(fact_6018_abs__one,axiom,
% 5.46/5.69 ( ( abs_abs_rat @ one_one_rat )
% 5.46/5.69 = one_one_rat ) ).
% 5.46/5.69
% 5.46/5.69 % abs_one
% 5.46/5.69 thf(fact_6019_abs__one,axiom,
% 5.46/5.69 ( ( abs_abs_int @ one_one_int )
% 5.46/5.69 = one_one_int ) ).
% 5.46/5.69
% 5.46/5.69 % abs_one
% 5.46/5.69 thf(fact_6020_abs__minus__commute,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.46/5.69 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_commute
% 5.46/5.69 thf(fact_6021_abs__minus__commute,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.46/5.69 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_commute
% 5.46/5.69 thf(fact_6022_abs__minus__commute,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.46/5.69 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_commute
% 5.46/5.69 thf(fact_6023_abs__minus__commute,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.46/5.69 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_commute
% 5.46/5.69 thf(fact_6024_abs__eq__iff,axiom,
% 5.46/5.69 ! [X2: int,Y2: int] :
% 5.46/5.69 ( ( ( abs_abs_int @ X2 )
% 5.46/5.69 = ( abs_abs_int @ Y2 ) )
% 5.46/5.69 = ( ( X2 = Y2 )
% 5.46/5.69 | ( X2
% 5.46/5.69 = ( uminus_uminus_int @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_iff
% 5.46/5.69 thf(fact_6025_abs__eq__iff,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ( abs_abs_real @ X2 )
% 5.46/5.69 = ( abs_abs_real @ Y2 ) )
% 5.46/5.69 = ( ( X2 = Y2 )
% 5.46/5.69 | ( X2
% 5.46/5.69 = ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_iff
% 5.46/5.69 thf(fact_6026_abs__eq__iff,axiom,
% 5.46/5.69 ! [X2: code_integer,Y2: code_integer] :
% 5.46/5.69 ( ( ( abs_abs_Code_integer @ X2 )
% 5.46/5.69 = ( abs_abs_Code_integer @ Y2 ) )
% 5.46/5.69 = ( ( X2 = Y2 )
% 5.46/5.69 | ( X2
% 5.46/5.69 = ( uminus1351360451143612070nteger @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_iff
% 5.46/5.69 thf(fact_6027_abs__eq__iff,axiom,
% 5.46/5.69 ! [X2: rat,Y2: rat] :
% 5.46/5.69 ( ( ( abs_abs_rat @ X2 )
% 5.46/5.69 = ( abs_abs_rat @ Y2 ) )
% 5.46/5.69 = ( ( X2 = Y2 )
% 5.46/5.69 | ( X2
% 5.46/5.69 = ( uminus_uminus_rat @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_iff
% 5.46/5.69 thf(fact_6028_power__abs,axiom,
% 5.46/5.69 ! [A: code_integer,N: nat] :
% 5.46/5.69 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.46/5.69 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_abs
% 5.46/5.69 thf(fact_6029_power__abs,axiom,
% 5.46/5.69 ! [A: rat,N: nat] :
% 5.46/5.69 ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 5.46/5.69 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_abs
% 5.46/5.69 thf(fact_6030_power__abs,axiom,
% 5.46/5.69 ! [A: real,N: nat] :
% 5.46/5.69 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 5.46/5.69 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_abs
% 5.46/5.69 thf(fact_6031_power__abs,axiom,
% 5.46/5.69 ! [A: int,N: nat] :
% 5.46/5.69 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 5.46/5.69 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_abs
% 5.46/5.69 thf(fact_6032_dvd__if__abs__eq,axiom,
% 5.46/5.69 ! [L2: real,K: real] :
% 5.46/5.69 ( ( ( abs_abs_real @ L2 )
% 5.46/5.69 = ( abs_abs_real @ K ) )
% 5.46/5.69 => ( dvd_dvd_real @ L2 @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % dvd_if_abs_eq
% 5.46/5.69 thf(fact_6033_dvd__if__abs__eq,axiom,
% 5.46/5.69 ! [L2: int,K: int] :
% 5.46/5.69 ( ( ( abs_abs_int @ L2 )
% 5.46/5.69 = ( abs_abs_int @ K ) )
% 5.46/5.69 => ( dvd_dvd_int @ L2 @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % dvd_if_abs_eq
% 5.46/5.69 thf(fact_6034_dvd__if__abs__eq,axiom,
% 5.46/5.69 ! [L2: code_integer,K: code_integer] :
% 5.46/5.69 ( ( ( abs_abs_Code_integer @ L2 )
% 5.46/5.69 = ( abs_abs_Code_integer @ K ) )
% 5.46/5.69 => ( dvd_dvd_Code_integer @ L2 @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % dvd_if_abs_eq
% 5.46/5.69 thf(fact_6035_dvd__if__abs__eq,axiom,
% 5.46/5.69 ! [L2: rat,K: rat] :
% 5.46/5.69 ( ( ( abs_abs_rat @ L2 )
% 5.46/5.69 = ( abs_abs_rat @ K ) )
% 5.46/5.69 => ( dvd_dvd_rat @ L2 @ K ) ) ).
% 5.46/5.69
% 5.46/5.69 % dvd_if_abs_eq
% 5.46/5.69 thf(fact_6036_abs__ge__zero,axiom,
% 5.46/5.69 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_zero
% 5.46/5.69 thf(fact_6037_abs__ge__zero,axiom,
% 5.46/5.69 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_zero
% 5.46/5.69 thf(fact_6038_abs__ge__zero,axiom,
% 5.46/5.69 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_zero
% 5.46/5.69 thf(fact_6039_abs__ge__zero,axiom,
% 5.46/5.69 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_zero
% 5.46/5.69 thf(fact_6040_abs__of__pos,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.69 => ( ( abs_abs_Code_integer @ A )
% 5.46/5.69 = A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_pos
% 5.46/5.69 thf(fact_6041_abs__of__pos,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( abs_abs_real @ A )
% 5.46/5.69 = A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_pos
% 5.46/5.69 thf(fact_6042_abs__of__pos,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( abs_abs_rat @ A )
% 5.46/5.69 = A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_pos
% 5.46/5.69 thf(fact_6043_abs__of__pos,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( abs_abs_int @ A )
% 5.46/5.69 = A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_pos
% 5.46/5.69 thf(fact_6044_abs__not__less__zero,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.46/5.69
% 5.46/5.69 % abs_not_less_zero
% 5.46/5.69 thf(fact_6045_abs__not__less__zero,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.46/5.69
% 5.46/5.69 % abs_not_less_zero
% 5.46/5.69 thf(fact_6046_abs__not__less__zero,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.46/5.69
% 5.46/5.69 % abs_not_less_zero
% 5.46/5.69 thf(fact_6047_abs__not__less__zero,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.46/5.69
% 5.46/5.69 % abs_not_less_zero
% 5.46/5.69 thf(fact_6048_abs__triangle__ineq,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq
% 5.46/5.69 thf(fact_6049_abs__triangle__ineq,axiom,
% 5.46/5.69 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq
% 5.46/5.69 thf(fact_6050_abs__triangle__ineq,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq
% 5.46/5.69 thf(fact_6051_abs__triangle__ineq,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq
% 5.46/5.69 thf(fact_6052_abs__mult__less,axiom,
% 5.46/5.69 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.46/5.69 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 5.46/5.69 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_less
% 5.46/5.69 thf(fact_6053_abs__mult__less,axiom,
% 5.46/5.69 ! [A: real,C: real,B: real,D2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.46/5.69 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D2 )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_less
% 5.46/5.69 thf(fact_6054_abs__mult__less,axiom,
% 5.46/5.69 ! [A: rat,C: rat,B: rat,D2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.46/5.69 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_less
% 5.46/5.69 thf(fact_6055_abs__mult__less,axiom,
% 5.46/5.69 ! [A: int,C: int,B: int,D2: int] :
% 5.46/5.69 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.46/5.69 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 5.46/5.69 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_less
% 5.46/5.69 thf(fact_6056_abs__triangle__ineq2,axiom,
% 5.46/5.69 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq2
% 5.46/5.69 thf(fact_6057_abs__triangle__ineq2,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq2
% 5.46/5.69 thf(fact_6058_abs__triangle__ineq2,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq2
% 5.46/5.69 thf(fact_6059_abs__triangle__ineq2,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq2
% 5.46/5.69 thf(fact_6060_abs__triangle__ineq3,axiom,
% 5.46/5.69 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq3
% 5.46/5.69 thf(fact_6061_abs__triangle__ineq3,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq3
% 5.46/5.69 thf(fact_6062_abs__triangle__ineq3,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq3
% 5.46/5.69 thf(fact_6063_abs__triangle__ineq3,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq3
% 5.46/5.69 thf(fact_6064_abs__triangle__ineq2__sym,axiom,
% 5.46/5.69 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq2_sym
% 5.46/5.69 thf(fact_6065_abs__triangle__ineq2__sym,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq2_sym
% 5.46/5.69 thf(fact_6066_abs__triangle__ineq2__sym,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq2_sym
% 5.46/5.69 thf(fact_6067_abs__triangle__ineq2__sym,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq2_sym
% 5.46/5.69 thf(fact_6068_nonzero__abs__divide,axiom,
% 5.46/5.69 ! [B: real,A: real] :
% 5.46/5.69 ( ( B != zero_zero_real )
% 5.46/5.69 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.69 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nonzero_abs_divide
% 5.46/5.69 thf(fact_6069_nonzero__abs__divide,axiom,
% 5.46/5.69 ! [B: rat,A: rat] :
% 5.46/5.69 ( ( B != zero_zero_rat )
% 5.46/5.69 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.46/5.69 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nonzero_abs_divide
% 5.46/5.69 thf(fact_6070_abs__ge__minus__self,axiom,
% 5.46/5.69 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_minus_self
% 5.46/5.69 thf(fact_6071_abs__ge__minus__self,axiom,
% 5.46/5.69 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_minus_self
% 5.46/5.69 thf(fact_6072_abs__ge__minus__self,axiom,
% 5.46/5.69 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_minus_self
% 5.46/5.69 thf(fact_6073_abs__ge__minus__self,axiom,
% 5.46/5.69 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ge_minus_self
% 5.46/5.69 thf(fact_6074_abs__le__iff,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.46/5.69 = ( ( ord_less_eq_real @ A @ B )
% 5.46/5.69 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_iff
% 5.46/5.69 thf(fact_6075_abs__le__iff,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.46/5.69 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.46/5.69 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_iff
% 5.46/5.69 thf(fact_6076_abs__le__iff,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.46/5.69 = ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.69 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_iff
% 5.46/5.69 thf(fact_6077_abs__le__iff,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.46/5.69 = ( ( ord_less_eq_int @ A @ B )
% 5.46/5.69 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_iff
% 5.46/5.69 thf(fact_6078_abs__le__D2,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.46/5.69 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_D2
% 5.46/5.69 thf(fact_6079_abs__le__D2,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.46/5.69 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_D2
% 5.46/5.69 thf(fact_6080_abs__le__D2,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.46/5.69 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_D2
% 5.46/5.69 thf(fact_6081_abs__le__D2,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.46/5.69 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_D2
% 5.46/5.69 thf(fact_6082_abs__leI,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.46/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_leI
% 5.46/5.69 thf(fact_6083_abs__leI,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.46/5.69 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.46/5.69 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_leI
% 5.46/5.69 thf(fact_6084_abs__leI,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ A @ B )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.46/5.69 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_leI
% 5.46/5.69 thf(fact_6085_abs__leI,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ A @ B )
% 5.46/5.69 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.46/5.69 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_leI
% 5.46/5.69 thf(fact_6086_abs__less__iff,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.46/5.69 = ( ( ord_less_int @ A @ B )
% 5.46/5.69 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_less_iff
% 5.46/5.69 thf(fact_6087_abs__less__iff,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.46/5.69 = ( ( ord_less_real @ A @ B )
% 5.46/5.69 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_less_iff
% 5.46/5.69 thf(fact_6088_abs__less__iff,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.46/5.69 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.46/5.69 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_less_iff
% 5.46/5.69 thf(fact_6089_abs__less__iff,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.46/5.69 = ( ( ord_less_rat @ A @ B )
% 5.46/5.69 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_less_iff
% 5.46/5.69 thf(fact_6090_tanh__real__lt__1,axiom,
% 5.46/5.69 ! [X2: real] : ( ord_less_real @ ( tanh_real @ X2 ) @ one_one_real ) ).
% 5.46/5.69
% 5.46/5.69 % tanh_real_lt_1
% 5.46/5.69 thf(fact_6091_dense__eq0__I,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ! [E2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ E2 ) )
% 5.46/5.69 => ( X2 = zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % dense_eq0_I
% 5.46/5.69 thf(fact_6092_dense__eq0__I,axiom,
% 5.46/5.69 ! [X2: rat] :
% 5.46/5.69 ( ! [E2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ E2 ) )
% 5.46/5.69 => ( X2 = zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % dense_eq0_I
% 5.46/5.69 thf(fact_6093_abs__eq__mult,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.69 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.46/5.69 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.46/5.69 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.46/5.69 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.46/5.69 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_mult
% 5.46/5.69 thf(fact_6094_abs__eq__mult,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.46/5.69 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.46/5.69 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.46/5.69 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.46/5.69 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_mult
% 5.46/5.69 thf(fact_6095_abs__eq__mult,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.46/5.69 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.46/5.69 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.46/5.69 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.46/5.69 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_mult
% 5.46/5.69 thf(fact_6096_abs__eq__mult,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.46/5.69 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.46/5.69 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.46/5.69 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.46/5.69 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_mult
% 5.46/5.69 thf(fact_6097_abs__mult__pos,axiom,
% 5.46/5.69 ! [X2: code_integer,Y2: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.46/5.69 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y2 ) @ X2 )
% 5.46/5.69 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y2 @ X2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_pos
% 5.46/5.69 thf(fact_6098_abs__mult__pos,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( times_times_real @ ( abs_abs_real @ Y2 ) @ X2 )
% 5.46/5.69 = ( abs_abs_real @ ( times_times_real @ Y2 @ X2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_pos
% 5.46/5.69 thf(fact_6099_abs__mult__pos,axiom,
% 5.46/5.69 ! [X2: rat,Y2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.46/5.69 => ( ( times_times_rat @ ( abs_abs_rat @ Y2 ) @ X2 )
% 5.46/5.69 = ( abs_abs_rat @ ( times_times_rat @ Y2 @ X2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_pos
% 5.46/5.69 thf(fact_6100_abs__mult__pos,axiom,
% 5.46/5.69 ! [X2: int,Y2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.69 => ( ( times_times_int @ ( abs_abs_int @ Y2 ) @ X2 )
% 5.46/5.69 = ( abs_abs_int @ ( times_times_int @ Y2 @ X2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mult_pos
% 5.46/5.69 thf(fact_6101_abs__eq__iff_H,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( ( abs_abs_real @ A )
% 5.46/5.69 = B )
% 5.46/5.69 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.46/5.69 & ( ( A = B )
% 5.46/5.69 | ( A
% 5.46/5.69 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_iff'
% 5.46/5.69 thf(fact_6102_abs__eq__iff_H,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( ( abs_abs_Code_integer @ A )
% 5.46/5.69 = B )
% 5.46/5.69 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.46/5.69 & ( ( A = B )
% 5.46/5.69 | ( A
% 5.46/5.69 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_iff'
% 5.46/5.69 thf(fact_6103_abs__eq__iff_H,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( ( abs_abs_rat @ A )
% 5.46/5.69 = B )
% 5.46/5.69 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.46/5.69 & ( ( A = B )
% 5.46/5.69 | ( A
% 5.46/5.69 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_iff'
% 5.46/5.69 thf(fact_6104_abs__eq__iff_H,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( ( abs_abs_int @ A )
% 5.46/5.69 = B )
% 5.46/5.69 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.46/5.69 & ( ( A = B )
% 5.46/5.69 | ( A
% 5.46/5.69 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_eq_iff'
% 5.46/5.69 thf(fact_6105_eq__abs__iff_H,axiom,
% 5.46/5.69 ! [A: real,B: real] :
% 5.46/5.69 ( ( A
% 5.46/5.69 = ( abs_abs_real @ B ) )
% 5.46/5.69 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 & ( ( B = A )
% 5.46/5.69 | ( B
% 5.46/5.69 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % eq_abs_iff'
% 5.46/5.69 thf(fact_6106_eq__abs__iff_H,axiom,
% 5.46/5.69 ! [A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( A
% 5.46/5.69 = ( abs_abs_Code_integer @ B ) )
% 5.46/5.69 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.69 & ( ( B = A )
% 5.46/5.69 | ( B
% 5.46/5.69 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % eq_abs_iff'
% 5.46/5.69 thf(fact_6107_eq__abs__iff_H,axiom,
% 5.46/5.69 ! [A: rat,B: rat] :
% 5.46/5.69 ( ( A
% 5.46/5.69 = ( abs_abs_rat @ B ) )
% 5.46/5.69 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 & ( ( B = A )
% 5.46/5.69 | ( B
% 5.46/5.69 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % eq_abs_iff'
% 5.46/5.69 thf(fact_6108_eq__abs__iff_H,axiom,
% 5.46/5.69 ! [A: int,B: int] :
% 5.46/5.69 ( ( A
% 5.46/5.69 = ( abs_abs_int @ B ) )
% 5.46/5.69 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 & ( ( B = A )
% 5.46/5.69 | ( B
% 5.46/5.69 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % eq_abs_iff'
% 5.46/5.69 thf(fact_6109_abs__minus__le__zero,axiom,
% 5.46/5.69 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_le_zero
% 5.46/5.69 thf(fact_6110_abs__minus__le__zero,axiom,
% 5.46/5.69 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_le_zero
% 5.46/5.69 thf(fact_6111_abs__minus__le__zero,axiom,
% 5.46/5.69 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_le_zero
% 5.46/5.69 thf(fact_6112_abs__minus__le__zero,axiom,
% 5.46/5.69 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.46/5.69
% 5.46/5.69 % abs_minus_le_zero
% 5.46/5.69 thf(fact_6113_abs__div__pos,axiom,
% 5.46/5.69 ! [Y2: real,X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.69 => ( ( divide_divide_real @ ( abs_abs_real @ X2 ) @ Y2 )
% 5.46/5.69 = ( abs_abs_real @ ( divide_divide_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_div_pos
% 5.46/5.69 thf(fact_6114_abs__div__pos,axiom,
% 5.46/5.69 ! [Y2: rat,X2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.46/5.69 => ( ( divide_divide_rat @ ( abs_abs_rat @ X2 ) @ Y2 )
% 5.46/5.69 = ( abs_abs_rat @ ( divide_divide_rat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_div_pos
% 5.46/5.69 thf(fact_6115_zero__le__power__abs,axiom,
% 5.46/5.69 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_power_abs
% 5.46/5.69 thf(fact_6116_zero__le__power__abs,axiom,
% 5.46/5.69 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_power_abs
% 5.46/5.69 thf(fact_6117_zero__le__power__abs,axiom,
% 5.46/5.69 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_power_abs
% 5.46/5.69 thf(fact_6118_zero__le__power__abs,axiom,
% 5.46/5.69 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_power_abs
% 5.46/5.69 thf(fact_6119_abs__if__raw,axiom,
% 5.46/5.69 ( abs_abs_int
% 5.46/5.69 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_if_raw
% 5.46/5.69 thf(fact_6120_abs__if__raw,axiom,
% 5.46/5.69 ( abs_abs_real
% 5.46/5.69 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_if_raw
% 5.46/5.69 thf(fact_6121_abs__if__raw,axiom,
% 5.46/5.69 ( abs_abs_Code_integer
% 5.46/5.69 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_if_raw
% 5.46/5.69 thf(fact_6122_abs__if__raw,axiom,
% 5.46/5.69 ( abs_abs_rat
% 5.46/5.69 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_if_raw
% 5.46/5.69 thf(fact_6123_abs__if,axiom,
% 5.46/5.69 ( abs_abs_int
% 5.46/5.69 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_if
% 5.46/5.69 thf(fact_6124_abs__if,axiom,
% 5.46/5.69 ( abs_abs_real
% 5.46/5.69 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_if
% 5.46/5.69 thf(fact_6125_abs__if,axiom,
% 5.46/5.69 ( abs_abs_Code_integer
% 5.46/5.69 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_if
% 5.46/5.69 thf(fact_6126_abs__if,axiom,
% 5.46/5.69 ( abs_abs_rat
% 5.46/5.69 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_if
% 5.46/5.69 thf(fact_6127_abs__of__neg,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.69 => ( ( abs_abs_int @ A )
% 5.46/5.69 = ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_neg
% 5.46/5.69 thf(fact_6128_abs__of__neg,axiom,
% 5.46/5.69 ! [A: real] :
% 5.46/5.69 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.69 => ( ( abs_abs_real @ A )
% 5.46/5.69 = ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_neg
% 5.46/5.69 thf(fact_6129_abs__of__neg,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.46/5.69 => ( ( abs_abs_Code_integer @ A )
% 5.46/5.69 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_neg
% 5.46/5.69 thf(fact_6130_abs__of__neg,axiom,
% 5.46/5.69 ! [A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.69 => ( ( abs_abs_rat @ A )
% 5.46/5.69 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_of_neg
% 5.46/5.69 thf(fact_6131_abs__diff__le__iff,axiom,
% 5.46/5.69 ! [X2: code_integer,A: code_integer,R: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 5.46/5.69 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 5.46/5.69 & ( ord_le3102999989581377725nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_le_iff
% 5.46/5.69 thf(fact_6132_abs__diff__le__iff,axiom,
% 5.46/5.69 ! [X2: real,A: real,R: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R )
% 5.46/5.69 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X2 )
% 5.46/5.69 & ( ord_less_eq_real @ X2 @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_le_iff
% 5.46/5.69 thf(fact_6133_abs__diff__le__iff,axiom,
% 5.46/5.69 ! [X2: rat,A: rat,R: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 5.46/5.69 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 5.46/5.69 & ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_le_iff
% 5.46/5.69 thf(fact_6134_abs__diff__le__iff,axiom,
% 5.46/5.69 ! [X2: int,A: int,R: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 5.46/5.69 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 5.46/5.69 & ( ord_less_eq_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_le_iff
% 5.46/5.69 thf(fact_6135_abs__diff__triangle__ineq,axiom,
% 5.46/5.69 ! [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 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_triangle_ineq
% 5.46/5.69 thf(fact_6136_abs__diff__triangle__ineq,axiom,
% 5.46/5.69 ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_triangle_ineq
% 5.46/5.69 thf(fact_6137_abs__diff__triangle__ineq,axiom,
% 5.46/5.69 ! [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 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_triangle_ineq
% 5.46/5.69 thf(fact_6138_abs__diff__triangle__ineq,axiom,
% 5.46/5.69 ! [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 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_triangle_ineq
% 5.46/5.69 thf(fact_6139_abs__triangle__ineq4,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq4
% 5.46/5.69 thf(fact_6140_abs__triangle__ineq4,axiom,
% 5.46/5.69 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq4
% 5.46/5.69 thf(fact_6141_abs__triangle__ineq4,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq4
% 5.46/5.69 thf(fact_6142_abs__triangle__ineq4,axiom,
% 5.46/5.69 ! [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 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_triangle_ineq4
% 5.46/5.69 thf(fact_6143_abs__diff__less__iff,axiom,
% 5.46/5.69 ! [X2: code_integer,A: code_integer,R: code_integer] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 5.46/5.69 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 5.46/5.69 & ( ord_le6747313008572928689nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_less_iff
% 5.46/5.69 thf(fact_6144_abs__diff__less__iff,axiom,
% 5.46/5.69 ! [X2: real,A: real,R: real] :
% 5.46/5.69 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R )
% 5.46/5.69 = ( ( ord_less_real @ ( minus_minus_real @ A @ R ) @ X2 )
% 5.46/5.69 & ( ord_less_real @ X2 @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_less_iff
% 5.46/5.69 thf(fact_6145_abs__diff__less__iff,axiom,
% 5.46/5.69 ! [X2: rat,A: rat,R: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 5.46/5.69 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 5.46/5.69 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_less_iff
% 5.46/5.69 thf(fact_6146_abs__diff__less__iff,axiom,
% 5.46/5.69 ! [X2: int,A: int,R: int] :
% 5.46/5.69 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 5.46/5.69 = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 5.46/5.69 & ( ord_less_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_diff_less_iff
% 5.46/5.69 thf(fact_6147_abs__real__def,axiom,
% 5.46/5.69 ( abs_abs_real
% 5.46/5.69 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_real_def
% 5.46/5.69 thf(fact_6148_lemma__interval__lt,axiom,
% 5.46/5.69 ! [A: real,X2: real,B: real] :
% 5.46/5.69 ( ( ord_less_real @ A @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ X2 @ B )
% 5.46/5.69 => ? [D3: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.69 & ! [Y4: real] :
% 5.46/5.69 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D3 )
% 5.46/5.69 => ( ( ord_less_real @ A @ Y4 )
% 5.46/5.69 & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % lemma_interval_lt
% 5.46/5.69 thf(fact_6149_sin__bound__lemma,axiom,
% 5.46/5.69 ! [X2: real,Y2: real,U: real,V: real] :
% 5.46/5.69 ( ( X2 = Y2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.46/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X2 @ U ) @ Y2 ) ) @ V ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sin_bound_lemma
% 5.46/5.69 thf(fact_6150_tanh__real__gt__neg1,axiom,
% 5.46/5.69 ! [X2: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % tanh_real_gt_neg1
% 5.46/5.69 thf(fact_6151_abs__add__one__gt__zero,axiom,
% 5.46/5.69 ! [X2: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_add_one_gt_zero
% 5.46/5.69 thf(fact_6152_abs__add__one__gt__zero,axiom,
% 5.46/5.69 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_add_one_gt_zero
% 5.46/5.69 thf(fact_6153_abs__add__one__gt__zero,axiom,
% 5.46/5.69 ! [X2: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_add_one_gt_zero
% 5.46/5.69 thf(fact_6154_abs__add__one__gt__zero,axiom,
% 5.46/5.69 ! [X2: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_add_one_gt_zero
% 5.46/5.69 thf(fact_6155_of__int__leD,axiom,
% 5.46/5.69 ! [N: int,X2: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.46/5.69 => ( ( N = zero_zero_int )
% 5.46/5.69 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_leD
% 5.46/5.69 thf(fact_6156_of__int__leD,axiom,
% 5.46/5.69 ! [N: int,X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.46/5.69 => ( ( N = zero_zero_int )
% 5.46/5.69 | ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_leD
% 5.46/5.69 thf(fact_6157_of__int__leD,axiom,
% 5.46/5.69 ! [N: int,X2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.46/5.69 => ( ( N = zero_zero_int )
% 5.46/5.69 | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_leD
% 5.46/5.69 thf(fact_6158_of__int__leD,axiom,
% 5.46/5.69 ! [N: int,X2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.46/5.69 => ( ( N = zero_zero_int )
% 5.46/5.69 | ( ord_less_eq_int @ one_one_int @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_leD
% 5.46/5.69 thf(fact_6159_of__int__lessD,axiom,
% 5.46/5.69 ! [N: int,X2: code_integer] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.46/5.69 => ( ( N = zero_zero_int )
% 5.46/5.69 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_lessD
% 5.46/5.69 thf(fact_6160_of__int__lessD,axiom,
% 5.46/5.69 ! [N: int,X2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.46/5.69 => ( ( N = zero_zero_int )
% 5.46/5.69 | ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_lessD
% 5.46/5.69 thf(fact_6161_of__int__lessD,axiom,
% 5.46/5.69 ! [N: int,X2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.46/5.69 => ( ( N = zero_zero_int )
% 5.46/5.69 | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_lessD
% 5.46/5.69 thf(fact_6162_of__int__lessD,axiom,
% 5.46/5.69 ! [N: int,X2: int] :
% 5.46/5.69 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.46/5.69 => ( ( N = zero_zero_int )
% 5.46/5.69 | ( ord_less_int @ one_one_int @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_lessD
% 5.46/5.69 thf(fact_6163_lemma__interval,axiom,
% 5.46/5.69 ! [A: real,X2: real,B: real] :
% 5.46/5.69 ( ( ord_less_real @ A @ X2 )
% 5.46/5.69 => ( ( ord_less_real @ X2 @ B )
% 5.46/5.69 => ? [D3: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.69 & ! [Y4: real] :
% 5.46/5.69 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D3 )
% 5.46/5.69 => ( ( ord_less_eq_real @ A @ Y4 )
% 5.46/5.69 & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % lemma_interval
% 5.46/5.69 thf(fact_6164_abs__le__square__iff,axiom,
% 5.46/5.69 ! [X2: code_integer,Y2: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ ( abs_abs_Code_integer @ Y2 ) )
% 5.46/5.69 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_square_iff
% 5.46/5.69 thf(fact_6165_abs__le__square__iff,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y2 ) )
% 5.46/5.69 = ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_square_iff
% 5.46/5.69 thf(fact_6166_abs__le__square__iff,axiom,
% 5.46/5.69 ! [X2: rat,Y2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ ( abs_abs_rat @ Y2 ) )
% 5.46/5.69 = ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_square_iff
% 5.46/5.69 thf(fact_6167_abs__le__square__iff,axiom,
% 5.46/5.69 ! [X2: int,Y2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y2 ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_le_square_iff
% 5.46/5.69 thf(fact_6168_abs__square__eq__1,axiom,
% 5.46/5.69 ! [X2: code_integer] :
% 5.46/5.69 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = one_one_Code_integer )
% 5.46/5.69 = ( ( abs_abs_Code_integer @ X2 )
% 5.46/5.69 = one_one_Code_integer ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_eq_1
% 5.46/5.69 thf(fact_6169_abs__square__eq__1,axiom,
% 5.46/5.69 ! [X2: rat] :
% 5.46/5.69 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = one_one_rat )
% 5.46/5.69 = ( ( abs_abs_rat @ X2 )
% 5.46/5.69 = one_one_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_eq_1
% 5.46/5.69 thf(fact_6170_abs__square__eq__1,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = one_one_real )
% 5.46/5.69 = ( ( abs_abs_real @ X2 )
% 5.46/5.69 = one_one_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_eq_1
% 5.46/5.69 thf(fact_6171_abs__square__eq__1,axiom,
% 5.46/5.69 ! [X2: int] :
% 5.46/5.69 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = one_one_int )
% 5.46/5.69 = ( ( abs_abs_int @ X2 )
% 5.46/5.69 = one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_eq_1
% 5.46/5.69 thf(fact_6172_power__even__abs,axiom,
% 5.46/5.69 ! [N: nat,A: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.46/5.69 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_even_abs
% 5.46/5.69 thf(fact_6173_power__even__abs,axiom,
% 5.46/5.69 ! [N: nat,A: rat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 5.46/5.69 = ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_even_abs
% 5.46/5.69 thf(fact_6174_power__even__abs,axiom,
% 5.46/5.69 ! [N: nat,A: real] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.46/5.69 = ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_even_abs
% 5.46/5.69 thf(fact_6175_power__even__abs,axiom,
% 5.46/5.69 ! [N: nat,A: int] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.46/5.69 = ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_even_abs
% 5.46/5.69 thf(fact_6176_power2__le__iff__abs__le,axiom,
% 5.46/5.69 ! [Y2: code_integer,X2: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y2 )
% 5.46/5.69 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power2_le_iff_abs_le
% 5.46/5.69 thf(fact_6177_power2__le__iff__abs__le,axiom,
% 5.46/5.69 ! [Y2: real,X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power2_le_iff_abs_le
% 5.46/5.69 thf(fact_6178_power2__le__iff__abs__le,axiom,
% 5.46/5.69 ! [Y2: rat,X2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power2_le_iff_abs_le
% 5.46/5.69 thf(fact_6179_power2__le__iff__abs__le,axiom,
% 5.46/5.69 ! [Y2: int,X2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.69 => ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power2_le_iff_abs_le
% 5.46/5.69 thf(fact_6180_abs__sqrt__wlog,axiom,
% 5.46/5.69 ! [P: code_integer > code_integer > $o,X2: code_integer] :
% 5.46/5.69 ( ! [X3: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.46/5.69 => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 => ( P @ ( abs_abs_Code_integer @ X2 ) @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_sqrt_wlog
% 5.46/5.69 thf(fact_6181_abs__sqrt__wlog,axiom,
% 5.46/5.69 ! [P: real > real > $o,X2: real] :
% 5.46/5.69 ( ! [X3: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.69 => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 => ( P @ ( abs_abs_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_sqrt_wlog
% 5.46/5.69 thf(fact_6182_abs__sqrt__wlog,axiom,
% 5.46/5.69 ! [P: rat > rat > $o,X2: rat] :
% 5.46/5.69 ( ! [X3: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.46/5.69 => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 => ( P @ ( abs_abs_rat @ X2 ) @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_sqrt_wlog
% 5.46/5.69 thf(fact_6183_abs__sqrt__wlog,axiom,
% 5.46/5.69 ! [P: int > int > $o,X2: int] :
% 5.46/5.69 ( ! [X3: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.46/5.69 => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 => ( P @ ( abs_abs_int @ X2 ) @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_sqrt_wlog
% 5.46/5.69 thf(fact_6184_abs__square__le__1,axiom,
% 5.46/5.69 ! [X2: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.46/5.69 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_le_1
% 5.46/5.69 thf(fact_6185_abs__square__le__1,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.46/5.69 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_le_1
% 5.46/5.69 thf(fact_6186_abs__square__le__1,axiom,
% 5.46/5.69 ! [X2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.46/5.69 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_le_1
% 5.46/5.69 thf(fact_6187_abs__square__le__1,axiom,
% 5.46/5.69 ! [X2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.46/5.69 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_le_1
% 5.46/5.69 thf(fact_6188_abs__square__less__1,axiom,
% 5.46/5.69 ! [X2: code_integer] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.46/5.69 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_less_1
% 5.46/5.69 thf(fact_6189_abs__square__less__1,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.46/5.69 = ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_less_1
% 5.46/5.69 thf(fact_6190_abs__square__less__1,axiom,
% 5.46/5.69 ! [X2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.46/5.69 = ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_less_1
% 5.46/5.69 thf(fact_6191_abs__square__less__1,axiom,
% 5.46/5.69 ! [X2: int] :
% 5.46/5.69 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.46/5.69 = ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_square_less_1
% 5.46/5.69 thf(fact_6192_power__mono__even,axiom,
% 5.46/5.69 ! [N: nat,A: code_integer,B: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.46/5.69 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_mono_even
% 5.46/5.69 thf(fact_6193_power__mono__even,axiom,
% 5.46/5.69 ! [N: nat,A: real,B: real] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_mono_even
% 5.46/5.69 thf(fact_6194_power__mono__even,axiom,
% 5.46/5.69 ! [N: nat,A: rat,B: rat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_mono_even
% 5.46/5.69 thf(fact_6195_power__mono__even,axiom,
% 5.46/5.69 ! [N: nat,A: int,B: int] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.46/5.69 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_mono_even
% 5.46/5.69 thf(fact_6196_exists__least__lemma,axiom,
% 5.46/5.69 ! [P: nat > $o] :
% 5.46/5.69 ( ~ ( P @ zero_zero_nat )
% 5.46/5.69 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.46/5.69 => ? [N3: nat] :
% 5.46/5.69 ( ~ ( P @ N3 )
% 5.46/5.69 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % exists_least_lemma
% 5.46/5.69 thf(fact_6197_ex__le__of__int,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ? [Z3: int] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.46/5.69
% 5.46/5.69 % ex_le_of_int
% 5.46/5.69 thf(fact_6198_ex__le__of__int,axiom,
% 5.46/5.69 ! [X2: rat] :
% 5.46/5.69 ? [Z3: int] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.46/5.69
% 5.46/5.69 % ex_le_of_int
% 5.46/5.69 thf(fact_6199_ex__of__int__less,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X2 ) ).
% 5.46/5.69
% 5.46/5.69 % ex_of_int_less
% 5.46/5.69 thf(fact_6200_ex__of__int__less,axiom,
% 5.46/5.69 ! [X2: rat] :
% 5.46/5.69 ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 ) ).
% 5.46/5.69
% 5.46/5.69 % ex_of_int_less
% 5.46/5.69 thf(fact_6201_ex__less__of__int,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ? [Z3: int] : ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.46/5.69
% 5.46/5.69 % ex_less_of_int
% 5.46/5.69 thf(fact_6202_ex__less__of__int,axiom,
% 5.46/5.69 ! [X2: rat] :
% 5.46/5.69 ? [Z3: int] : ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.46/5.69
% 5.46/5.69 % ex_less_of_int
% 5.46/5.69 thf(fact_6203_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.46/5.69 thf(fact_6204_round__unique,axiom,
% 5.46/5.69 ! [X2: real,Y2: int] :
% 5.46/5.69 ( ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y2 ) )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y2 ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 => ( ( archim8280529875227126926d_real @ X2 )
% 5.46/5.69 = Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_unique
% 5.46/5.69 thf(fact_6205_round__unique,axiom,
% 5.46/5.69 ! [X2: rat,Y2: int] :
% 5.46/5.69 ( ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y2 ) )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y2 ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.69 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.46/5.69 = Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_unique
% 5.46/5.69 thf(fact_6206_round__unique_H,axiom,
% 5.46/5.69 ! [X2: real,N: int] :
% 5.46/5.69 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.69 => ( ( archim8280529875227126926d_real @ X2 )
% 5.46/5.69 = N ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_unique'
% 5.46/5.69 thf(fact_6207_round__unique_H,axiom,
% 5.46/5.69 ! [X2: rat,N: int] :
% 5.46/5.69 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.46/5.69 = N ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_unique'
% 5.46/5.69 thf(fact_6208_of__int__round__abs__le,axiom,
% 5.46/5.69 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ X2 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_round_abs_le
% 5.46/5.69 thf(fact_6209_of__int__round__abs__le,axiom,
% 5.46/5.69 ! [X2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ X2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_round_abs_le
% 5.46/5.69 thf(fact_6210_arctan__double,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.69 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X2 ) )
% 5.46/5.69 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % arctan_double
% 5.46/5.69 thf(fact_6211_of__int__round__gt,axiom,
% 5.46/5.69 ! [X2: real] : ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_round_gt
% 5.46/5.69 thf(fact_6212_of__int__round__gt,axiom,
% 5.46/5.69 ! [X2: rat] : ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_round_gt
% 5.46/5.69 thf(fact_6213_of__int__round__ge,axiom,
% 5.46/5.69 ! [X2: real] : ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_round_ge
% 5.46/5.69 thf(fact_6214_of__int__round__ge,axiom,
% 5.46/5.69 ! [X2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_round_ge
% 5.46/5.69 thf(fact_6215_zabs__less__one__iff,axiom,
% 5.46/5.69 ! [Z: int] :
% 5.46/5.69 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.46/5.69 = ( Z = zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % zabs_less_one_iff
% 5.46/5.69 thf(fact_6216_arctan__less__zero__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( arctan @ X2 ) @ zero_zero_real )
% 5.46/5.69 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % arctan_less_zero_iff
% 5.46/5.69 thf(fact_6217_zero__less__arctan__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X2 ) )
% 5.46/5.69 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_arctan_iff
% 5.46/5.69 thf(fact_6218_zero__le__arctan__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X2 ) )
% 5.46/5.69 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_arctan_iff
% 5.46/5.69 thf(fact_6219_arctan__le__zero__iff,axiom,
% 5.46/5.69 ! [X2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( arctan @ X2 ) @ zero_zero_real )
% 5.46/5.69 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % arctan_le_zero_iff
% 5.46/5.69 thf(fact_6220_round__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.46/5.69 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_numeral
% 5.46/5.69 thf(fact_6221_round__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.46/5.69 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_numeral
% 5.46/5.69 thf(fact_6222_round__1,axiom,
% 5.46/5.69 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.46/5.69 = one_one_int ) ).
% 5.46/5.69
% 5.46/5.69 % round_1
% 5.46/5.69 thf(fact_6223_round__1,axiom,
% 5.46/5.69 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.46/5.69 = one_one_int ) ).
% 5.46/5.69
% 5.46/5.69 % round_1
% 5.46/5.69 thf(fact_6224_round__neg__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_neg_numeral
% 5.46/5.69 thf(fact_6225_round__neg__numeral,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_neg_numeral
% 5.46/5.69 thf(fact_6226_arctan__less__iff,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y2 ) )
% 5.46/5.69 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % arctan_less_iff
% 5.46/5.69 thf(fact_6227_arctan__monotone,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.69 => ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % arctan_monotone
% 5.46/5.69 thf(fact_6228_arctan__monotone_H,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( arctan @ X2 ) @ ( arctan @ Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % arctan_monotone'
% 5.46/5.69 thf(fact_6229_arctan__le__iff,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( arctan @ X2 ) @ ( arctan @ Y2 ) )
% 5.46/5.69 = ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % arctan_le_iff
% 5.46/5.69 thf(fact_6230_abs__div,axiom,
% 5.46/5.69 ! [Y2: int,X2: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ Y2 @ X2 )
% 5.46/5.69 => ( ( abs_abs_int @ ( divide_divide_int @ X2 @ Y2 ) )
% 5.46/5.69 = ( divide_divide_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_div
% 5.46/5.69 thf(fact_6231_round__mono,axiom,
% 5.46/5.69 ! [X2: rat,Y2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.46/5.69 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X2 ) @ ( archim7778729529865785530nd_rat @ Y2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_mono
% 5.46/5.69 thf(fact_6232_zabs__def,axiom,
% 5.46/5.69 ( abs_abs_int
% 5.46/5.69 = ( ^ [I4: int] : ( if_int @ ( ord_less_int @ I4 @ zero_zero_int ) @ ( uminus_uminus_int @ I4 ) @ I4 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zabs_def
% 5.46/5.69 thf(fact_6233_abs__mod__less,axiom,
% 5.46/5.69 ! [L2: int,K: int] :
% 5.46/5.69 ( ( L2 != zero_zero_int )
% 5.46/5.69 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % abs_mod_less
% 5.46/5.69 thf(fact_6234_even__add__abs__iff,axiom,
% 5.46/5.69 ! [K: int,L2: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 5.46/5.69 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_add_abs_iff
% 5.46/5.69 thf(fact_6235_even__abs__add__iff,axiom,
% 5.46/5.69 ! [K: int,L2: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 5.46/5.69 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_abs_add_iff
% 5.46/5.69 thf(fact_6236_round__diff__minimal,axiom,
% 5.46/5.69 ! [Z: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_diff_minimal
% 5.46/5.69 thf(fact_6237_round__diff__minimal,axiom,
% 5.46/5.69 ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % round_diff_minimal
% 5.46/5.69 thf(fact_6238_nat__intermed__int__val,axiom,
% 5.46/5.69 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.46/5.69 ( ! [I2: nat] :
% 5.46/5.69 ( ( ( ord_less_eq_nat @ M @ I2 )
% 5.46/5.69 & ( ord_less_nat @ I2 @ N ) )
% 5.46/5.69 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.46/5.69 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.69 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.46/5.69 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.46/5.69 => ? [I2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ M @ I2 )
% 5.46/5.69 & ( ord_less_eq_nat @ I2 @ N )
% 5.46/5.69 & ( ( F @ I2 )
% 5.46/5.69 = K ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nat_intermed_int_val
% 5.46/5.69 thf(fact_6239_incr__lemma,axiom,
% 5.46/5.69 ! [D2: int,Z: int,X2: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.46/5.69 => ( ord_less_int @ Z @ ( plus_plus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % incr_lemma
% 5.46/5.69 thf(fact_6240_decr__lemma,axiom,
% 5.46/5.69 ! [D2: int,X2: int,Z: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.46/5.69 => ( ord_less_int @ ( minus_minus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 5.46/5.69
% 5.46/5.69 % decr_lemma
% 5.46/5.69 thf(fact_6241_nat__ivt__aux,axiom,
% 5.46/5.69 ! [N: nat,F: nat > int,K: int] :
% 5.46/5.69 ( ! [I2: nat] :
% 5.46/5.69 ( ( ord_less_nat @ I2 @ N )
% 5.46/5.69 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.46/5.69 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.46/5.69 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.46/5.69 => ? [I2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ I2 @ N )
% 5.46/5.69 & ( ( F @ I2 )
% 5.46/5.69 = K ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nat_ivt_aux
% 5.46/5.69 thf(fact_6242_nat0__intermed__int__val,axiom,
% 5.46/5.69 ! [N: nat,F: nat > int,K: int] :
% 5.46/5.69 ( ! [I2: nat] :
% 5.46/5.69 ( ( ord_less_nat @ I2 @ N )
% 5.46/5.69 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.46/5.69 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.46/5.69 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.46/5.69 => ? [I2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ I2 @ N )
% 5.46/5.69 & ( ( F @ I2 )
% 5.46/5.69 = K ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nat0_intermed_int_val
% 5.46/5.69 thf(fact_6243_arctan__add,axiom,
% 5.46/5.69 ! [X2: real,Y2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.69 => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.46/5.69 => ( ( plus_plus_real @ ( arctan @ X2 ) @ ( arctan @ Y2 ) )
% 5.46/5.69 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % arctan_add
% 5.46/5.69 thf(fact_6244_of__int__round__le,axiom,
% 5.46/5.69 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_round_le
% 5.46/5.69 thf(fact_6245_of__int__round__le,axiom,
% 5.46/5.69 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % of_int_round_le
% 5.46/5.69 thf(fact_6246_set__decode__0,axiom,
% 5.46/5.69 ! [X2: nat] :
% 5.46/5.69 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X2 ) )
% 5.46/5.69 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % set_decode_0
% 5.46/5.69 thf(fact_6247_set__decode__Suc,axiom,
% 5.46/5.69 ! [N: nat,X2: nat] :
% 5.46/5.69 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X2 ) )
% 5.46/5.69 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % set_decode_Suc
% 5.46/5.69 thf(fact_6248_add__scale__eq__noteq,axiom,
% 5.46/5.69 ! [R: complex,A: complex,B: complex,C: complex,D2: complex] :
% 5.46/5.69 ( ( R != zero_zero_complex )
% 5.46/5.69 => ( ( ( A = B )
% 5.46/5.69 & ( C != D2 ) )
% 5.46/5.69 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
% 5.46/5.69 != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_scale_eq_noteq
% 5.46/5.69 thf(fact_6249_add__scale__eq__noteq,axiom,
% 5.46/5.69 ! [R: real,A: real,B: real,C: real,D2: real] :
% 5.46/5.69 ( ( R != zero_zero_real )
% 5.46/5.69 => ( ( ( A = B )
% 5.46/5.69 & ( C != D2 ) )
% 5.46/5.69 => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
% 5.46/5.69 != ( plus_plus_real @ B @ ( times_times_real @ R @ D2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_scale_eq_noteq
% 5.46/5.69 thf(fact_6250_add__scale__eq__noteq,axiom,
% 5.46/5.69 ! [R: rat,A: rat,B: rat,C: rat,D2: rat] :
% 5.46/5.69 ( ( R != zero_zero_rat )
% 5.46/5.69 => ( ( ( A = B )
% 5.46/5.69 & ( C != D2 ) )
% 5.46/5.69 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 5.46/5.69 != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_scale_eq_noteq
% 5.46/5.69 thf(fact_6251_add__scale__eq__noteq,axiom,
% 5.46/5.69 ! [R: nat,A: nat,B: nat,C: nat,D2: nat] :
% 5.46/5.69 ( ( R != zero_zero_nat )
% 5.46/5.69 => ( ( ( A = B )
% 5.46/5.69 & ( C != D2 ) )
% 5.46/5.69 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 5.46/5.69 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_scale_eq_noteq
% 5.46/5.69 thf(fact_6252_add__scale__eq__noteq,axiom,
% 5.46/5.69 ! [R: int,A: int,B: int,C: int,D2: int] :
% 5.46/5.69 ( ( R != zero_zero_int )
% 5.46/5.69 => ( ( ( A = B )
% 5.46/5.69 & ( C != D2 ) )
% 5.46/5.69 => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 5.46/5.69 != ( plus_plus_int @ B @ ( times_times_int @ R @ D2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_scale_eq_noteq
% 5.46/5.69 thf(fact_6253_Sum__Icc__int,axiom,
% 5.46/5.69 ! [M: int,N: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ M @ N )
% 5.46/5.69 => ( ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [X: int] : X
% 5.46/5.69 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.46/5.69 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % Sum_Icc_int
% 5.46/5.69 thf(fact_6254_set__decode__def,axiom,
% 5.46/5.69 ( nat_set_decode
% 5.46/5.69 = ( ^ [X: nat] :
% 5.46/5.69 ( collect_nat
% 5.46/5.69 @ ^ [N2: nat] :
% 5.46/5.69 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % set_decode_def
% 5.46/5.69 thf(fact_6255_even__set__encode__iff,axiom,
% 5.46/5.69 ! [A2: set_nat] :
% 5.46/5.69 ( ( finite_finite_nat @ A2 )
% 5.46/5.69 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.46/5.69 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_set_encode_iff
% 5.46/5.69 thf(fact_6256_sum__abs,axiom,
% 5.46/5.69 ! [F: int > int,A2: set_int] :
% 5.46/5.69 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.46/5.69 @ ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_abs
% 5.46/5.69 thf(fact_6257_sum__abs,axiom,
% 5.46/5.69 ! [F: nat > real,A2: set_nat] :
% 5.46/5.69 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.46/5.69 @ ( groups6591440286371151544t_real
% 5.46/5.69 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_abs
% 5.46/5.69 thf(fact_6258_sum__abs__ge__zero,axiom,
% 5.46/5.69 ! [F: int > int,A2: set_int] :
% 5.46/5.69 ( ord_less_eq_int @ zero_zero_int
% 5.46/5.69 @ ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_abs_ge_zero
% 5.46/5.69 thf(fact_6259_sum__abs__ge__zero,axiom,
% 5.46/5.69 ! [F: nat > real,A2: set_nat] :
% 5.46/5.69 ( ord_less_eq_real @ zero_zero_real
% 5.46/5.69 @ ( groups6591440286371151544t_real
% 5.46/5.69 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_abs_ge_zero
% 5.46/5.69 thf(fact_6260_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.46/5.69 ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6261_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.46/5.69 ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6262_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.46/5.69 ( ! [I2: nat] :
% 5.46/5.69 ( ( member_nat @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6263_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.46/5.69 ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6264_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.46/5.69 ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6265_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.46/5.69 ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6266_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.46/5.69 ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6267_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.46/5.69 ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6268_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_real,F: real > int,G: real > int] :
% 5.46/5.69 ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6269_sum__mono,axiom,
% 5.46/5.69 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.46/5.69 ( ! [I2: nat] :
% 5.46/5.69 ( ( member_nat @ I2 @ K5 )
% 5.46/5.69 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono
% 5.46/5.69 thf(fact_6270_sum__distrib__left,axiom,
% 5.46/5.69 ! [R: int,F: int > int,A2: set_int] :
% 5.46/5.69 ( ( times_times_int @ R @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.46/5.69 = ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [N2: int] : ( times_times_int @ R @ ( F @ N2 ) )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_distrib_left
% 5.46/5.69 thf(fact_6271_sum__distrib__left,axiom,
% 5.46/5.69 ! [R: complex,F: complex > complex,A2: set_complex] :
% 5.46/5.69 ( ( times_times_complex @ R @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.46/5.69 = ( groups7754918857620584856omplex
% 5.46/5.69 @ ^ [N2: complex] : ( times_times_complex @ R @ ( F @ N2 ) )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_distrib_left
% 5.46/5.69 thf(fact_6272_sum__distrib__left,axiom,
% 5.46/5.69 ! [R: nat,F: nat > nat,A2: set_nat] :
% 5.46/5.69 ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.46/5.69 = ( groups3542108847815614940at_nat
% 5.46/5.69 @ ^ [N2: nat] : ( times_times_nat @ R @ ( F @ N2 ) )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_distrib_left
% 5.46/5.69 thf(fact_6273_sum__distrib__left,axiom,
% 5.46/5.69 ! [R: real,F: nat > real,A2: set_nat] :
% 5.46/5.69 ( ( times_times_real @ R @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.46/5.69 = ( groups6591440286371151544t_real
% 5.46/5.69 @ ^ [N2: nat] : ( times_times_real @ R @ ( F @ N2 ) )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_distrib_left
% 5.46/5.69 thf(fact_6274_sum__distrib__right,axiom,
% 5.46/5.69 ! [F: int > int,A2: set_int,R: int] :
% 5.46/5.69 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R )
% 5.46/5.69 = ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_distrib_right
% 5.46/5.69 thf(fact_6275_sum__distrib__right,axiom,
% 5.46/5.69 ! [F: complex > complex,A2: set_complex,R: complex] :
% 5.46/5.69 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 5.46/5.69 = ( groups7754918857620584856omplex
% 5.46/5.69 @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_distrib_right
% 5.46/5.69 thf(fact_6276_sum__distrib__right,axiom,
% 5.46/5.69 ! [F: nat > nat,A2: set_nat,R: nat] :
% 5.46/5.69 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
% 5.46/5.69 = ( groups3542108847815614940at_nat
% 5.46/5.69 @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_distrib_right
% 5.46/5.69 thf(fact_6277_sum__distrib__right,axiom,
% 5.46/5.69 ! [F: nat > real,A2: set_nat,R: real] :
% 5.46/5.69 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 5.46/5.69 = ( groups6591440286371151544t_real
% 5.46/5.69 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_distrib_right
% 5.46/5.69 thf(fact_6278_sum__product,axiom,
% 5.46/5.69 ! [F: int > int,A2: set_int,G: int > int,B3: set_int] :
% 5.46/5.69 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B3 ) )
% 5.46/5.69 = ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [I4: int] :
% 5.46/5.69 ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [J3: int] : ( times_times_int @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.46/5.69 @ B3 )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_product
% 5.46/5.69 thf(fact_6279_sum__product,axiom,
% 5.46/5.69 ! [F: complex > complex,A2: set_complex,G: complex > complex,B3: set_complex] :
% 5.46/5.69 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B3 ) )
% 5.46/5.69 = ( groups7754918857620584856omplex
% 5.46/5.69 @ ^ [I4: complex] :
% 5.46/5.69 ( groups7754918857620584856omplex
% 5.46/5.69 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.46/5.69 @ B3 )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_product
% 5.46/5.69 thf(fact_6280_sum__product,axiom,
% 5.46/5.69 ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
% 5.46/5.69 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
% 5.46/5.69 = ( groups3542108847815614940at_nat
% 5.46/5.69 @ ^ [I4: nat] :
% 5.46/5.69 ( groups3542108847815614940at_nat
% 5.46/5.69 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.46/5.69 @ B3 )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_product
% 5.46/5.69 thf(fact_6281_sum__product,axiom,
% 5.46/5.69 ! [F: nat > real,A2: set_nat,G: nat > real,B3: set_nat] :
% 5.46/5.69 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B3 ) )
% 5.46/5.69 = ( groups6591440286371151544t_real
% 5.46/5.69 @ ^ [I4: nat] :
% 5.46/5.69 ( groups6591440286371151544t_real
% 5.46/5.69 @ ^ [J3: nat] : ( times_times_real @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.46/5.69 @ B3 )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_product
% 5.46/5.69 thf(fact_6282_sum_Odistrib,axiom,
% 5.46/5.69 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.46/5.69 ( ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [X: int] : ( plus_plus_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.69 @ A2 )
% 5.46/5.69 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.distrib
% 5.46/5.69 thf(fact_6283_sum_Odistrib,axiom,
% 5.46/5.69 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 5.46/5.69 ( ( groups7754918857620584856omplex
% 5.46/5.69 @ ^ [X: complex] : ( plus_plus_complex @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.69 @ A2 )
% 5.46/5.69 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.distrib
% 5.46/5.69 thf(fact_6284_sum_Odistrib,axiom,
% 5.46/5.69 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.46/5.69 ( ( groups3542108847815614940at_nat
% 5.46/5.69 @ ^ [X: nat] : ( plus_plus_nat @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.69 @ A2 )
% 5.46/5.69 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.distrib
% 5.46/5.69 thf(fact_6285_sum_Odistrib,axiom,
% 5.46/5.69 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 5.46/5.69 ( ( groups6591440286371151544t_real
% 5.46/5.69 @ ^ [X: nat] : ( plus_plus_real @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.69 @ A2 )
% 5.46/5.69 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.distrib
% 5.46/5.69 thf(fact_6286_sum__subtractf,axiom,
% 5.46/5.69 ! [F: int > int,G: int > int,A2: set_int] :
% 5.46/5.69 ( ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [X: int] : ( minus_minus_int @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.69 @ A2 )
% 5.46/5.69 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_subtractf
% 5.46/5.69 thf(fact_6287_sum__subtractf,axiom,
% 5.46/5.69 ! [F: complex > complex,G: complex > complex,A2: set_complex] :
% 5.46/5.69 ( ( groups7754918857620584856omplex
% 5.46/5.69 @ ^ [X: complex] : ( minus_minus_complex @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.69 @ A2 )
% 5.46/5.69 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_subtractf
% 5.46/5.69 thf(fact_6288_sum__subtractf,axiom,
% 5.46/5.69 ! [F: nat > real,G: nat > real,A2: set_nat] :
% 5.46/5.69 ( ( groups6591440286371151544t_real
% 5.46/5.69 @ ^ [X: nat] : ( minus_minus_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.69 @ A2 )
% 5.46/5.69 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_subtractf
% 5.46/5.69 thf(fact_6289_sum__divide__distrib,axiom,
% 5.46/5.69 ! [F: complex > complex,A2: set_complex,R: complex] :
% 5.46/5.69 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 5.46/5.69 = ( groups7754918857620584856omplex
% 5.46/5.69 @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_divide_distrib
% 5.46/5.69 thf(fact_6290_sum__divide__distrib,axiom,
% 5.46/5.69 ! [F: nat > real,A2: set_nat,R: real] :
% 5.46/5.69 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 5.46/5.69 = ( groups6591440286371151544t_real
% 5.46/5.69 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R )
% 5.46/5.69 @ A2 ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_divide_distrib
% 5.46/5.69 thf(fact_6291_mod__sum__eq,axiom,
% 5.46/5.69 ! [F: int > int,A: int,A2: set_int] :
% 5.46/5.69 ( ( modulo_modulo_int
% 5.46/5.69 @ ( groups4538972089207619220nt_int
% 5.46/5.69 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.46/5.69 @ A2 )
% 5.46/5.69 @ A )
% 5.46/5.69 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % mod_sum_eq
% 5.46/5.69 thf(fact_6292_mod__sum__eq,axiom,
% 5.46/5.69 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.46/5.69 ( ( modulo_modulo_nat
% 5.46/5.69 @ ( groups3542108847815614940at_nat
% 5.46/5.69 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A )
% 5.46/5.69 @ A2 )
% 5.46/5.69 @ A )
% 5.46/5.69 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.46/5.69
% 5.46/5.69 % mod_sum_eq
% 5.46/5.69 thf(fact_6293_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > real] :
% 5.46/5.69 ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6294_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > real] :
% 5.46/5.69 ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6295_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > real] :
% 5.46/5.69 ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6296_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > rat] :
% 5.46/5.69 ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6297_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > rat] :
% 5.46/5.69 ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6298_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_nat,F: nat > rat] :
% 5.46/5.69 ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6299_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > rat] :
% 5.46/5.69 ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6300_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > nat] :
% 5.46/5.69 ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6301_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > nat] :
% 5.46/5.69 ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6302_sum__nonneg,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > nat] :
% 5.46/5.69 ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg
% 5.46/5.69 thf(fact_6303_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > real] :
% 5.46/5.69 ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6304_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > real] :
% 5.46/5.69 ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6305_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > real] :
% 5.46/5.69 ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6306_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > rat] :
% 5.46/5.69 ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6307_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > rat] :
% 5.46/5.69 ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6308_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_nat,F: nat > rat] :
% 5.46/5.69 ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6309_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > rat] :
% 5.46/5.69 ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6310_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > nat] :
% 5.46/5.69 ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.46/5.69 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6311_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > nat] :
% 5.46/5.69 ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.46/5.69 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6312_sum__nonpos,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > nat] :
% 5.46/5.69 ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.46/5.69 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonpos
% 5.46/5.69 thf(fact_6313_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: real > rat,I5: set_real,G: real > rat,I: real] :
% 5.46/5.69 ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 5.46/5.69 = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_real @ I @ I5 )
% 5.46/5.69 => ( ( finite_finite_real @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6314_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: nat > rat,I5: set_nat,G: nat > rat,I: nat] :
% 5.46/5.69 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 5.46/5.69 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: nat] :
% 5.46/5.69 ( ( member_nat @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_nat @ I @ I5 )
% 5.46/5.69 => ( ( finite_finite_nat @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6315_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: int > rat,I5: set_int,G: int > rat,I: int] :
% 5.46/5.69 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 5.46/5.69 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_int @ I @ I5 )
% 5.46/5.69 => ( ( finite_finite_int @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6316_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: complex > rat,I5: set_complex,G: complex > rat,I: complex] :
% 5.46/5.69 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 5.46/5.69 = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_complex @ I @ I5 )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6317_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: real > nat,I5: set_real,G: real > nat,I: real] :
% 5.46/5.69 ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 5.46/5.69 = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_real @ I @ I5 )
% 5.46/5.69 => ( ( finite_finite_real @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6318_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: int > nat,I5: set_int,G: int > nat,I: int] :
% 5.46/5.69 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 5.46/5.69 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_int @ I @ I5 )
% 5.46/5.69 => ( ( finite_finite_int @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6319_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: complex > nat,I5: set_complex,G: complex > nat,I: complex] :
% 5.46/5.69 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 5.46/5.69 = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_complex @ I @ I5 )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6320_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: real > int,I5: set_real,G: real > int,I: real] :
% 5.46/5.69 ( ( ( groups1932886352136224148al_int @ F @ I5 )
% 5.46/5.69 = ( groups1932886352136224148al_int @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_real @ I @ I5 )
% 5.46/5.69 => ( ( finite_finite_real @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6321_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: nat > int,I5: set_nat,G: nat > int,I: nat] :
% 5.46/5.69 ( ( ( groups3539618377306564664at_int @ F @ I5 )
% 5.46/5.69 = ( groups3539618377306564664at_int @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: nat] :
% 5.46/5.69 ( ( member_nat @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_nat @ I @ I5 )
% 5.46/5.69 => ( ( finite_finite_nat @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6322_sum__mono__inv,axiom,
% 5.46/5.69 ! [F: complex > int,I5: set_complex,G: complex > int,I: complex] :
% 5.46/5.69 ( ( ( groups5690904116761175830ex_int @ F @ I5 )
% 5.46/5.69 = ( groups5690904116761175830ex_int @ G @ I5 ) )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.46/5.69 => ( ( member_complex @ I @ I5 )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ I5 )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = ( G @ I ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_mono_inv
% 5.46/5.69 thf(fact_6323_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ( finite_finite_int @ T )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S )
% 5.46/5.69 => ? [Xa: int] :
% 5.46/5.69 ( ( member_int @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6324_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S )
% 5.46/5.69 => ? [Xa: complex] :
% 5.46/5.69 ( ( member_complex @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6325_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.46/5.69 => ( ( finite_finite_int @ T )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ S )
% 5.46/5.69 => ? [Xa: int] :
% 5.46/5.69 ( ( member_int @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6326_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ S )
% 5.46/5.69 => ? [Xa: complex] :
% 5.46/5.69 ( ( member_complex @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6327_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ S )
% 5.46/5.69 => ( ( finite_finite_nat @ T )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ S )
% 5.46/5.69 => ? [Xa: nat] :
% 5.46/5.69 ( ( member_nat @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6328_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_nat,T: set_int,G: int > rat,I: int > nat,F: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ S )
% 5.46/5.69 => ( ( finite_finite_int @ T )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ S )
% 5.46/5.69 => ? [Xa: int] :
% 5.46/5.69 ( ( member_int @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6329_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_nat,T: set_complex,G: complex > rat,I: complex > nat,F: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ S )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ S )
% 5.46/5.69 => ? [Xa: complex] :
% 5.46/5.69 ( ( member_complex @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6330_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_int,T: set_nat,G: nat > rat,I: nat > int,F: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ( finite_finite_nat @ T )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S )
% 5.46/5.69 => ? [Xa: nat] :
% 5.46/5.69 ( ( member_nat @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6331_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_int,T: set_int,G: int > rat,I: int > int,F: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ( finite_finite_int @ T )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S )
% 5.46/5.69 => ? [Xa: int] :
% 5.46/5.69 ( ( member_int @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6332_sum__le__included,axiom,
% 5.46/5.69 ! [S: set_int,T: set_complex,G: complex > rat,I: complex > int,F: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ T )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S )
% 5.46/5.69 => ? [Xa: complex] :
% 5.46/5.69 ( ( member_complex @ Xa @ T )
% 5.46/5.69 & ( ( I @ Xa )
% 5.46/5.69 = X3 )
% 5.46/5.69 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_le_included
% 5.46/5.69 thf(fact_6333_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > real] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 5.46/5.69 = zero_zero_real )
% 5.46/5.69 = ( ! [X: real] :
% 5.46/5.69 ( ( member_real @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6334_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 5.46/5.69 = zero_zero_real )
% 5.46/5.69 = ( ! [X: int] :
% 5.46/5.69 ( ( member_int @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6335_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 5.46/5.69 = zero_zero_real )
% 5.46/5.69 = ( ! [X: complex] :
% 5.46/5.69 ( ( member_complex @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6336_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > rat] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 = ( ! [X: real] :
% 5.46/5.69 ( ( member_real @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6337_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_nat,F: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ A2 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 = ( ! [X: nat] :
% 5.46/5.69 ( ( member_nat @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6338_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 = ( ! [X: int] :
% 5.46/5.69 ( ( member_int @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6339_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 = ( ! [X: complex] :
% 5.46/5.69 ( ( member_complex @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6340_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > nat] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 = ( ! [X: real] :
% 5.46/5.69 ( ( member_real @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_nat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6341_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 = ( ! [X: int] :
% 5.46/5.69 ( ( member_int @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_nat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6342_sum__nonneg__eq__0__iff,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > nat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.69 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 = ( ! [X: complex] :
% 5.46/5.69 ( ( member_complex @ X @ A2 )
% 5.46/5.69 => ( ( F @ X )
% 5.46/5.69 = zero_zero_nat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_eq_0_iff
% 5.46/5.69 thf(fact_6343_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > real,G: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: int] :
% 5.46/5.69 ( ( member_int @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6344_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: complex] :
% 5.46/5.69 ( ( member_complex @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6345_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ A2 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: nat] :
% 5.46/5.69 ( ( member_nat @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6346_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: int] :
% 5.46/5.69 ( ( member_int @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6347_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: complex] :
% 5.46/5.69 ( ( member_complex @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6348_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: int] :
% 5.46/5.69 ( ( member_int @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6349_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: complex] :
% 5.46/5.69 ( ( member_complex @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6350_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 5.46/5.69 ( ( finite_finite_nat @ A2 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: nat] :
% 5.46/5.69 ( ( member_nat @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6351_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: complex] :
% 5.46/5.69 ( ( member_complex @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6352_sum__strict__mono__ex1,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > int,G: int > int] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ? [X4: int] :
% 5.46/5.69 ( ( member_int @ X4 @ A2 )
% 5.46/5.69 & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.46/5.69 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono_ex1
% 5.46/5.69 thf(fact_6353_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 5.46/5.69 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.46/5.69 => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite_finite_nat @ S2 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups2073611262835488442omplex @ H2 @ S2 ) @ ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6354_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: complex > complex > $o,S2: set_int,H2: int > complex,G: int > complex] :
% 5.46/5.69 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.46/5.69 => ( ! [X15: complex,Y15: complex,X22: complex,Y23: complex] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite_finite_int @ S2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups3049146728041665814omplex @ H2 @ S2 ) @ ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6355_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 5.46/5.69 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 5.46/5.69 => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite_finite_int @ S2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups8778361861064173332t_real @ H2 @ S2 ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6356_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 5.46/5.69 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 5.46/5.69 => ( ! [X15: real,Y15: real,X22: real,Y23: real] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6357_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 5.46/5.69 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.46/5.69 => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite_finite_nat @ S2 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6358_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 5.46/5.69 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.46/5.69 => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite_finite_int @ S2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups3906332499630173760nt_rat @ H2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6359_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 5.46/5.69 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 5.46/5.69 => ( ! [X15: rat,Y15: rat,X22: rat,Y23: rat] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6360_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 5.46/5.69 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 5.46/5.69 => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite_finite_int @ S2 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups4541462559716669496nt_nat @ H2 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6361_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 5.46/5.69 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 5.46/5.69 => ( ! [X15: nat,Y15: nat,X22: nat,Y23: nat] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6362_sum_Orelated,axiom,
% 5.46/5.69 ! [R2: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 5.46/5.69 ( ( R2 @ zero_zero_int @ zero_zero_int )
% 5.46/5.69 => ( ! [X15: int,Y15: int,X22: int,Y23: int] :
% 5.46/5.69 ( ( ( R2 @ X15 @ X22 )
% 5.46/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.46/5.69 => ( R2 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X22 @ Y23 ) ) )
% 5.46/5.69 => ( ( finite_finite_nat @ S2 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ S2 )
% 5.46/5.69 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( R2 @ ( groups3539618377306564664at_int @ H2 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.related
% 5.46/5.69 thf(fact_6363_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_complex )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6364_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > real,G: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_int )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6365_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > real,G: real > real] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_real )
% 5.46/5.69 => ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6366_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_complex )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6367_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_nat )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6368_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_int )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6369_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_real )
% 5.46/5.69 => ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6370_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_complex )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6371_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_int )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6372_sum__strict__mono,axiom,
% 5.46/5.69 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ( A2 != bot_bot_set_real )
% 5.46/5.69 => ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ A2 )
% 5.46/5.69 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.46/5.69 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_strict_mono
% 5.46/5.69 thf(fact_6373_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 5.46/5.69 ( ( finite_finite_real @ S4 )
% 5.46/5.69 => ( ( finite_finite_real @ T4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.46/5.69 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups5754745047067104278omplex @ G @ S2 )
% 5.46/5.69 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6374_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > complex,H2: int > complex] :
% 5.46/5.69 ( ( finite_finite_real @ S4 )
% 5.46/5.69 => ( ( finite_finite_int @ T4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.46/5.69 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups5754745047067104278omplex @ G @ S2 )
% 5.46/5.69 = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6375_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > complex,H2: real > complex] :
% 5.46/5.69 ( ( finite_finite_int @ S4 )
% 5.46/5.69 => ( ( finite_finite_real @ T4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.46/5.69 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups3049146728041665814omplex @ G @ S2 )
% 5.46/5.69 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6376_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > complex,H2: int > complex] :
% 5.46/5.69 ( ( finite_finite_int @ S4 )
% 5.46/5.69 => ( ( finite_finite_int @ T4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.46/5.69 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups3049146728041665814omplex @ G @ S2 )
% 5.46/5.69 = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6377_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > real,H2: real > real] :
% 5.46/5.69 ( ( finite_finite_real @ S4 )
% 5.46/5.69 => ( ( finite_finite_real @ T4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.46/5.69 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups8097168146408367636l_real @ G @ S2 )
% 5.46/5.69 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6378_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > real,H2: int > real] :
% 5.46/5.69 ( ( finite_finite_real @ S4 )
% 5.46/5.69 => ( ( finite_finite_int @ T4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.46/5.69 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups8097168146408367636l_real @ G @ S2 )
% 5.46/5.69 = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6379_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_real,T4: set_complex,S2: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > real,H2: complex > real] :
% 5.46/5.69 ( ( finite_finite_real @ S4 )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ T4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.46/5.69 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.46/5.69 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups8097168146408367636l_real @ G @ S2 )
% 5.46/5.69 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6380_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > real,H2: real > real] :
% 5.46/5.69 ( ( finite_finite_int @ S4 )
% 5.46/5.69 => ( ( finite_finite_real @ T4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.46/5.69 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups8778361861064173332t_real @ G @ S2 )
% 5.46/5.69 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6381_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > real,H2: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ S4 )
% 5.46/5.69 => ( ( finite_finite_int @ T4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.46/5.69 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups8778361861064173332t_real @ G @ S2 )
% 5.46/5.69 = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6382_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.46/5.69 ! [S4: set_int,T4: set_complex,S2: set_int,I: complex > int,J: int > complex,T3: set_complex,G: int > real,H2: complex > real] :
% 5.46/5.69 ( ( finite_finite_int @ S4 )
% 5.46/5.69 => ( ( finite3207457112153483333omplex @ T4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( ( I @ ( J @ A5 ) )
% 5.46/5.69 = A5 ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.46/5.69 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.46/5.69 => ( ( J @ ( I @ B5 ) )
% 5.46/5.69 = B5 ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.46/5.69 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S4 )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ T4 )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ S2 )
% 5.46/5.69 => ( ( H2 @ ( J @ A5 ) )
% 5.46/5.69 = ( G @ A5 ) ) )
% 5.46/5.69 => ( ( groups8778361861064173332t_real @ G @ S2 )
% 5.46/5.69 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.reindex_bij_witness_not_neutral
% 5.46/5.69 thf(fact_6383_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_real,F: real > real,I: real] :
% 5.46/5.69 ( ( finite_finite_real @ S )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 5.46/5.69 = zero_zero_real )
% 5.46/5.69 => ( ( member_real @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_real ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6384_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_int,F: int > real,I: int] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 5.46/5.69 = zero_zero_real )
% 5.46/5.69 => ( ( member_int @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_real ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6385_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_complex,F: complex > real,I: complex] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 5.46/5.69 = zero_zero_real )
% 5.46/5.69 => ( ( member_complex @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_real ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6386_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_real,F: real > rat,I: real] :
% 5.46/5.69 ( ( finite_finite_real @ S )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 => ( ( member_real @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6387_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_nat,F: nat > rat,I: nat] :
% 5.46/5.69 ( ( finite_finite_nat @ S )
% 5.46/5.69 => ( ! [I2: nat] :
% 5.46/5.69 ( ( member_nat @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 => ( ( member_nat @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6388_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_int,F: int > rat,I: int] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 => ( ( member_int @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6389_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_complex,F: complex > rat,I: complex] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 5.46/5.69 = zero_zero_rat )
% 5.46/5.69 => ( ( member_complex @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6390_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_real,F: real > nat,I: real] :
% 5.46/5.69 ( ( finite_finite_real @ S )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 => ( ( member_real @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_nat ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6391_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_int,F: int > nat,I: int] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 => ( ( member_int @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_nat ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6392_sum__nonneg__0,axiom,
% 5.46/5.69 ! [S: set_complex,F: complex > nat,I: complex] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 => ( ( member_complex @ I @ S )
% 5.46/5.69 => ( ( F @ I )
% 5.46/5.69 = zero_zero_nat ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_0
% 5.46/5.69 thf(fact_6393_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_real,F: real > real,B3: real,I: real] :
% 5.46/5.69 ( ( finite_finite_real @ S )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_real @ I @ S )
% 5.46/5.69 => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6394_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_int,F: int > real,B3: real,I: int] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_int @ I @ S )
% 5.46/5.69 => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6395_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_complex,F: complex > real,B3: real,I: complex] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_complex @ I @ S )
% 5.46/5.69 => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6396_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_real,F: real > rat,B3: rat,I: real] :
% 5.46/5.69 ( ( finite_finite_real @ S )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_real @ I @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6397_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_nat,F: nat > rat,B3: rat,I: nat] :
% 5.46/5.69 ( ( finite_finite_nat @ S )
% 5.46/5.69 => ( ! [I2: nat] :
% 5.46/5.69 ( ( member_nat @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_nat @ I @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6398_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_int,F: int > rat,B3: rat,I: int] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_int @ I @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6399_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_complex,F: complex > rat,B3: rat,I: complex] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_complex @ I @ S )
% 5.46/5.69 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6400_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_real,F: real > nat,B3: nat,I: real] :
% 5.46/5.69 ( ( finite_finite_real @ S )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_real @ I @ S )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6401_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_int,F: int > nat,B3: nat,I: int] :
% 5.46/5.69 ( ( finite_finite_int @ S )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_int @ I @ S )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6402_sum__nonneg__leq__bound,axiom,
% 5.46/5.69 ! [S: set_complex,F: complex > nat,B3: nat,I: complex] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ S )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 5.46/5.69 = B3 )
% 5.46/5.69 => ( ( member_complex @ I @ S )
% 5.46/5.69 => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_nonneg_leq_bound
% 5.46/5.69 thf(fact_6403_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_real,G: real > complex] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ( groups5754745047067104278omplex @ G
% 5.46/5.69 @ ( minus_minus_set_real @ A2
% 5.46/5.69 @ ( collect_real
% 5.46/5.69 @ ^ [X: real] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_complex ) ) ) )
% 5.46/5.69 = ( groups5754745047067104278omplex @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6404_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_int,G: int > complex] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ( groups3049146728041665814omplex @ G
% 5.46/5.69 @ ( minus_minus_set_int @ A2
% 5.46/5.69 @ ( collect_int
% 5.46/5.69 @ ^ [X: int] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_complex ) ) ) )
% 5.46/5.69 = ( groups3049146728041665814omplex @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6405_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_real,G: real > real] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ( groups8097168146408367636l_real @ G
% 5.46/5.69 @ ( minus_minus_set_real @ A2
% 5.46/5.69 @ ( collect_real
% 5.46/5.69 @ ^ [X: real] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_real ) ) ) )
% 5.46/5.69 = ( groups8097168146408367636l_real @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6406_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_int,G: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ( groups8778361861064173332t_real @ G
% 5.46/5.69 @ ( minus_minus_set_int @ A2
% 5.46/5.69 @ ( collect_int
% 5.46/5.69 @ ^ [X: int] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_real ) ) ) )
% 5.46/5.69 = ( groups8778361861064173332t_real @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6407_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_complex,G: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ( groups5808333547571424918x_real @ G
% 5.46/5.69 @ ( minus_811609699411566653omplex @ A2
% 5.46/5.69 @ ( collect_complex
% 5.46/5.69 @ ^ [X: complex] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_real ) ) ) )
% 5.46/5.69 = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6408_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_real,G: real > rat] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ( groups1300246762558778688al_rat @ G
% 5.46/5.69 @ ( minus_minus_set_real @ A2
% 5.46/5.69 @ ( collect_real
% 5.46/5.69 @ ^ [X: real] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_rat ) ) ) )
% 5.46/5.69 = ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6409_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_int,G: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ( groups3906332499630173760nt_rat @ G
% 5.46/5.69 @ ( minus_minus_set_int @ A2
% 5.46/5.69 @ ( collect_int
% 5.46/5.69 @ ^ [X: int] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_rat ) ) ) )
% 5.46/5.69 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6410_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_complex,G: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.69 => ( ( groups5058264527183730370ex_rat @ G
% 5.46/5.69 @ ( minus_811609699411566653omplex @ A2
% 5.46/5.69 @ ( collect_complex
% 5.46/5.69 @ ^ [X: complex] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_rat ) ) ) )
% 5.46/5.69 = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6411_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_real,G: real > nat] :
% 5.46/5.69 ( ( finite_finite_real @ A2 )
% 5.46/5.69 => ( ( groups1935376822645274424al_nat @ G
% 5.46/5.69 @ ( minus_minus_set_real @ A2
% 5.46/5.69 @ ( collect_real
% 5.46/5.69 @ ^ [X: real] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_nat ) ) ) )
% 5.46/5.69 = ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6412_sum_Osetdiff__irrelevant,axiom,
% 5.46/5.69 ! [A2: set_int,G: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ A2 )
% 5.46/5.69 => ( ( groups4541462559716669496nt_nat @ G
% 5.46/5.69 @ ( minus_minus_set_int @ A2
% 5.46/5.69 @ ( collect_int
% 5.46/5.69 @ ^ [X: int] :
% 5.46/5.69 ( ( G @ X )
% 5.46/5.69 = zero_zero_nat ) ) ) )
% 5.46/5.69 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.setdiff_irrelevant
% 5.46/5.69 thf(fact_6413_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_real,I: real,F: real > real] :
% 5.46/5.69 ( ( finite_finite_real @ I5 )
% 5.46/5.69 => ( ( member_real @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6414_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_int,I: int,F: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ I5 )
% 5.46/5.69 => ( ( member_int @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6415_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_complex,I: complex,F: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ I5 )
% 5.46/5.69 => ( ( member_complex @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6416_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_real,I: real,F: real > rat] :
% 5.46/5.69 ( ( finite_finite_real @ I5 )
% 5.46/5.69 => ( ( member_real @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6417_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_nat,I: nat,F: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ I5 )
% 5.46/5.69 => ( ( member_nat @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: nat] :
% 5.46/5.69 ( ( member_nat @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6418_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_int,I: int,F: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ I5 )
% 5.46/5.69 => ( ( member_int @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6419_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_complex,I: complex,F: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ I5 )
% 5.46/5.69 => ( ( member_complex @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6420_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_real,I: real,F: real > nat] :
% 5.46/5.69 ( ( finite_finite_real @ I5 )
% 5.46/5.69 => ( ( member_real @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6421_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_int,I: int,F: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ I5 )
% 5.46/5.69 => ( ( member_int @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6422_sum__pos2,axiom,
% 5.46/5.69 ! [I5: set_complex,I: complex,F: complex > nat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ I5 )
% 5.46/5.69 => ( ( member_complex @ I @ I5 )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos2
% 5.46/5.69 thf(fact_6423_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_complex,F: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_complex )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6424_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_int,F: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_int )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6425_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_real,F: real > real] :
% 5.46/5.69 ( ( finite_finite_real @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_real )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6426_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_complex,F: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_complex )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6427_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_nat,F: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_nat )
% 5.46/5.69 => ( ! [I2: nat] :
% 5.46/5.69 ( ( member_nat @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6428_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_int,F: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_int )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6429_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_real,F: real > rat] :
% 5.46/5.69 ( ( finite_finite_real @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_real )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6430_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_complex,F: complex > nat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_complex )
% 5.46/5.69 => ( ! [I2: complex] :
% 5.46/5.69 ( ( member_complex @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6431_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_int,F: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_int )
% 5.46/5.69 => ( ! [I2: int] :
% 5.46/5.69 ( ( member_int @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6432_sum__pos,axiom,
% 5.46/5.69 ! [I5: set_real,F: real > nat] :
% 5.46/5.69 ( ( finite_finite_real @ I5 )
% 5.46/5.69 => ( ( I5 != bot_bot_set_real )
% 5.46/5.69 => ( ! [I2: real] :
% 5.46/5.69 ( ( member_real @ I2 @ I5 )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_pos
% 5.46/5.69 thf(fact_6433_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 5.46/5.69 ( ( finite_finite_real @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.46/5.69 = ( groups5754745047067104278omplex @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups5754745047067104278omplex @ G @ C4 )
% 5.46/5.69 = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6434_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_int,A2: set_int,B3: set_int,G: int > complex,H2: int > complex] :
% 5.46/5.69 ( ( finite_finite_int @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ( ( groups3049146728041665814omplex @ G @ A2 )
% 5.46/5.69 = ( groups3049146728041665814omplex @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups3049146728041665814omplex @ G @ C4 )
% 5.46/5.69 = ( groups3049146728041665814omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6435_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 5.46/5.69 ( ( finite_finite_real @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.46/5.69 = ( groups8097168146408367636l_real @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups8097168146408367636l_real @ G @ C4 )
% 5.46/5.69 = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6436_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_int,A2: set_int,B3: set_int,G: int > real,H2: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.46/5.69 = ( groups8778361861064173332t_real @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups8778361861064173332t_real @ G @ C4 )
% 5.46/5.69 = ( groups8778361861064173332t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6437_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: complex] :
% 5.46/5.69 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.46/5.69 = ( groups5808333547571424918x_real @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups5808333547571424918x_real @ G @ C4 )
% 5.46/5.69 = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6438_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 5.46/5.69 ( ( finite_finite_real @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.46/5.69 = ( groups1300246762558778688al_rat @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups1300246762558778688al_rat @ G @ C4 )
% 5.46/5.69 = ( groups1300246762558778688al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6439_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_int,A2: set_int,B3: set_int,G: int > rat,H2: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.46/5.69 = ( groups3906332499630173760nt_rat @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 5.46/5.69 = ( groups3906332499630173760nt_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6440_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: complex] :
% 5.46/5.69 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.46/5.69 = ( groups5058264527183730370ex_rat @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 5.46/5.69 = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6441_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 5.46/5.69 ( ( finite_finite_real @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.46/5.69 = ( groups1935376822645274424al_nat @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 5.46/5.69 = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6442_sum_Osame__carrier,axiom,
% 5.46/5.69 ! [C4: set_int,A2: set_int,B3: set_int,G: int > nat,H2: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.46/5.69 = ( groups4541462559716669496nt_nat @ H2 @ B3 ) )
% 5.46/5.69 = ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 5.46/5.69 = ( groups4541462559716669496nt_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrier
% 5.46/5.69 thf(fact_6443_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 5.46/5.69 ( ( finite_finite_real @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 5.46/5.69 = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.46/5.69 = ( groups5754745047067104278omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6444_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_int,A2: set_int,B3: set_int,G: int > complex,H2: int > complex] :
% 5.46/5.69 ( ( finite_finite_int @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ( ( groups3049146728041665814omplex @ G @ C4 )
% 5.46/5.69 = ( groups3049146728041665814omplex @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups3049146728041665814omplex @ G @ A2 )
% 5.46/5.69 = ( groups3049146728041665814omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6445_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 5.46/5.69 ( ( finite_finite_real @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 5.46/5.69 = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.46/5.69 = ( groups8097168146408367636l_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6446_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_int,A2: set_int,B3: set_int,G: int > real,H2: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( ( groups8778361861064173332t_real @ G @ C4 )
% 5.46/5.69 = ( groups8778361861064173332t_real @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.46/5.69 = ( groups8778361861064173332t_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6447_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: complex] :
% 5.46/5.69 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 5.46/5.69 = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.46/5.69 = ( groups5808333547571424918x_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6448_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 5.46/5.69 ( ( finite_finite_real @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( ( groups1300246762558778688al_rat @ G @ C4 )
% 5.46/5.69 = ( groups1300246762558778688al_rat @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.46/5.69 = ( groups1300246762558778688al_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6449_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_int,A2: set_int,B3: set_int,G: int > rat,H2: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( ( groups3906332499630173760nt_rat @ G @ C4 )
% 5.46/5.69 = ( groups3906332499630173760nt_rat @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.46/5.69 = ( groups3906332499630173760nt_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6450_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: complex] :
% 5.46/5.69 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ! [B5: complex] :
% 5.46/5.69 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 5.46/5.69 = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.46/5.69 = ( groups5058264527183730370ex_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6451_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 5.46/5.69 ( ( finite_finite_real @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: real] :
% 5.46/5.69 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ! [B5: real] :
% 5.46/5.69 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 5.46/5.69 = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.46/5.69 = ( groups1935376822645274424al_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6452_sum_Osame__carrierI,axiom,
% 5.46/5.69 ! [C4: set_int,A2: set_int,B3: set_int,G: int > nat,H2: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.46/5.69 => ( ! [A5: int] :
% 5.46/5.69 ( ( member_int @ A5 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.46/5.69 => ( ( G @ A5 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ! [B5: int] :
% 5.46/5.69 ( ( member_int @ B5 @ ( minus_minus_set_int @ C4 @ B3 ) )
% 5.46/5.69 => ( ( H2 @ B5 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 5.46/5.69 = ( groups4541462559716669496nt_nat @ H2 @ C4 ) )
% 5.46/5.69 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.46/5.69 = ( groups4541462559716669496nt_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.same_carrierI
% 5.46/5.69 thf(fact_6453_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_int,S2: set_int,G: int > complex] :
% 5.46/5.69 ( ( finite_finite_int @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ( groups3049146728041665814omplex @ G @ S2 )
% 5.46/5.69 = ( groups3049146728041665814omplex @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6454_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_int,S2: set_int,G: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( groups8778361861064173332t_real @ G @ S2 )
% 5.46/5.69 = ( groups8778361861064173332t_real @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6455_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( groups5808333547571424918x_real @ G @ S2 )
% 5.46/5.69 = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6456_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_int,S2: set_int,G: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 5.46/5.69 = ( groups3906332499630173760nt_rat @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6457_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 5.46/5.69 = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6458_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_int,S2: set_int,G: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 5.46/5.69 = ( groups4541462559716669496nt_nat @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6459_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 5.46/5.69 = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6460_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_int ) )
% 5.46/5.69 => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 5.46/5.69 = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6461_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 5.46/5.69 ( ( finite_finite_nat @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ( groups2073611262835488442omplex @ G @ S2 )
% 5.46/5.69 = ( groups2073611262835488442omplex @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6462_sum_Omono__neutral__left,axiom,
% 5.46/5.69 ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( groups2906978787729119204at_rat @ G @ S2 )
% 5.46/5.69 = ( groups2906978787729119204at_rat @ G @ T3 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_left
% 5.46/5.69 thf(fact_6463_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_int,S2: set_int,G: int > complex] :
% 5.46/5.69 ( ( finite_finite_int @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ( groups3049146728041665814omplex @ G @ T3 )
% 5.46/5.69 = ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6464_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_int,S2: set_int,G: int > real] :
% 5.46/5.69 ( ( finite_finite_int @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( groups8778361861064173332t_real @ G @ T3 )
% 5.46/5.69 = ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6465_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_real ) )
% 5.46/5.69 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.46/5.69 = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6466_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_int,S2: set_int,G: int > rat] :
% 5.46/5.69 ( ( finite_finite_int @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( groups3906332499630173760nt_rat @ G @ T3 )
% 5.46/5.69 = ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6467_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 5.46/5.69 = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6468_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_int,S2: set_int,G: int > nat] :
% 5.46/5.69 ( ( finite_finite_int @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ( groups4541462559716669496nt_nat @ G @ T3 )
% 5.46/5.69 = ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6469_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_nat ) )
% 5.46/5.69 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 5.46/5.69 = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6470_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 5.46/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.69 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: complex] :
% 5.46/5.69 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_int ) )
% 5.46/5.69 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 5.46/5.69 = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6471_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 5.46/5.69 ( ( finite_finite_nat @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ( groups2073611262835488442omplex @ G @ T3 )
% 5.46/5.69 = ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6472_sum_Omono__neutral__right,axiom,
% 5.46/5.69 ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 5.46/5.69 ( ( finite_finite_nat @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: nat] :
% 5.46/5.69 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = zero_zero_rat ) )
% 5.46/5.69 => ( ( groups2906978787729119204at_rat @ G @ T3 )
% 5.46/5.69 = ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_right
% 5.46/5.69 thf(fact_6473_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.69 ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 5.46/5.69 ( ( finite_finite_real @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.46/5.69 => ( ( H2 @ X3 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [X3: real] :
% 5.46/5.69 ( ( member_real @ X3 @ S2 )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = ( H2 @ X3 ) ) )
% 5.46/5.69 => ( ( groups5754745047067104278omplex @ G @ S2 )
% 5.46/5.69 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum.mono_neutral_cong_left
% 5.46/5.69 thf(fact_6474_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.69 ! [T3: set_int,S2: set_int,H2: int > complex,G: int > complex] :
% 5.46/5.69 ( ( finite_finite_int @ T3 )
% 5.46/5.69 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.69 => ( ( H2 @ X3 )
% 5.46/5.69 = zero_zero_complex ) )
% 5.46/5.69 => ( ! [X3: int] :
% 5.46/5.69 ( ( member_int @ X3 @ S2 )
% 5.46/5.69 => ( ( G @ X3 )
% 5.46/5.69 = ( H2 @ X3 ) ) )
% 5.46/5.69 => ( ( groups3049146728041665814omplex @ G @ S2 )
% 5.46/5.69 = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_left
% 5.46/5.70 thf(fact_6475_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.70 ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 5.46/5.70 ( ( finite_finite_real @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.46/5.70 => ( ( H2 @ X3 )
% 5.46/5.70 = zero_zero_real ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups8097168146408367636l_real @ G @ S2 )
% 5.46/5.70 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_left
% 5.46/5.70 thf(fact_6476_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.70 ! [T3: set_int,S2: set_int,H2: int > real,G: int > real] :
% 5.46/5.70 ( ( finite_finite_int @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.70 => ( ( H2 @ X3 )
% 5.46/5.70 = zero_zero_real ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups8778361861064173332t_real @ G @ S2 )
% 5.46/5.70 = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_left
% 5.46/5.70 thf(fact_6477_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.70 ! [T3: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.70 => ( ( H2 @ X3 )
% 5.46/5.70 = zero_zero_real ) )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups5808333547571424918x_real @ G @ S2 )
% 5.46/5.70 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_left
% 5.46/5.70 thf(fact_6478_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.70 ! [T3: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 5.46/5.70 ( ( finite_finite_real @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.46/5.70 => ( ( H2 @ X3 )
% 5.46/5.70 = zero_zero_rat ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 5.46/5.70 = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_left
% 5.46/5.70 thf(fact_6479_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.70 ! [T3: set_int,S2: set_int,H2: int > rat,G: int > rat] :
% 5.46/5.70 ( ( finite_finite_int @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.70 => ( ( H2 @ X3 )
% 5.46/5.70 = zero_zero_rat ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 5.46/5.70 = ( groups3906332499630173760nt_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_left
% 5.46/5.70 thf(fact_6480_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.70 ! [T3: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.70 => ( ( H2 @ X3 )
% 5.46/5.70 = zero_zero_rat ) )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 5.46/5.70 = ( groups5058264527183730370ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_left
% 5.46/5.70 thf(fact_6481_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.70 ! [T3: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 5.46/5.70 ( ( finite_finite_real @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.46/5.70 => ( ( H2 @ X3 )
% 5.46/5.70 = zero_zero_nat ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 5.46/5.70 = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_left
% 5.46/5.70 thf(fact_6482_sum_Omono__neutral__cong__left,axiom,
% 5.46/5.70 ! [T3: set_int,S2: set_int,H2: int > nat,G: int > nat] :
% 5.46/5.70 ( ( finite_finite_int @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.70 => ( ( H2 @ X3 )
% 5.46/5.70 = zero_zero_nat ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 5.46/5.70 = ( groups4541462559716669496nt_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_left
% 5.46/5.70 thf(fact_6483_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 5.46/5.70 ( ( finite_finite_real @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_complex ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups5754745047067104278omplex @ G @ T3 )
% 5.46/5.70 = ( groups5754745047067104278omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6484_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_int,S2: set_int,G: int > complex,H2: int > complex] :
% 5.46/5.70 ( ( finite_finite_int @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_complex ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups3049146728041665814omplex @ G @ T3 )
% 5.46/5.70 = ( groups3049146728041665814omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6485_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 5.46/5.70 ( ( finite_finite_real @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_real ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups8097168146408367636l_real @ G @ T3 )
% 5.46/5.70 = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6486_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_int,S2: set_int,G: int > real,H2: int > real] :
% 5.46/5.70 ( ( finite_finite_int @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_real ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups8778361861064173332t_real @ G @ T3 )
% 5.46/5.70 = ( groups8778361861064173332t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6487_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_real ) )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.46/5.70 = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6488_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 5.46/5.70 ( ( finite_finite_real @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_rat ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 5.46/5.70 = ( groups1300246762558778688al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6489_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_int,S2: set_int,G: int > rat,H2: int > rat] :
% 5.46/5.70 ( ( finite_finite_int @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_rat ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups3906332499630173760nt_rat @ G @ T3 )
% 5.46/5.70 = ( groups3906332499630173760nt_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6490_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ T3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_rat ) )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 5.46/5.70 = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6491_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 5.46/5.70 ( ( finite_finite_real @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_nat ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 5.46/5.70 = ( groups1935376822645274424al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6492_sum_Omono__neutral__cong__right,axiom,
% 5.46/5.70 ! [T3: set_int,S2: set_int,G: int > nat,H2: int > nat] :
% 5.46/5.70 ( ( finite_finite_int @ T3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = zero_zero_nat ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ S2 )
% 5.46/5.70 => ( ( G @ X3 )
% 5.46/5.70 = ( H2 @ X3 ) ) )
% 5.46/5.70 => ( ( groups4541462559716669496nt_nat @ G @ T3 )
% 5.46/5.70 = ( groups4541462559716669496nt_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.mono_neutral_cong_right
% 5.46/5.70 thf(fact_6493_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,G: int > real] :
% 5.46/5.70 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.46/5.70 => ( ( finite_finite_int @ A2 )
% 5.46/5.70 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.46/5.70 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups8778361861064173332t_real @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6494_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,G: complex > real] :
% 5.46/5.70 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.46/5.70 => ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.70 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.46/5.70 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5808333547571424918x_real @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6495_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,G: int > rat] :
% 5.46/5.70 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.46/5.70 => ( ( finite_finite_int @ A2 )
% 5.46/5.70 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.46/5.70 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6496_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,G: complex > rat] :
% 5.46/5.70 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.46/5.70 => ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.70 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.46/5.70 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5058264527183730370ex_rat @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6497_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,G: int > nat] :
% 5.46/5.70 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.46/5.70 => ( ( finite_finite_int @ A2 )
% 5.46/5.70 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.46/5.70 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6498_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,G: complex > nat] :
% 5.46/5.70 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.46/5.70 => ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.70 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.46/5.70 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5693394587270226106ex_nat @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6499_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,G: complex > int] :
% 5.46/5.70 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.46/5.70 => ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.70 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.46/5.70 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5690904116761175830ex_int @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6500_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_nat,A2: set_nat,G: nat > rat] :
% 5.46/5.70 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.46/5.70 => ( ( finite_finite_nat @ A2 )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 5.46/5.70 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6501_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_nat,A2: set_nat,G: nat > int] :
% 5.46/5.70 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.46/5.70 => ( ( finite_finite_nat @ A2 )
% 5.46/5.70 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 5.46/5.70 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6502_sum_Osubset__diff,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,G: int > int] :
% 5.46/5.70 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.46/5.70 => ( ( finite_finite_int @ A2 )
% 5.46/5.70 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 5.46/5.70 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4538972089207619220nt_int @ G @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.subset_diff
% 5.46/5.70 thf(fact_6503_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_int,B3: set_int,F: int > rat] :
% 5.46/5.70 ( ( finite_finite_int @ A2 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.46/5.70 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6504_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_complex,B3: set_complex,F: complex > rat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.46/5.70 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6505_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_complex,B3: set_complex,F: complex > int] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.46/5.70 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6506_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 5.46/5.70 ( ( finite6177210948735845034at_nat @ A2 )
% 5.46/5.70 => ( ( ord_le3146513528884898305at_nat @ B3 @ A2 )
% 5.46/5.70 => ( ( groups342789780944988191at_rat @ F @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_rat @ ( groups342789780944988191at_rat @ F @ A2 ) @ ( groups342789780944988191at_rat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6507_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > int] :
% 5.46/5.70 ( ( finite6177210948735845034at_nat @ A2 )
% 5.46/5.70 => ( ( ord_le3146513528884898305at_nat @ B3 @ A2 )
% 5.46/5.70 => ( ( groups975429370522433651at_int @ F @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_int @ ( groups975429370522433651at_int @ F @ A2 ) @ ( groups975429370522433651at_int @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6508_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_nat,B3: set_nat,F: nat > rat] :
% 5.46/5.70 ( ( finite_finite_nat @ A2 )
% 5.46/5.70 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6509_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_nat,B3: set_nat,F: nat > int] :
% 5.46/5.70 ( ( finite_finite_nat @ A2 )
% 5.46/5.70 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.46/5.70 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6510_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_int,B3: set_int,F: int > int] :
% 5.46/5.70 ( ( finite_finite_int @ A2 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.46/5.70 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6511_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_complex,B3: set_complex,F: complex > complex] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.46/5.70 => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6512_sum__diff,axiom,
% 5.46/5.70 ! [A2: set_nat,B3: set_nat,F: nat > real] :
% 5.46/5.70 ( ( finite_finite_nat @ A2 )
% 5.46/5.70 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff
% 5.46/5.70 thf(fact_6513_subset__decode__imp__le,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.46/5.70 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % subset_decode_imp_le
% 5.46/5.70 thf(fact_6514_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_real,A2: set_real,F: real > real] :
% 5.46/5.70 ( ( finite_finite_real @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: real] :
% 5.46/5.70 ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6515_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,F: int > real] :
% 5.46/5.70 ( ( finite_finite_int @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: int] :
% 5.46/5.70 ( ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6516_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,F: complex > real] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ B3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: complex] :
% 5.46/5.70 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6517_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_real,A2: set_real,F: real > rat] :
% 5.46/5.70 ( ( finite_finite_real @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: real] :
% 5.46/5.70 ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6518_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,F: int > rat] :
% 5.46/5.70 ( ( finite_finite_int @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: int] :
% 5.46/5.70 ( ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6519_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,F: complex > rat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ B3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: complex] :
% 5.46/5.70 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6520_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_real,A2: set_real,F: real > nat] :
% 5.46/5.70 ( ( finite_finite_real @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: real] :
% 5.46/5.70 ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6521_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,F: int > nat] :
% 5.46/5.70 ( ( finite_finite_int @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: int] :
% 5.46/5.70 ( ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6522_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ B3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: complex] :
% 5.46/5.70 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6523_sum__mono2,axiom,
% 5.46/5.70 ! [B3: set_real,A2: set_real,F: real > int] :
% 5.46/5.70 ( ( finite_finite_real @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.46/5.70 => ( ! [B5: real] :
% 5.46/5.70 ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.46/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 5.46/5.70 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_mono2
% 5.46/5.70 thf(fact_6524_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_real,A2: set_real,B: real,F: real > real] :
% 5.46/5.70 ( ( finite_finite_real @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.46/5.70 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6525_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,B: int,F: int > real] :
% 5.46/5.70 ( ( finite_finite_int @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.46/5.70 => ( ( member_int @ B @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6526_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ B3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.46/5.70 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6527_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_real,A2: set_real,B: real,F: real > rat] :
% 5.46/5.70 ( ( finite_finite_real @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.46/5.70 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6528_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,B: int,F: int > rat] :
% 5.46/5.70 ( ( finite_finite_int @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.46/5.70 => ( ( member_int @ B @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6529_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ B3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.46/5.70 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6530_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_real,A2: set_real,B: real,F: real > nat] :
% 5.46/5.70 ( ( finite_finite_real @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.46/5.70 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6531_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,B: int,F: int > nat] :
% 5.46/5.70 ( ( finite_finite_int @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.46/5.70 => ( ( member_int @ B @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6532_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ B3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.46/5.70 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6533_sum__strict__mono2,axiom,
% 5.46/5.70 ! [B3: set_real,A2: set_real,B: real,F: real > int] :
% 5.46/5.70 ( ( finite_finite_real @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.46/5.70 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.46/5.70 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.46/5.70 => ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ B3 )
% 5.46/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_strict_mono2
% 5.46/5.70 thf(fact_6534_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_complex,X2: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.46/5.70 ( ! [I2: complex] :
% 5.46/5.70 ( ( member_complex @ I2 @ I5 )
% 5.46/5.70 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups6621422865394947399nteger @ X2 @ I5 )
% 5.46/5.70 = one_one_Code_integer )
% 5.46/5.70 => ( ! [I2: complex] :
% 5.46/5.70 ( ( member_complex @ I2 @ I5 )
% 5.46/5.70 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_le3102999989581377725nteger
% 5.46/5.70 @ ( abs_abs_Code_integer
% 5.46/5.70 @ ( minus_8373710615458151222nteger
% 5.46/5.70 @ ( groups6621422865394947399nteger
% 5.46/5.70 @ ^ [I4: complex] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6535_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_real,X2: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.46/5.70 ( ! [I2: real] :
% 5.46/5.70 ( ( member_real @ I2 @ I5 )
% 5.46/5.70 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups7713935264441627589nteger @ X2 @ I5 )
% 5.46/5.70 = one_one_Code_integer )
% 5.46/5.70 => ( ! [I2: real] :
% 5.46/5.70 ( ( member_real @ I2 @ I5 )
% 5.46/5.70 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_le3102999989581377725nteger
% 5.46/5.70 @ ( abs_abs_Code_integer
% 5.46/5.70 @ ( minus_8373710615458151222nteger
% 5.46/5.70 @ ( groups7713935264441627589nteger
% 5.46/5.70 @ ^ [I4: real] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6536_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_nat,X2: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.46/5.70 ( ! [I2: nat] :
% 5.46/5.70 ( ( member_nat @ I2 @ I5 )
% 5.46/5.70 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups7501900531339628137nteger @ X2 @ I5 )
% 5.46/5.70 = one_one_Code_integer )
% 5.46/5.70 => ( ! [I2: nat] :
% 5.46/5.70 ( ( member_nat @ I2 @ I5 )
% 5.46/5.70 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_le3102999989581377725nteger
% 5.46/5.70 @ ( abs_abs_Code_integer
% 5.46/5.70 @ ( minus_8373710615458151222nteger
% 5.46/5.70 @ ( groups7501900531339628137nteger
% 5.46/5.70 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6537_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_int,X2: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.46/5.70 ( ! [I2: int] :
% 5.46/5.70 ( ( member_int @ I2 @ I5 )
% 5.46/5.70 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups7873554091576472773nteger @ X2 @ I5 )
% 5.46/5.70 = one_one_Code_integer )
% 5.46/5.70 => ( ! [I2: int] :
% 5.46/5.70 ( ( member_int @ I2 @ I5 )
% 5.46/5.70 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_le3102999989581377725nteger
% 5.46/5.70 @ ( abs_abs_Code_integer
% 5.46/5.70 @ ( minus_8373710615458151222nteger
% 5.46/5.70 @ ( groups7873554091576472773nteger
% 5.46/5.70 @ ^ [I4: int] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6538_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_complex,X2: complex > real,A: complex > real,B: real,Delta: real] :
% 5.46/5.70 ( ! [I2: complex] :
% 5.46/5.70 ( ( member_complex @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups5808333547571424918x_real @ X2 @ I5 )
% 5.46/5.70 = one_one_real )
% 5.46/5.70 => ( ! [I2: complex] :
% 5.46/5.70 ( ( member_complex @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_less_eq_real
% 5.46/5.70 @ ( abs_abs_real
% 5.46/5.70 @ ( minus_minus_real
% 5.46/5.70 @ ( groups5808333547571424918x_real
% 5.46/5.70 @ ^ [I4: complex] : ( times_times_real @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6539_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_real,X2: real > real,A: real > real,B: real,Delta: real] :
% 5.46/5.70 ( ! [I2: real] :
% 5.46/5.70 ( ( member_real @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups8097168146408367636l_real @ X2 @ I5 )
% 5.46/5.70 = one_one_real )
% 5.46/5.70 => ( ! [I2: real] :
% 5.46/5.70 ( ( member_real @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_less_eq_real
% 5.46/5.70 @ ( abs_abs_real
% 5.46/5.70 @ ( minus_minus_real
% 5.46/5.70 @ ( groups8097168146408367636l_real
% 5.46/5.70 @ ^ [I4: real] : ( times_times_real @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6540_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_int,X2: int > real,A: int > real,B: real,Delta: real] :
% 5.46/5.70 ( ! [I2: int] :
% 5.46/5.70 ( ( member_int @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups8778361861064173332t_real @ X2 @ I5 )
% 5.46/5.70 = one_one_real )
% 5.46/5.70 => ( ! [I2: int] :
% 5.46/5.70 ( ( member_int @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_less_eq_real
% 5.46/5.70 @ ( abs_abs_real
% 5.46/5.70 @ ( minus_minus_real
% 5.46/5.70 @ ( groups8778361861064173332t_real
% 5.46/5.70 @ ^ [I4: int] : ( times_times_real @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6541_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_complex,X2: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 5.46/5.70 ( ! [I2: complex] :
% 5.46/5.70 ( ( member_complex @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups5058264527183730370ex_rat @ X2 @ I5 )
% 5.46/5.70 = one_one_rat )
% 5.46/5.70 => ( ! [I2: complex] :
% 5.46/5.70 ( ( member_complex @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_less_eq_rat
% 5.46/5.70 @ ( abs_abs_rat
% 5.46/5.70 @ ( minus_minus_rat
% 5.46/5.70 @ ( groups5058264527183730370ex_rat
% 5.46/5.70 @ ^ [I4: complex] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6542_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_real,X2: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.46/5.70 ( ! [I2: real] :
% 5.46/5.70 ( ( member_real @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups1300246762558778688al_rat @ X2 @ I5 )
% 5.46/5.70 = one_one_rat )
% 5.46/5.70 => ( ! [I2: real] :
% 5.46/5.70 ( ( member_real @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_less_eq_rat
% 5.46/5.70 @ ( abs_abs_rat
% 5.46/5.70 @ ( minus_minus_rat
% 5.46/5.70 @ ( groups1300246762558778688al_rat
% 5.46/5.70 @ ^ [I4: real] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6543_convex__sum__bound__le,axiom,
% 5.46/5.70 ! [I5: set_nat,X2: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.46/5.70 ( ! [I2: nat] :
% 5.46/5.70 ( ( member_nat @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.46/5.70 => ( ( ( groups2906978787729119204at_rat @ X2 @ I5 )
% 5.46/5.70 = one_one_rat )
% 5.46/5.70 => ( ! [I2: nat] :
% 5.46/5.70 ( ( member_nat @ I2 @ I5 )
% 5.46/5.70 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.46/5.70 => ( ord_less_eq_rat
% 5.46/5.70 @ ( abs_abs_rat
% 5.46/5.70 @ ( minus_minus_rat
% 5.46/5.70 @ ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 @ B ) )
% 5.46/5.70 @ Delta ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_sum_bound_le
% 5.46/5.70 thf(fact_6544_add__0__iff,axiom,
% 5.46/5.70 ! [B: complex,A: complex] :
% 5.46/5.70 ( ( B
% 5.46/5.70 = ( plus_plus_complex @ B @ A ) )
% 5.46/5.70 = ( A = zero_zero_complex ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_0_iff
% 5.46/5.70 thf(fact_6545_add__0__iff,axiom,
% 5.46/5.70 ! [B: real,A: real] :
% 5.46/5.70 ( ( B
% 5.46/5.70 = ( plus_plus_real @ B @ A ) )
% 5.46/5.70 = ( A = zero_zero_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_0_iff
% 5.46/5.70 thf(fact_6546_add__0__iff,axiom,
% 5.46/5.70 ! [B: rat,A: rat] :
% 5.46/5.70 ( ( B
% 5.46/5.70 = ( plus_plus_rat @ B @ A ) )
% 5.46/5.70 = ( A = zero_zero_rat ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_0_iff
% 5.46/5.70 thf(fact_6547_add__0__iff,axiom,
% 5.46/5.70 ! [B: nat,A: nat] :
% 5.46/5.70 ( ( B
% 5.46/5.70 = ( plus_plus_nat @ B @ A ) )
% 5.46/5.70 = ( A = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_0_iff
% 5.46/5.70 thf(fact_6548_add__0__iff,axiom,
% 5.46/5.70 ! [B: int,A: int] :
% 5.46/5.70 ( ( B
% 5.46/5.70 = ( plus_plus_int @ B @ A ) )
% 5.46/5.70 = ( A = zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_0_iff
% 5.46/5.70 thf(fact_6549_crossproduct__noteq,axiom,
% 5.46/5.70 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.70 ( ( ( A != B )
% 5.46/5.70 & ( C != D2 ) )
% 5.46/5.70 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) )
% 5.46/5.70 != ( plus_plus_real @ ( times_times_real @ A @ D2 ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % crossproduct_noteq
% 5.46/5.70 thf(fact_6550_crossproduct__noteq,axiom,
% 5.46/5.70 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.46/5.70 ( ( ( A != B )
% 5.46/5.70 & ( C != D2 ) )
% 5.46/5.70 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 5.46/5.70 != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % crossproduct_noteq
% 5.46/5.70 thf(fact_6551_crossproduct__noteq,axiom,
% 5.46/5.70 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.46/5.70 ( ( ( A != B )
% 5.46/5.70 & ( C != D2 ) )
% 5.46/5.70 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 5.46/5.70 != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % crossproduct_noteq
% 5.46/5.70 thf(fact_6552_crossproduct__noteq,axiom,
% 5.46/5.70 ! [A: int,B: int,C: int,D2: int] :
% 5.46/5.70 ( ( ( A != B )
% 5.46/5.70 & ( C != D2 ) )
% 5.46/5.70 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 5.46/5.70 != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % crossproduct_noteq
% 5.46/5.70 thf(fact_6553_crossproduct__eq,axiom,
% 5.46/5.70 ! [W: real,Y2: real,X2: real,Z: real] :
% 5.46/5.70 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y2 ) @ ( times_times_real @ X2 @ Z ) )
% 5.46/5.70 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X2 @ Y2 ) ) )
% 5.46/5.70 = ( ( W = X2 )
% 5.46/5.70 | ( Y2 = Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % crossproduct_eq
% 5.46/5.70 thf(fact_6554_crossproduct__eq,axiom,
% 5.46/5.70 ! [W: rat,Y2: rat,X2: rat,Z: rat] :
% 5.46/5.70 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y2 ) @ ( times_times_rat @ X2 @ Z ) )
% 5.46/5.70 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X2 @ Y2 ) ) )
% 5.46/5.70 = ( ( W = X2 )
% 5.46/5.70 | ( Y2 = Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % crossproduct_eq
% 5.46/5.70 thf(fact_6555_crossproduct__eq,axiom,
% 5.46/5.70 ! [W: nat,Y2: nat,X2: nat,Z: nat] :
% 5.46/5.70 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y2 ) @ ( times_times_nat @ X2 @ Z ) )
% 5.46/5.70 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X2 @ Y2 ) ) )
% 5.46/5.70 = ( ( W = X2 )
% 5.46/5.70 | ( Y2 = Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % crossproduct_eq
% 5.46/5.70 thf(fact_6556_crossproduct__eq,axiom,
% 5.46/5.70 ! [W: int,Y2: int,X2: int,Z: int] :
% 5.46/5.70 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y2 ) @ ( times_times_int @ X2 @ Z ) )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X2 @ Y2 ) ) )
% 5.46/5.70 = ( ( W = X2 )
% 5.46/5.70 | ( Y2 = Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % crossproduct_eq
% 5.46/5.70 thf(fact_6557_infinite__int__iff__unbounded,axiom,
% 5.46/5.70 ! [S2: set_int] :
% 5.46/5.70 ( ( ~ ( finite_finite_int @ S2 ) )
% 5.46/5.70 = ( ! [M3: int] :
% 5.46/5.70 ? [N2: int] :
% 5.46/5.70 ( ( ord_less_int @ M3 @ ( abs_abs_int @ N2 ) )
% 5.46/5.70 & ( member_int @ N2 @ S2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % infinite_int_iff_unbounded
% 5.46/5.70 thf(fact_6558_mask__numeral,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 5.46/5.70 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_numeral
% 5.46/5.70 thf(fact_6559_mask__numeral,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 5.46/5.70 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_numeral
% 5.46/5.70 thf(fact_6560_num_Osize__gen_I3_J,axiom,
% 5.46/5.70 ! [X33: num] :
% 5.46/5.70 ( ( size_num @ ( bit1 @ X33 ) )
% 5.46/5.70 = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % num.size_gen(3)
% 5.46/5.70 thf(fact_6561_take__bit__rec,axiom,
% 5.46/5.70 ( bit_se1745604003318907178nteger
% 5.46/5.70 = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_rec
% 5.46/5.70 thf(fact_6562_take__bit__rec,axiom,
% 5.46/5.70 ( bit_se2923211474154528505it_int
% 5.46/5.70 = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_rec
% 5.46/5.70 thf(fact_6563_take__bit__rec,axiom,
% 5.46/5.70 ( bit_se2925701944663578781it_nat
% 5.46/5.70 = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_rec
% 5.46/5.70 thf(fact_6564_num_Osize__gen_I2_J,axiom,
% 5.46/5.70 ! [X23: num] :
% 5.46/5.70 ( ( size_num @ ( bit0 @ X23 ) )
% 5.46/5.70 = ( plus_plus_nat @ ( size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % num.size_gen(2)
% 5.46/5.70 thf(fact_6565_tanh__real__altdef,axiom,
% 5.46/5.70 ( tanh_real
% 5.46/5.70 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % tanh_real_altdef
% 5.46/5.70 thf(fact_6566_mask__nat__positive__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.70 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_nat_positive_iff
% 5.46/5.70 thf(fact_6567_take__bit__of__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_0
% 5.46/5.70 thf(fact_6568_take__bit__of__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_0
% 5.46/5.70 thf(fact_6569_exp__less__mono,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.70 => ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_less_mono
% 5.46/5.70 thf(fact_6570_exp__less__cancel__iff,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) )
% 5.46/5.70 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_less_cancel_iff
% 5.46/5.70 thf(fact_6571_exp__le__cancel__iff,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_le_cancel_iff
% 5.46/5.70 thf(fact_6572_concat__bit__of__zero__2,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % concat_bit_of_zero_2
% 5.46/5.70 thf(fact_6573_exp__zero,axiom,
% 5.46/5.70 ( ( exp_complex @ zero_zero_complex )
% 5.46/5.70 = one_one_complex ) ).
% 5.46/5.70
% 5.46/5.70 % exp_zero
% 5.46/5.70 thf(fact_6574_exp__zero,axiom,
% 5.46/5.70 ( ( exp_real @ zero_zero_real )
% 5.46/5.70 = one_one_real ) ).
% 5.46/5.70
% 5.46/5.70 % exp_zero
% 5.46/5.70 thf(fact_6575_take__bit__0,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_0
% 5.46/5.70 thf(fact_6576_take__bit__0,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_0
% 5.46/5.70 thf(fact_6577_take__bit__Suc__1,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_1
% 5.46/5.70 thf(fact_6578_take__bit__Suc__1,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 5.46/5.70 = one_one_nat ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_1
% 5.46/5.70 thf(fact_6579_take__bit__numeral__1,axiom,
% 5.46/5.70 ! [L2: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ one_one_int )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_1
% 5.46/5.70 thf(fact_6580_take__bit__numeral__1,axiom,
% 5.46/5.70 ! [L2: num] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ one_one_nat )
% 5.46/5.70 = one_one_nat ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_1
% 5.46/5.70 thf(fact_6581_mask__0,axiom,
% 5.46/5.70 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % mask_0
% 5.46/5.70 thf(fact_6582_mask__0,axiom,
% 5.46/5.70 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % mask_0
% 5.46/5.70 thf(fact_6583_mask__eq__0__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( bit_se2002935070580805687sk_nat @ N )
% 5.46/5.70 = zero_zero_nat )
% 5.46/5.70 = ( N = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_eq_0_iff
% 5.46/5.70 thf(fact_6584_mask__eq__0__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( bit_se2000444600071755411sk_int @ N )
% 5.46/5.70 = zero_zero_int )
% 5.46/5.70 = ( N = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_eq_0_iff
% 5.46/5.70 thf(fact_6585_exp__eq__one__iff,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ( exp_real @ X2 )
% 5.46/5.70 = one_one_real )
% 5.46/5.70 = ( X2 = zero_zero_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_eq_one_iff
% 5.46/5.70 thf(fact_6586_take__bit__of__1__eq__0__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.46/5.70 = zero_zero_int )
% 5.46/5.70 = ( N = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_1_eq_0_iff
% 5.46/5.70 thf(fact_6587_take__bit__of__1__eq__0__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.46/5.70 = zero_zero_nat )
% 5.46/5.70 = ( N = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_1_eq_0_iff
% 5.46/5.70 thf(fact_6588_mask__Suc__0,axiom,
% 5.46/5.70 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.46/5.70 = one_one_nat ) ).
% 5.46/5.70
% 5.46/5.70 % mask_Suc_0
% 5.46/5.70 thf(fact_6589_mask__Suc__0,axiom,
% 5.46/5.70 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % mask_Suc_0
% 5.46/5.70 thf(fact_6590_one__less__exp__iff,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_less_exp_iff
% 5.46/5.70 thf(fact_6591_exp__less__one__iff,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.46/5.70 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_less_one_iff
% 5.46/5.70 thf(fact_6592_one__le__exp__iff,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_le_exp_iff
% 5.46/5.70 thf(fact_6593_exp__le__one__iff,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_le_one_iff
% 5.46/5.70 thf(fact_6594_take__bit__minus__one__eq__mask,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.70 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_minus_one_eq_mask
% 5.46/5.70 thf(fact_6595_take__bit__minus__one__eq__mask,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_minus_one_eq_mask
% 5.46/5.70 thf(fact_6596_exp__ln__iff,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.46/5.70 = X2 )
% 5.46/5.70 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_ln_iff
% 5.46/5.70 thf(fact_6597_exp__ln,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.46/5.70 = X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_ln
% 5.46/5.70 thf(fact_6598_take__bit__of__Suc__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.70 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_Suc_0
% 5.46/5.70 thf(fact_6599_sum_Ocl__ivl__Suc,axiom,
% 5.46/5.70 ! [N: nat,M: nat,G: nat > complex] :
% 5.46/5.70 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = zero_zero_complex ) )
% 5.46/5.70 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.cl_ivl_Suc
% 5.46/5.70 thf(fact_6600_sum_Ocl__ivl__Suc,axiom,
% 5.46/5.70 ! [N: nat,M: nat,G: nat > rat] :
% 5.46/5.70 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = zero_zero_rat ) )
% 5.46/5.70 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.cl_ivl_Suc
% 5.46/5.70 thf(fact_6601_sum_Ocl__ivl__Suc,axiom,
% 5.46/5.70 ! [N: nat,M: nat,G: nat > int] :
% 5.46/5.70 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = zero_zero_int ) )
% 5.46/5.70 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.cl_ivl_Suc
% 5.46/5.70 thf(fact_6602_sum_Ocl__ivl__Suc,axiom,
% 5.46/5.70 ! [N: nat,M: nat,G: nat > nat] :
% 5.46/5.70 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = zero_zero_nat ) )
% 5.46/5.70 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.cl_ivl_Suc
% 5.46/5.70 thf(fact_6603_sum_Ocl__ivl__Suc,axiom,
% 5.46/5.70 ! [N: nat,M: nat,G: nat > real] :
% 5.46/5.70 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = zero_zero_real ) )
% 5.46/5.70 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.cl_ivl_Suc
% 5.46/5.70 thf(fact_6604_take__bit__of__1,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 5.46/5.70 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_1
% 5.46/5.70 thf(fact_6605_take__bit__of__1,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.46/5.70 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_1
% 5.46/5.70 thf(fact_6606_take__bit__of__1,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.46/5.70 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_1
% 5.46/5.70 thf(fact_6607_sum__zero__power,axiom,
% 5.46/5.70 ! [A2: set_nat,C: nat > complex] :
% 5.46/5.70 ( ( ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( C @ zero_zero_nat ) ) )
% 5.46/5.70 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = zero_zero_complex ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_zero_power
% 5.46/5.70 thf(fact_6608_sum__zero__power,axiom,
% 5.46/5.70 ! [A2: set_nat,C: nat > rat] :
% 5.46/5.70 ( ( ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( C @ zero_zero_nat ) ) )
% 5.46/5.70 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = zero_zero_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_zero_power
% 5.46/5.70 thf(fact_6609_sum__zero__power,axiom,
% 5.46/5.70 ! [A2: set_nat,C: nat > real] :
% 5.46/5.70 ( ( ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( C @ zero_zero_nat ) ) )
% 5.46/5.70 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = zero_zero_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_zero_power
% 5.46/5.70 thf(fact_6610_even__take__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,A: code_integer] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 5.46/5.70 = ( ( N = zero_zero_nat )
% 5.46/5.70 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_take_bit_eq
% 5.46/5.70 thf(fact_6611_even__take__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,A: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.46/5.70 = ( ( N = zero_zero_nat )
% 5.46/5.70 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_take_bit_eq
% 5.46/5.70 thf(fact_6612_even__take__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,A: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.46/5.70 = ( ( N = zero_zero_nat )
% 5.46/5.70 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_take_bit_eq
% 5.46/5.70 thf(fact_6613_sum__zero__power_H,axiom,
% 5.46/5.70 ! [A2: set_nat,C: nat > complex,D2: nat > complex] :
% 5.46/5.70 ( ( ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D2 @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.46/5.70 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D2 @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = zero_zero_complex ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_zero_power'
% 5.46/5.70 thf(fact_6614_sum__zero__power_H,axiom,
% 5.46/5.70 ! [A2: set_nat,C: nat > rat,D2: nat > rat] :
% 5.46/5.70 ( ( ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D2 @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.46/5.70 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D2 @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = zero_zero_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_zero_power'
% 5.46/5.70 thf(fact_6615_sum__zero__power_H,axiom,
% 5.46/5.70 ! [A2: set_nat,C: nat > real,D2: nat > real] :
% 5.46/5.70 ( ( ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D2 @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.46/5.70 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.46/5.70 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.70 => ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D2 @ I4 ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = zero_zero_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_zero_power'
% 5.46/5.70 thf(fact_6616_take__bit__Suc__0,axiom,
% 5.46/5.70 ! [A: code_integer] :
% 5.46/5.70 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.46/5.70 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_0
% 5.46/5.70 thf(fact_6617_take__bit__Suc__0,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.46/5.70 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_0
% 5.46/5.70 thf(fact_6618_take__bit__Suc__0,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.46/5.70 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_0
% 5.46/5.70 thf(fact_6619_take__bit__of__exp,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_exp
% 5.46/5.70 thf(fact_6620_take__bit__of__exp,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_exp
% 5.46/5.70 thf(fact_6621_take__bit__of__exp,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_exp
% 5.46/5.70 thf(fact_6622_take__bit__of__2,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.70 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_2
% 5.46/5.70 thf(fact_6623_take__bit__of__2,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.70 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_2
% 5.46/5.70 thf(fact_6624_take__bit__of__2,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_2
% 5.46/5.70 thf(fact_6625_of__int__mask__eq,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.70 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_int_mask_eq
% 5.46/5.70 thf(fact_6626_take__bit__of__int,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.46/5.70 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_int
% 5.46/5.70 thf(fact_6627_take__bit__add,axiom,
% 5.46/5.70 ! [N: nat,A: int,B: int] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_add
% 5.46/5.70 thf(fact_6628_take__bit__add,axiom,
% 5.46/5.70 ! [N: nat,A: nat,B: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 5.46/5.70 = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_add
% 5.46/5.70 thf(fact_6629_take__bit__tightened,axiom,
% 5.46/5.70 ! [N: nat,A: int,B: int,M: nat] :
% 5.46/5.70 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.46/5.70 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_tightened
% 5.46/5.70 thf(fact_6630_take__bit__tightened,axiom,
% 5.46/5.70 ! [N: nat,A: nat,B: nat,M: nat] :
% 5.46/5.70 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.46/5.70 = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 5.46/5.70 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.46/5.70 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_tightened
% 5.46/5.70 thf(fact_6631_take__bit__nat__less__eq__self,axiom,
% 5.46/5.70 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_nat_less_eq_self
% 5.46/5.70 thf(fact_6632_take__bit__tightened__less__eq__nat,axiom,
% 5.46/5.70 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_tightened_less_eq_nat
% 5.46/5.70 thf(fact_6633_exp__less__cancel,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) )
% 5.46/5.70 => ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_less_cancel
% 5.46/5.70 thf(fact_6634_take__bit__minus,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_minus
% 5.46/5.70 thf(fact_6635_exp__times__arg__commute,axiom,
% 5.46/5.70 ! [A2: complex] :
% 5.46/5.70 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.46/5.70 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_times_arg_commute
% 5.46/5.70 thf(fact_6636_exp__times__arg__commute,axiom,
% 5.46/5.70 ! [A2: real] :
% 5.46/5.70 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.46/5.70 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_times_arg_commute
% 5.46/5.70 thf(fact_6637_take__bit__mult,axiom,
% 5.46/5.70 ! [N: nat,K: int,L2: int] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_mult
% 5.46/5.70 thf(fact_6638_take__bit__diff,axiom,
% 5.46/5.70 ! [N: nat,K: int,L2: int] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_diff
% 5.46/5.70 thf(fact_6639_concat__bit__eq__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int,L2: int,R: int,S: int] :
% 5.46/5.70 ( ( ( bit_concat_bit @ N @ K @ L2 )
% 5.46/5.70 = ( bit_concat_bit @ N @ R @ S ) )
% 5.46/5.70 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ R ) )
% 5.46/5.70 & ( L2 = S ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % concat_bit_eq_iff
% 5.46/5.70 thf(fact_6640_concat__bit__take__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,B: int] :
% 5.46/5.70 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.46/5.70 = ( bit_concat_bit @ N @ B ) ) ).
% 5.46/5.70
% 5.46/5.70 % concat_bit_take_bit_eq
% 5.46/5.70 thf(fact_6641_less__eq__mask,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_eq_mask
% 5.46/5.70 thf(fact_6642_take__bit__eq__mask__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.70 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.70 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.46/5.70 = zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_mask_iff
% 5.46/5.70 thf(fact_6643_exp__total,axiom,
% 5.46/5.70 ! [Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.70 => ? [X3: real] :
% 5.46/5.70 ( ( exp_real @ X3 )
% 5.46/5.70 = Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_total
% 5.46/5.70 thf(fact_6644_exp__gt__zero,axiom,
% 5.46/5.70 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_gt_zero
% 5.46/5.70 thf(fact_6645_not__exp__less__zero,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ~ ( ord_less_real @ ( exp_real @ X2 ) @ zero_zero_real ) ).
% 5.46/5.70
% 5.46/5.70 % not_exp_less_zero
% 5.46/5.70 thf(fact_6646_not__exp__le__zero,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ~ ( ord_less_eq_real @ ( exp_real @ X2 ) @ zero_zero_real ) ).
% 5.46/5.70
% 5.46/5.70 % not_exp_le_zero
% 5.46/5.70 thf(fact_6647_exp__ge__zero,axiom,
% 5.46/5.70 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_ge_zero
% 5.46/5.70 thf(fact_6648_sum__cong__Suc,axiom,
% 5.46/5.70 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.46/5.70 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.46/5.70 => ( ! [X3: nat] :
% 5.46/5.70 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.46/5.70 => ( ( F @ ( suc @ X3 ) )
% 5.46/5.70 = ( G @ ( suc @ X3 ) ) ) )
% 5.46/5.70 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.46/5.70 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_cong_Suc
% 5.46/5.70 thf(fact_6649_sum__cong__Suc,axiom,
% 5.46/5.70 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.46/5.70 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.46/5.70 => ( ! [X3: nat] :
% 5.46/5.70 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.46/5.70 => ( ( F @ ( suc @ X3 ) )
% 5.46/5.70 = ( G @ ( suc @ X3 ) ) ) )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.46/5.70 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_cong_Suc
% 5.46/5.70 thf(fact_6650_take__bit__tightened__less__eq__int,axiom,
% 5.46/5.70 ! [M: nat,N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_tightened_less_eq_int
% 5.46/5.70 thf(fact_6651_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,A: int,B: int] :
% 5.46/5.70 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.46/5.70 = ( bit_ri631733984087533419it_int @ N @ B ) )
% 5.46/5.70 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % signed_take_bit_eq_iff_take_bit_eq
% 5.46/5.70 thf(fact_6652_take__bit__nonnegative,axiom,
% 5.46/5.70 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_nonnegative
% 5.46/5.70 thf(fact_6653_take__bit__int__less__eq__self__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.46/5.70 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_less_eq_self_iff
% 5.46/5.70 thf(fact_6654_not__take__bit__negative,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % not_take_bit_negative
% 5.46/5.70 thf(fact_6655_take__bit__int__greater__self__iff,axiom,
% 5.46/5.70 ! [K: int,N: nat] :
% 5.46/5.70 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.46/5.70 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_greater_self_iff
% 5.46/5.70 thf(fact_6656_signed__take__bit__take__bit,axiom,
% 5.46/5.70 ! [M: nat,N: nat,A: int] :
% 5.46/5.70 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.46/5.70 = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % signed_take_bit_take_bit
% 5.46/5.70 thf(fact_6657_mult__exp__exp,axiom,
% 5.46/5.70 ! [X2: complex,Y2: complex] :
% 5.46/5.70 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y2 ) )
% 5.46/5.70 = ( exp_complex @ ( plus_plus_complex @ X2 @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mult_exp_exp
% 5.46/5.70 thf(fact_6658_mult__exp__exp,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) )
% 5.46/5.70 = ( exp_real @ ( plus_plus_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mult_exp_exp
% 5.46/5.70 thf(fact_6659_exp__add__commuting,axiom,
% 5.46/5.70 ! [X2: complex,Y2: complex] :
% 5.46/5.70 ( ( ( times_times_complex @ X2 @ Y2 )
% 5.46/5.70 = ( times_times_complex @ Y2 @ X2 ) )
% 5.46/5.70 => ( ( exp_complex @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.46/5.70 = ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_add_commuting
% 5.46/5.70 thf(fact_6660_exp__add__commuting,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ( times_times_real @ X2 @ Y2 )
% 5.46/5.70 = ( times_times_real @ Y2 @ X2 ) )
% 5.46/5.70 => ( ( exp_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.46/5.70 = ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_add_commuting
% 5.46/5.70 thf(fact_6661_exp__diff,axiom,
% 5.46/5.70 ! [X2: complex,Y2: complex] :
% 5.46/5.70 ( ( exp_complex @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.46/5.70 = ( divide1717551699836669952omplex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_diff
% 5.46/5.70 thf(fact_6662_exp__diff,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( exp_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.46/5.70 = ( divide_divide_real @ ( exp_real @ X2 ) @ ( exp_real @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_diff
% 5.46/5.70 thf(fact_6663_take__bit__unset__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,M: nat,A: int] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.46/5.70 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_unset_bit_eq
% 5.46/5.70 thf(fact_6664_take__bit__unset__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,M: nat,A: nat] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.46/5.70 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.46/5.70 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_unset_bit_eq
% 5.46/5.70 thf(fact_6665_take__bit__set__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,M: nat,A: int] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.46/5.70 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_set_bit_eq
% 5.46/5.70 thf(fact_6666_take__bit__set__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,M: nat,A: nat] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.46/5.70 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.46/5.70 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_set_bit_eq
% 5.46/5.70 thf(fact_6667_take__bit__flip__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,M: nat,A: int] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.46/5.70 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_flip_bit_eq
% 5.46/5.70 thf(fact_6668_take__bit__flip__bit__eq,axiom,
% 5.46/5.70 ! [N: nat,M: nat,A: nat] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.46/5.70 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.46/5.70 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_flip_bit_eq
% 5.46/5.70 thf(fact_6669_sum__subtractf__nat,axiom,
% 5.46/5.70 ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 5.46/5.70 ( ! [X3: product_prod_nat_nat] :
% 5.46/5.70 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.46/5.70 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ( groups977919841031483927at_nat
% 5.46/5.70 @ ^ [X: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_subtractf_nat
% 5.46/5.70 thf(fact_6670_sum__subtractf__nat,axiom,
% 5.46/5.70 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.46/5.70 ( ! [X3: complex] :
% 5.46/5.70 ( ( member_complex @ X3 @ A2 )
% 5.46/5.70 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ( groups5693394587270226106ex_nat
% 5.46/5.70 @ ^ [X: complex] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_subtractf_nat
% 5.46/5.70 thf(fact_6671_sum__subtractf__nat,axiom,
% 5.46/5.70 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.46/5.70 ( ! [X3: real] :
% 5.46/5.70 ( ( member_real @ X3 @ A2 )
% 5.46/5.70 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ( groups1935376822645274424al_nat
% 5.46/5.70 @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_subtractf_nat
% 5.46/5.70 thf(fact_6672_sum__subtractf__nat,axiom,
% 5.46/5.70 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.46/5.70 ( ! [X3: int] :
% 5.46/5.70 ( ( member_int @ X3 @ A2 )
% 5.46/5.70 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ( groups4541462559716669496nt_nat
% 5.46/5.70 @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_subtractf_nat
% 5.46/5.70 thf(fact_6673_sum__subtractf__nat,axiom,
% 5.46/5.70 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.46/5.70 ( ! [X3: nat] :
% 5.46/5.70 ( ( member_nat @ X3 @ A2 )
% 5.46/5.70 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.46/5.70 => ( ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.70 @ A2 )
% 5.46/5.70 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_subtractf_nat
% 5.46/5.70 thf(fact_6674_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.46/5.70 ! [G: nat > nat,M: nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.46/5.70 = ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.shift_bounds_cl_Suc_ivl
% 5.46/5.70 thf(fact_6675_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.46/5.70 ! [G: nat > real,M: nat,N: nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.46/5.70 = ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.shift_bounds_cl_Suc_ivl
% 5.46/5.70 thf(fact_6676_mask__nonnegative__int,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_nonnegative_int
% 5.46/5.70 thf(fact_6677_not__mask__negative__int,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % not_mask_negative_int
% 5.46/5.70 thf(fact_6678_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.46/5.70 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.46/5.70 = ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.shift_bounds_cl_nat_ivl
% 5.46/5.70 thf(fact_6679_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.46/5.70 ! [G: nat > real,M: nat,K: nat,N: nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.46/5.70 = ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.shift_bounds_cl_nat_ivl
% 5.46/5.70 thf(fact_6680_sum__eq__Suc0__iff,axiom,
% 5.46/5.70 ! [A2: set_int,F: int > nat] :
% 5.46/5.70 ( ( finite_finite_int @ A2 )
% 5.46/5.70 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.46/5.70 = ( suc @ zero_zero_nat ) )
% 5.46/5.70 = ( ? [X: int] :
% 5.46/5.70 ( ( member_int @ X @ A2 )
% 5.46/5.70 & ( ( F @ X )
% 5.46/5.70 = ( suc @ zero_zero_nat ) )
% 5.46/5.70 & ! [Y: int] :
% 5.46/5.70 ( ( member_int @ Y @ A2 )
% 5.46/5.70 => ( ( X != Y )
% 5.46/5.70 => ( ( F @ Y )
% 5.46/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_eq_Suc0_iff
% 5.46/5.70 thf(fact_6681_sum__eq__Suc0__iff,axiom,
% 5.46/5.70 ! [A2: set_complex,F: complex > nat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.70 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.46/5.70 = ( suc @ zero_zero_nat ) )
% 5.46/5.70 = ( ? [X: complex] :
% 5.46/5.70 ( ( member_complex @ X @ A2 )
% 5.46/5.70 & ( ( F @ X )
% 5.46/5.70 = ( suc @ zero_zero_nat ) )
% 5.46/5.70 & ! [Y: complex] :
% 5.46/5.70 ( ( member_complex @ Y @ A2 )
% 5.46/5.70 => ( ( X != Y )
% 5.46/5.70 => ( ( F @ Y )
% 5.46/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_eq_Suc0_iff
% 5.46/5.70 thf(fact_6682_sum__eq__Suc0__iff,axiom,
% 5.46/5.70 ! [A2: set_nat,F: nat > nat] :
% 5.46/5.70 ( ( finite_finite_nat @ A2 )
% 5.46/5.70 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.46/5.70 = ( suc @ zero_zero_nat ) )
% 5.46/5.70 = ( ? [X: nat] :
% 5.46/5.70 ( ( member_nat @ X @ A2 )
% 5.46/5.70 & ( ( F @ X )
% 5.46/5.70 = ( suc @ zero_zero_nat ) )
% 5.46/5.70 & ! [Y: nat] :
% 5.46/5.70 ( ( member_nat @ Y @ A2 )
% 5.46/5.70 => ( ( X != Y )
% 5.46/5.70 => ( ( F @ Y )
% 5.46/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_eq_Suc0_iff
% 5.46/5.70 thf(fact_6683_sum__SucD,axiom,
% 5.46/5.70 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.46/5.70 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.46/5.70 = ( suc @ N ) )
% 5.46/5.70 => ? [X3: nat] :
% 5.46/5.70 ( ( member_nat @ X3 @ A2 )
% 5.46/5.70 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_SucD
% 5.46/5.70 thf(fact_6684_sum__eq__1__iff,axiom,
% 5.46/5.70 ! [A2: set_int,F: int > nat] :
% 5.46/5.70 ( ( finite_finite_int @ A2 )
% 5.46/5.70 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.46/5.70 = one_one_nat )
% 5.46/5.70 = ( ? [X: int] :
% 5.46/5.70 ( ( member_int @ X @ A2 )
% 5.46/5.70 & ( ( F @ X )
% 5.46/5.70 = one_one_nat )
% 5.46/5.70 & ! [Y: int] :
% 5.46/5.70 ( ( member_int @ Y @ A2 )
% 5.46/5.70 => ( ( X != Y )
% 5.46/5.70 => ( ( F @ Y )
% 5.46/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_eq_1_iff
% 5.46/5.70 thf(fact_6685_sum__eq__1__iff,axiom,
% 5.46/5.70 ! [A2: set_complex,F: complex > nat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.70 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.46/5.70 = one_one_nat )
% 5.46/5.70 = ( ? [X: complex] :
% 5.46/5.70 ( ( member_complex @ X @ A2 )
% 5.46/5.70 & ( ( F @ X )
% 5.46/5.70 = one_one_nat )
% 5.46/5.70 & ! [Y: complex] :
% 5.46/5.70 ( ( member_complex @ Y @ A2 )
% 5.46/5.70 => ( ( X != Y )
% 5.46/5.70 => ( ( F @ Y )
% 5.46/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_eq_1_iff
% 5.46/5.70 thf(fact_6686_sum__eq__1__iff,axiom,
% 5.46/5.70 ! [A2: set_nat,F: nat > nat] :
% 5.46/5.70 ( ( finite_finite_nat @ A2 )
% 5.46/5.70 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.46/5.70 = one_one_nat )
% 5.46/5.70 = ( ? [X: nat] :
% 5.46/5.70 ( ( member_nat @ X @ A2 )
% 5.46/5.70 & ( ( F @ X )
% 5.46/5.70 = one_one_nat )
% 5.46/5.70 & ! [Y: nat] :
% 5.46/5.70 ( ( member_nat @ Y @ A2 )
% 5.46/5.70 => ( ( X != Y )
% 5.46/5.70 => ( ( F @ Y )
% 5.46/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_eq_1_iff
% 5.46/5.70 thf(fact_6687_exp__gt__one,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_gt_one
% 5.46/5.70 thf(fact_6688_take__bit__signed__take__bit,axiom,
% 5.46/5.70 ! [M: nat,N: nat,A: int] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 5.46/5.70 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_signed_take_bit
% 5.46/5.70 thf(fact_6689_exp__ge__add__one__self,axiom,
% 5.46/5.70 ! [X2: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_ge_add_one_self
% 5.46/5.70 thf(fact_6690_exp__minus__inverse,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) )
% 5.46/5.70 = one_one_real ) ).
% 5.46/5.70
% 5.46/5.70 % exp_minus_inverse
% 5.46/5.70 thf(fact_6691_exp__minus__inverse,axiom,
% 5.46/5.70 ! [X2: complex] :
% 5.46/5.70 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) )
% 5.46/5.70 = one_one_complex ) ).
% 5.46/5.70
% 5.46/5.70 % exp_minus_inverse
% 5.46/5.70 thf(fact_6692_take__bit__decr__eq,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.70 != zero_zero_int )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.46/5.70 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_decr_eq
% 5.46/5.70 thf(fact_6693_sum__power__add,axiom,
% 5.46/5.70 ! [X2: complex,M: nat,I5: set_nat] :
% 5.46/5.70 ( ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 = ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ I5 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power_add
% 5.46/5.70 thf(fact_6694_sum__power__add,axiom,
% 5.46/5.70 ! [X2: rat,M: nat,I5: set_nat] :
% 5.46/5.70 ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 = ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ I5 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power_add
% 5.46/5.70 thf(fact_6695_sum__power__add,axiom,
% 5.46/5.70 ! [X2: int,M: nat,I5: set_nat] :
% 5.46/5.70 ( ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 = ( times_times_int @ ( power_power_int @ X2 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ I5 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power_add
% 5.46/5.70 thf(fact_6696_sum__power__add,axiom,
% 5.46/5.70 ! [X2: real,M: nat,I5: set_nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.46/5.70 @ I5 )
% 5.46/5.70 = ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ I5 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power_add
% 5.46/5.70 thf(fact_6697_sum_OatLeastAtMost__rev,axiom,
% 5.46/5.70 ! [G: nat > nat,N: nat,M: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.46/5.70 = ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeastAtMost_rev
% 5.46/5.70 thf(fact_6698_sum_OatLeastAtMost__rev,axiom,
% 5.46/5.70 ! [G: nat > real,N: nat,M: nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.46/5.70 = ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeastAtMost_rev
% 5.46/5.70 thf(fact_6699_less__mask,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.70 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_mask
% 5.46/5.70 thf(fact_6700_sum__nth__roots,axiom,
% 5.46/5.70 ! [N: nat,C: complex] :
% 5.46/5.70 ( ( ord_less_nat @ one_one_nat @ N )
% 5.46/5.70 => ( ( groups7754918857620584856omplex
% 5.46/5.70 @ ^ [X: complex] : X
% 5.46/5.70 @ ( collect_complex
% 5.46/5.70 @ ^ [Z4: complex] :
% 5.46/5.70 ( ( power_power_complex @ Z4 @ N )
% 5.46/5.70 = C ) ) )
% 5.46/5.70 = zero_zero_complex ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_nth_roots
% 5.46/5.70 thf(fact_6701_sum__roots__unity,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ one_one_nat @ N )
% 5.46/5.70 => ( ( groups7754918857620584856omplex
% 5.46/5.70 @ ^ [X: complex] : X
% 5.46/5.70 @ ( collect_complex
% 5.46/5.70 @ ^ [Z4: complex] :
% 5.46/5.70 ( ( power_power_complex @ Z4 @ N )
% 5.46/5.70 = one_one_complex ) ) )
% 5.46/5.70 = zero_zero_complex ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_roots_unity
% 5.46/5.70 thf(fact_6702_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.70 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.70 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_mask_iff_exp_dvd
% 5.46/5.70 thf(fact_6703_sum__diff__nat,axiom,
% 5.46/5.70 ! [B3: set_int,A2: set_int,F: int > nat] :
% 5.46/5.70 ( ( finite_finite_int @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.46/5.70 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff_nat
% 5.46/5.70 thf(fact_6704_sum__diff__nat,axiom,
% 5.46/5.70 ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 5.46/5.70 ( ( finite3207457112153483333omplex @ B3 )
% 5.46/5.70 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.46/5.70 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff_nat
% 5.46/5.70 thf(fact_6705_sum__diff__nat,axiom,
% 5.46/5.70 ! [B3: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.46/5.70 ( ( finite6177210948735845034at_nat @ B3 )
% 5.46/5.70 => ( ( ord_le3146513528884898305at_nat @ B3 @ A2 )
% 5.46/5.70 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff_nat
% 5.46/5.70 thf(fact_6706_sum__diff__nat,axiom,
% 5.46/5.70 ! [B3: set_nat,A2: set_nat,F: nat > nat] :
% 5.46/5.70 ( ( finite_finite_nat @ B3 )
% 5.46/5.70 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.46/5.70 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.46/5.70 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff_nat
% 5.46/5.70 thf(fact_6707_exp__ge__add__one__self__aux,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_ge_add_one_self_aux
% 5.46/5.70 thf(fact_6708_sum__shift__lb__Suc0__0,axiom,
% 5.46/5.70 ! [F: nat > complex,K: nat] :
% 5.46/5.70 ( ( ( F @ zero_zero_nat )
% 5.46/5.70 = zero_zero_complex )
% 5.46/5.70 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.46/5.70 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_shift_lb_Suc0_0
% 5.46/5.70 thf(fact_6709_sum__shift__lb__Suc0__0,axiom,
% 5.46/5.70 ! [F: nat > rat,K: nat] :
% 5.46/5.70 ( ( ( F @ zero_zero_nat )
% 5.46/5.70 = zero_zero_rat )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.46/5.70 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_shift_lb_Suc0_0
% 5.46/5.70 thf(fact_6710_sum__shift__lb__Suc0__0,axiom,
% 5.46/5.70 ! [F: nat > int,K: nat] :
% 5.46/5.70 ( ( ( F @ zero_zero_nat )
% 5.46/5.70 = zero_zero_int )
% 5.46/5.70 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.46/5.70 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_shift_lb_Suc0_0
% 5.46/5.70 thf(fact_6711_sum__shift__lb__Suc0__0,axiom,
% 5.46/5.70 ! [F: nat > nat,K: nat] :
% 5.46/5.70 ( ( ( F @ zero_zero_nat )
% 5.46/5.70 = zero_zero_nat )
% 5.46/5.70 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.46/5.70 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_shift_lb_Suc0_0
% 5.46/5.70 thf(fact_6712_sum__shift__lb__Suc0__0,axiom,
% 5.46/5.70 ! [F: nat > real,K: nat] :
% 5.46/5.70 ( ( ( F @ zero_zero_nat )
% 5.46/5.70 = zero_zero_real )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.46/5.70 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_shift_lb_Suc0_0
% 5.46/5.70 thf(fact_6713_sum_OatLeast0__atMost__Suc,axiom,
% 5.46/5.70 ! [G: nat > rat,N: nat] :
% 5.46/5.70 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeast0_atMost_Suc
% 5.46/5.70 thf(fact_6714_sum_OatLeast0__atMost__Suc,axiom,
% 5.46/5.70 ! [G: nat > int,N: nat] :
% 5.46/5.70 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeast0_atMost_Suc
% 5.46/5.70 thf(fact_6715_sum_OatLeast0__atMost__Suc,axiom,
% 5.46/5.70 ! [G: nat > nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeast0_atMost_Suc
% 5.46/5.70 thf(fact_6716_sum_OatLeast0__atMost__Suc,axiom,
% 5.46/5.70 ! [G: nat > real,N: nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeast0_atMost_Suc
% 5.46/5.70 thf(fact_6717_lemma__exp__total,axiom,
% 5.46/5.70 ! [Y2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ one_one_real @ Y2 )
% 5.46/5.70 => ? [X3: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.70 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y2 @ one_one_real ) )
% 5.46/5.70 & ( ( exp_real @ X3 )
% 5.46/5.70 = Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lemma_exp_total
% 5.46/5.70 thf(fact_6718_sum_OatLeast__Suc__atMost,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > rat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeast_Suc_atMost
% 5.46/5.70 thf(fact_6719_sum_OatLeast__Suc__atMost,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > int] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeast_Suc_atMost
% 5.46/5.70 thf(fact_6720_sum_OatLeast__Suc__atMost,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeast_Suc_atMost
% 5.46/5.70 thf(fact_6721_sum_OatLeast__Suc__atMost,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > real] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.atLeast_Suc_atMost
% 5.46/5.70 thf(fact_6722_sum_Onat__ivl__Suc_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > rat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.nat_ivl_Suc'
% 5.46/5.70 thf(fact_6723_sum_Onat__ivl__Suc_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > int] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.70 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.nat_ivl_Suc'
% 5.46/5.70 thf(fact_6724_sum_Onat__ivl__Suc_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.70 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.nat_ivl_Suc'
% 5.46/5.70 thf(fact_6725_sum_Onat__ivl__Suc_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > real] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.nat_ivl_Suc'
% 5.46/5.70 thf(fact_6726_ln__ge__iff,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ Y2 @ ( ln_ln_real @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_real @ ( exp_real @ Y2 ) @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ln_ge_iff
% 5.46/5.70 thf(fact_6727_ln__x__over__x__mono,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.70 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y2 ) @ Y2 ) @ ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ln_x_over_x_mono
% 5.46/5.70 thf(fact_6728_sum_OSuc__reindex__ivl,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > rat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_rat @ ( G @ M )
% 5.46/5.70 @ ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.Suc_reindex_ivl
% 5.46/5.70 thf(fact_6729_sum_OSuc__reindex__ivl,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > int] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( G @ M )
% 5.46/5.70 @ ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.Suc_reindex_ivl
% 5.46/5.70 thf(fact_6730_sum_OSuc__reindex__ivl,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( G @ M )
% 5.46/5.70 @ ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.Suc_reindex_ivl
% 5.46/5.70 thf(fact_6731_sum_OSuc__reindex__ivl,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > real] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_real @ ( G @ M )
% 5.46/5.70 @ ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.Suc_reindex_ivl
% 5.46/5.70 thf(fact_6732_sum__Suc__diff,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > rat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_Suc_diff
% 5.46/5.70 thf(fact_6733_sum__Suc__diff,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > int] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.70 => ( ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_Suc_diff
% 5.46/5.70 thf(fact_6734_sum__Suc__diff,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > real] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.70 => ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_Suc_diff
% 5.46/5.70 thf(fact_6735_take__bit__Suc__bit0,axiom,
% 5.46/5.70 ! [N: nat,K: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.46/5.70 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_bit0
% 5.46/5.70 thf(fact_6736_take__bit__Suc__bit0,axiom,
% 5.46/5.70 ! [N: nat,K: num] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.70 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_bit0
% 5.46/5.70 thf(fact_6737_take__bit__eq__mod,axiom,
% 5.46/5.70 ( bit_se1745604003318907178nteger
% 5.46/5.70 = ( ^ [N2: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_mod
% 5.46/5.70 thf(fact_6738_take__bit__eq__mod,axiom,
% 5.46/5.70 ( bit_se2923211474154528505it_int
% 5.46/5.70 = ( ^ [N2: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_mod
% 5.46/5.70 thf(fact_6739_take__bit__eq__mod,axiom,
% 5.46/5.70 ( bit_se2925701944663578781it_nat
% 5.46/5.70 = ( ^ [N2: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_mod
% 5.46/5.70 thf(fact_6740_take__bit__nat__eq__self,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.46/5.70 = M ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_nat_eq_self
% 5.46/5.70 thf(fact_6741_take__bit__nat__less__exp,axiom,
% 5.46/5.70 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_nat_less_exp
% 5.46/5.70 thf(fact_6742_take__bit__nat__eq__self__iff,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.46/5.70 = M )
% 5.46/5.70 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_nat_eq_self_iff
% 5.46/5.70 thf(fact_6743_take__bit__nat__def,axiom,
% 5.46/5.70 ( bit_se2925701944663578781it_nat
% 5.46/5.70 = ( ^ [N2: nat,M3: nat] : ( modulo_modulo_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_nat_def
% 5.46/5.70 thf(fact_6744_exp__le,axiom,
% 5.46/5.70 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_le
% 5.46/5.70 thf(fact_6745_sum_Oub__add__nat,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > rat,P2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.46/5.70 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.ub_add_nat
% 5.46/5.70 thf(fact_6746_sum_Oub__add__nat,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > int,P2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.46/5.70 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.ub_add_nat
% 5.46/5.70 thf(fact_6747_sum_Oub__add__nat,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > nat,P2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.46/5.70 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.ub_add_nat
% 5.46/5.70 thf(fact_6748_sum_Oub__add__nat,axiom,
% 5.46/5.70 ! [M: nat,N: nat,G: nat > real,P2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.46/5.70 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.ub_add_nat
% 5.46/5.70 thf(fact_6749_take__bit__int__less__exp,axiom,
% 5.46/5.70 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_less_exp
% 5.46/5.70 thf(fact_6750_take__bit__int__def,axiom,
% 5.46/5.70 ( bit_se2923211474154528505it_int
% 5.46/5.70 = ( ^ [N2: nat,K2: int] : ( modulo_modulo_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_def
% 5.46/5.70 thf(fact_6751_set__encode__def,axiom,
% 5.46/5.70 ( nat_set_encode
% 5.46/5.70 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % set_encode_def
% 5.46/5.70 thf(fact_6752_tanh__altdef,axiom,
% 5.46/5.70 ( tanh_real
% 5.46/5.70 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % tanh_altdef
% 5.46/5.70 thf(fact_6753_tanh__altdef,axiom,
% 5.46/5.70 ( tanh_complex
% 5.46/5.70 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % tanh_altdef
% 5.46/5.70 thf(fact_6754_num_Osize__gen_I1_J,axiom,
% 5.46/5.70 ( ( size_num @ one )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % num.size_gen(1)
% 5.46/5.70 thf(fact_6755_take__bit__eq__0__iff,axiom,
% 5.46/5.70 ! [N: nat,A: code_integer] :
% 5.46/5.70 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.46/5.70 = zero_z3403309356797280102nteger )
% 5.46/5.70 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_0_iff
% 5.46/5.70 thf(fact_6756_take__bit__eq__0__iff,axiom,
% 5.46/5.70 ! [N: nat,A: int] :
% 5.46/5.70 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.46/5.70 = zero_zero_int )
% 5.46/5.70 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_0_iff
% 5.46/5.70 thf(fact_6757_take__bit__eq__0__iff,axiom,
% 5.46/5.70 ! [N: nat,A: nat] :
% 5.46/5.70 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.46/5.70 = zero_zero_nat )
% 5.46/5.70 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_0_iff
% 5.46/5.70 thf(fact_6758_take__bit__numeral__bit0,axiom,
% 5.46/5.70 ! [L2: num,K: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.46/5.70 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_bit0
% 5.46/5.70 thf(fact_6759_take__bit__numeral__bit0,axiom,
% 5.46/5.70 ! [L2: num,K: num] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.70 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_bit0
% 5.46/5.70 thf(fact_6760_take__bit__nat__less__self__iff,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.46/5.70 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_nat_less_self_iff
% 5.46/5.70 thf(fact_6761_Suc__mask__eq__exp,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.70 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % Suc_mask_eq_exp
% 5.46/5.70 thf(fact_6762_mask__nat__less__exp,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_nat_less_exp
% 5.46/5.70 thf(fact_6763_exp__half__le2,axiom,
% 5.46/5.70 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_half_le2
% 5.46/5.70 thf(fact_6764_take__bit__Suc__minus__bit0,axiom,
% 5.46/5.70 ! [N: nat,K: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.70 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_minus_bit0
% 5.46/5.70 thf(fact_6765_take__bit__int__greater__eq__self__iff,axiom,
% 5.46/5.70 ! [K: int,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.46/5.70 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_greater_eq_self_iff
% 5.46/5.70 thf(fact_6766_take__bit__int__less__self__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.46/5.70 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_less_self_iff
% 5.46/5.70 thf(fact_6767_exp__double,axiom,
% 5.46/5.70 ! [Z: complex] :
% 5.46/5.70 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.46/5.70 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_double
% 5.46/5.70 thf(fact_6768_exp__double,axiom,
% 5.46/5.70 ! [Z: real] :
% 5.46/5.70 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.46/5.70 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_double
% 5.46/5.70 thf(fact_6769_sum__natinterval__diff,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > complex] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = zero_zero_complex ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_natinterval_diff
% 5.46/5.70 thf(fact_6770_sum__natinterval__diff,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > rat] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = zero_zero_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_natinterval_diff
% 5.46/5.70 thf(fact_6771_sum__natinterval__diff,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > int] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = zero_zero_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_natinterval_diff
% 5.46/5.70 thf(fact_6772_sum__natinterval__diff,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > real] :
% 5.46/5.70 ( ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = zero_zero_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_natinterval_diff
% 5.46/5.70 thf(fact_6773_sum__telescope_H_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > rat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.46/5.70 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_telescope''
% 5.46/5.70 thf(fact_6774_sum__telescope_H_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > int] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.46/5.70 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_telescope''
% 5.46/5.70 thf(fact_6775_sum__telescope_H_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat,F: nat > real] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.46/5.70 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_telescope''
% 5.46/5.70 thf(fact_6776_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 5.46/5.70 = ( N = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % semiring_bit_operations_class.even_mask_iff
% 5.46/5.70 thf(fact_6777_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.70 = ( N = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % semiring_bit_operations_class.even_mask_iff
% 5.46/5.70 thf(fact_6778_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.70 = ( N = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % semiring_bit_operations_class.even_mask_iff
% 5.46/5.70 thf(fact_6779_take__bit__int__eq__self,axiom,
% 5.46/5.70 ! [K: int,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.70 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.70 = K ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_eq_self
% 5.46/5.70 thf(fact_6780_take__bit__int__eq__self__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.70 = K )
% 5.46/5.70 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.70 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_eq_self_iff
% 5.46/5.70 thf(fact_6781_mask__nat__def,axiom,
% 5.46/5.70 ( bit_se2002935070580805687sk_nat
% 5.46/5.70 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_nat_def
% 5.46/5.70 thf(fact_6782_mask__half__int,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.70 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_half_int
% 5.46/5.70 thf(fact_6783_take__bit__numeral__minus__bit0,axiom,
% 5.46/5.70 ! [L2: num,K: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.70 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_minus_bit0
% 5.46/5.70 thf(fact_6784_take__bit__incr__eq,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.70 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.46/5.70 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_incr_eq
% 5.46/5.70 thf(fact_6785_mask__eq__sum__exp,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.46/5.70 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.70 @ ( collect_nat
% 5.46/5.70 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_eq_sum_exp
% 5.46/5.70 thf(fact_6786_mask__eq__sum__exp,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.46/5.70 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 @ ( collect_nat
% 5.46/5.70 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_eq_sum_exp
% 5.46/5.70 thf(fact_6787_mask__int__def,axiom,
% 5.46/5.70 ( bit_se2000444600071755411sk_int
% 5.46/5.70 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_int_def
% 5.46/5.70 thf(fact_6788_sum__gp__multiplied,axiom,
% 5.46/5.70 ! [M: nat,N: nat,X2: complex] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.46/5.70 = ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp_multiplied
% 5.46/5.70 thf(fact_6789_sum__gp__multiplied,axiom,
% 5.46/5.70 ! [M: nat,N: nat,X2: rat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.46/5.70 = ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp_multiplied
% 5.46/5.70 thf(fact_6790_sum__gp__multiplied,axiom,
% 5.46/5.70 ! [M: nat,N: nat,X2: int] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.46/5.70 = ( minus_minus_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp_multiplied
% 5.46/5.70 thf(fact_6791_sum__gp__multiplied,axiom,
% 5.46/5.70 ! [M: nat,N: nat,X2: real] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.46/5.70 = ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp_multiplied
% 5.46/5.70 thf(fact_6792_sum_Oin__pairs,axiom,
% 5.46/5.70 ! [G: nat > rat,M: nat,N: nat] :
% 5.46/5.70 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.70 = ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.in_pairs
% 5.46/5.70 thf(fact_6793_sum_Oin__pairs,axiom,
% 5.46/5.70 ! [G: nat > int,M: nat,N: nat] :
% 5.46/5.70 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.70 = ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.in_pairs
% 5.46/5.70 thf(fact_6794_sum_Oin__pairs,axiom,
% 5.46/5.70 ! [G: nat > nat,M: nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.70 = ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.in_pairs
% 5.46/5.70 thf(fact_6795_sum_Oin__pairs,axiom,
% 5.46/5.70 ! [G: nat > real,M: nat,N: nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.70 = ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.in_pairs
% 5.46/5.70 thf(fact_6796_take__bit__Suc__minus__1__eq,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.70 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_minus_1_eq
% 5.46/5.70 thf(fact_6797_take__bit__Suc__minus__1__eq,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_minus_1_eq
% 5.46/5.70 thf(fact_6798_take__bit__Suc__bit1,axiom,
% 5.46/5.70 ! [N: nat,K: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_bit1
% 5.46/5.70 thf(fact_6799_take__bit__Suc__bit1,axiom,
% 5.46/5.70 ! [N: nat,K: num] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_bit1
% 5.46/5.70 thf(fact_6800_take__bit__numeral__minus__1__eq,axiom,
% 5.46/5.70 ! [K: num] :
% 5.46/5.70 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.70 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_minus_1_eq
% 5.46/5.70 thf(fact_6801_take__bit__numeral__minus__1__eq,axiom,
% 5.46/5.70 ! [K: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_minus_1_eq
% 5.46/5.70 thf(fact_6802_take__bit__Suc,axiom,
% 5.46/5.70 ! [N: nat,A: code_integer] :
% 5.46/5.70 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 5.46/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc
% 5.46/5.70 thf(fact_6803_take__bit__Suc,axiom,
% 5.46/5.70 ! [N: nat,A: int] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc
% 5.46/5.70 thf(fact_6804_take__bit__Suc,axiom,
% 5.46/5.70 ! [N: nat,A: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 5.46/5.70 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc
% 5.46/5.70 thf(fact_6805_mask__eq__exp__minus__1,axiom,
% 5.46/5.70 ( bit_se2002935070580805687sk_nat
% 5.46/5.70 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_eq_exp_minus_1
% 5.46/5.70 thf(fact_6806_mask__eq__exp__minus__1,axiom,
% 5.46/5.70 ( bit_se2000444600071755411sk_int
% 5.46/5.70 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_eq_exp_minus_1
% 5.46/5.70 thf(fact_6807_infinite__nat__iff__unbounded,axiom,
% 5.46/5.70 ! [S2: set_nat] :
% 5.46/5.70 ( ( ~ ( finite_finite_nat @ S2 ) )
% 5.46/5.70 = ( ! [M3: nat] :
% 5.46/5.70 ? [N2: nat] :
% 5.46/5.70 ( ( ord_less_nat @ M3 @ N2 )
% 5.46/5.70 & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % infinite_nat_iff_unbounded
% 5.46/5.70 thf(fact_6808_unbounded__k__infinite,axiom,
% 5.46/5.70 ! [K: nat,S2: set_nat] :
% 5.46/5.70 ( ! [M4: nat] :
% 5.46/5.70 ( ( ord_less_nat @ K @ M4 )
% 5.46/5.70 => ? [N7: nat] :
% 5.46/5.70 ( ( ord_less_nat @ M4 @ N7 )
% 5.46/5.70 & ( member_nat @ N7 @ S2 ) ) )
% 5.46/5.70 => ~ ( finite_finite_nat @ S2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % unbounded_k_infinite
% 5.46/5.70 thf(fact_6809_infinite__nat__iff__unbounded__le,axiom,
% 5.46/5.70 ! [S2: set_nat] :
% 5.46/5.70 ( ( ~ ( finite_finite_nat @ S2 ) )
% 5.46/5.70 = ( ! [M3: nat] :
% 5.46/5.70 ? [N2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.70 & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % infinite_nat_iff_unbounded_le
% 5.46/5.70 thf(fact_6810_exp__bound,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.70 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_bound
% 5.46/5.70 thf(fact_6811_take__bit__int__less__eq,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_less_eq
% 5.46/5.70 thf(fact_6812_take__bit__int__greater__eq,axiom,
% 5.46/5.70 ! [K: int,N: nat] :
% 5.46/5.70 ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_int_greater_eq
% 5.46/5.70 thf(fact_6813_signed__take__bit__eq__take__bit__shift,axiom,
% 5.46/5.70 ( bit_ri631733984087533419it_int
% 5.46/5.70 = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % signed_take_bit_eq_take_bit_shift
% 5.46/5.70 thf(fact_6814_mask__eq__sum__exp__nat,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.70 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 @ ( collect_nat
% 5.46/5.70 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mask_eq_sum_exp_nat
% 5.46/5.70 thf(fact_6815_stable__imp__take__bit__eq,axiom,
% 5.46/5.70 ! [A: code_integer,N: nat] :
% 5.46/5.70 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.70 = A )
% 5.46/5.70 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.46/5.70 = zero_z3403309356797280102nteger ) )
% 5.46/5.70 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.46/5.70 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % stable_imp_take_bit_eq
% 5.46/5.70 thf(fact_6816_stable__imp__take__bit__eq,axiom,
% 5.46/5.70 ! [A: int,N: nat] :
% 5.46/5.70 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.70 = A )
% 5.46/5.70 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.46/5.70 = zero_zero_int ) )
% 5.46/5.70 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.46/5.70 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % stable_imp_take_bit_eq
% 5.46/5.70 thf(fact_6817_stable__imp__take__bit__eq,axiom,
% 5.46/5.70 ! [A: nat,N: nat] :
% 5.46/5.70 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = A )
% 5.46/5.70 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.46/5.70 = zero_zero_nat ) )
% 5.46/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.46/5.70 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % stable_imp_take_bit_eq
% 5.46/5.70 thf(fact_6818_gauss__sum__nat,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [X: nat] : X
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.70 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % gauss_sum_nat
% 5.46/5.70 thf(fact_6819_take__bit__numeral__bit1,axiom,
% 5.46/5.70 ! [L2: num,K: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_bit1
% 5.46/5.70 thf(fact_6820_take__bit__numeral__bit1,axiom,
% 5.46/5.70 ! [L2: num,K: num] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_bit1
% 5.46/5.70 thf(fact_6821_real__exp__bound__lemma,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_exp_bound_lemma
% 5.46/5.70 thf(fact_6822_take__bit__minus__small__eq,axiom,
% 5.46/5.70 ! [K: int,N: nat] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.70 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.46/5.70 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_minus_small_eq
% 5.46/5.70 thf(fact_6823_arith__series__nat,axiom,
% 5.46/5.70 ! [A: nat,D2: nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D2 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.70 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % arith_series_nat
% 5.46/5.70 thf(fact_6824_Sum__Icc__nat,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [X: nat] : X
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % Sum_Icc_nat
% 5.46/5.70 thf(fact_6825_exp__lower__Taylor__quadratic,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( divide_divide_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_lower_Taylor_quadratic
% 5.46/5.70 thf(fact_6826_take__bit__numeral__minus__bit1,axiom,
% 5.46/5.70 ! [L2: num,K: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_numeral_minus_bit1
% 5.46/5.70 thf(fact_6827_take__bit__Suc__minus__bit1,axiom,
% 5.46/5.70 ! [N: nat,K: num] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_Suc_minus_bit1
% 5.46/5.70 thf(fact_6828_sum__gp,axiom,
% 5.46/5.70 ! [N: nat,M: nat,X2: complex] :
% 5.46/5.70 ( ( ( ord_less_nat @ N @ M )
% 5.46/5.70 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = zero_zero_complex ) )
% 5.46/5.70 & ( ~ ( ord_less_nat @ N @ M )
% 5.46/5.70 => ( ( ( X2 = one_one_complex )
% 5.46/5.70 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.46/5.70 & ( ( X2 != one_one_complex )
% 5.46/5.70 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp
% 5.46/5.70 thf(fact_6829_sum__gp,axiom,
% 5.46/5.70 ! [N: nat,M: nat,X2: rat] :
% 5.46/5.70 ( ( ( ord_less_nat @ N @ M )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = zero_zero_rat ) )
% 5.46/5.70 & ( ~ ( ord_less_nat @ N @ M )
% 5.46/5.70 => ( ( ( X2 = one_one_rat )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.46/5.70 & ( ( X2 != one_one_rat )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp
% 5.46/5.70 thf(fact_6830_sum__gp,axiom,
% 5.46/5.70 ! [N: nat,M: nat,X2: real] :
% 5.46/5.70 ( ( ( ord_less_nat @ N @ M )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = zero_zero_real ) )
% 5.46/5.70 & ( ~ ( ord_less_nat @ N @ M )
% 5.46/5.70 => ( ( ( X2 = one_one_real )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.46/5.70 & ( ( X2 != one_one_real )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp
% 5.46/5.70 thf(fact_6831_log__base__10__eq1,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.70 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_base_10_eq1
% 5.46/5.70 thf(fact_6832_gauss__sum__from__Suc__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.46/5.70 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % gauss_sum_from_Suc_0
% 5.46/5.70 thf(fact_6833_gauss__sum__from__Suc__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.46/5.70 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % gauss_sum_from_Suc_0
% 5.46/5.70 thf(fact_6834_and__int__unfold,axiom,
% 5.46/5.70 ( bit_se725231765392027082nd_int
% 5.46/5.70 = ( ^ [K2: int,L: int] :
% 5.46/5.70 ( if_int
% 5.46/5.70 @ ( ( K2 = zero_zero_int )
% 5.46/5.70 | ( L = zero_zero_int ) )
% 5.46/5.70 @ zero_zero_int
% 5.46/5.70 @ ( if_int
% 5.46/5.70 @ ( K2
% 5.46/5.70 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 @ L
% 5.46/5.70 @ ( if_int
% 5.46/5.70 @ ( L
% 5.46/5.70 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 @ K2
% 5.46/5.70 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_int_unfold
% 5.46/5.70 thf(fact_6835_of__nat__eq__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ( semiri1314217659103216013at_int @ M )
% 5.46/5.70 = ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( M = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_iff
% 5.46/5.70 thf(fact_6836_of__nat__eq__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ( semiri5074537144036343181t_real @ M )
% 5.46/5.70 = ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 = ( M = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_iff
% 5.46/5.70 thf(fact_6837_of__nat__eq__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.46/5.70 = ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.70 = ( M = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_iff
% 5.46/5.70 thf(fact_6838_of__nat__eq__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ( semiri8010041392384452111omplex @ M )
% 5.46/5.70 = ( semiri8010041392384452111omplex @ N ) )
% 5.46/5.70 = ( M = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_iff
% 5.46/5.70 thf(fact_6839_of__nat__eq__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ( semiri681578069525770553at_rat @ M )
% 5.46/5.70 = ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.70 = ( M = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_iff
% 5.46/5.70 thf(fact_6840_and_Oright__idem,axiom,
% 5.46/5.70 ! [A: int,B: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.46/5.70 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.right_idem
% 5.46/5.70 thf(fact_6841_and_Oright__idem,axiom,
% 5.46/5.70 ! [A: nat,B: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.46/5.70 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.right_idem
% 5.46/5.70 thf(fact_6842_and_Oleft__idem,axiom,
% 5.46/5.70 ! [A: int,B: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.46/5.70 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.left_idem
% 5.46/5.70 thf(fact_6843_and_Oleft__idem,axiom,
% 5.46/5.70 ! [A: nat,B: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.46/5.70 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.left_idem
% 5.46/5.70 thf(fact_6844_and_Oidem,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.46/5.70 = A ) ).
% 5.46/5.70
% 5.46/5.70 % and.idem
% 5.46/5.70 thf(fact_6845_and_Oidem,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.46/5.70 = A ) ).
% 5.46/5.70
% 5.46/5.70 % and.idem
% 5.46/5.70 thf(fact_6846_int__eq__iff__numeral,axiom,
% 5.46/5.70 ! [M: nat,V: num] :
% 5.46/5.70 ( ( ( semiri1314217659103216013at_int @ M )
% 5.46/5.70 = ( numeral_numeral_int @ V ) )
% 5.46/5.70 = ( M
% 5.46/5.70 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_eq_iff_numeral
% 5.46/5.70 thf(fact_6847_bit_Oconj__zero__right,axiom,
% 5.46/5.70 ! [X2: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ X2 @ zero_zero_int )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % bit.conj_zero_right
% 5.46/5.70 thf(fact_6848_bit_Oconj__zero__left,axiom,
% 5.46/5.70 ! [X2: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X2 )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % bit.conj_zero_left
% 5.46/5.70 thf(fact_6849_zero__and__eq,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % zero_and_eq
% 5.46/5.70 thf(fact_6850_zero__and__eq,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % zero_and_eq
% 5.46/5.70 thf(fact_6851_and__zero__eq,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % and_zero_eq
% 5.46/5.70 thf(fact_6852_and__zero__eq,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % and_zero_eq
% 5.46/5.70 thf(fact_6853_abs__of__nat,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.46/5.70 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % abs_of_nat
% 5.46/5.70 thf(fact_6854_abs__of__nat,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % abs_of_nat
% 5.46/5.70 thf(fact_6855_abs__of__nat,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % abs_of_nat
% 5.46/5.70 thf(fact_6856_abs__of__nat,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.70 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % abs_of_nat
% 5.46/5.70 thf(fact_6857_take__bit__and,axiom,
% 5.46/5.70 ! [N: nat,A: int,B: int] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.46/5.70 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_and
% 5.46/5.70 thf(fact_6858_take__bit__and,axiom,
% 5.46/5.70 ! [N: nat,A: nat,B: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.46/5.70 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_and
% 5.46/5.70 thf(fact_6859_height__double__log__univ__size,axiom,
% 5.46/5.70 ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 5.46/5.70 ( ( U
% 5.46/5.70 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 5.46/5.70 => ( ( vEBT_invar_vebt @ T @ Deg )
% 5.46/5.70 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % height_double_log_univ_size
% 5.46/5.70 thf(fact_6860_of__nat__eq__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( ( semiri1314217659103216013at_int @ M )
% 5.46/5.70 = zero_zero_int )
% 5.46/5.70 = ( M = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_0_iff
% 5.46/5.70 thf(fact_6861_of__nat__eq__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( ( semiri5074537144036343181t_real @ M )
% 5.46/5.70 = zero_zero_real )
% 5.46/5.70 = ( M = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_0_iff
% 5.46/5.70 thf(fact_6862_of__nat__eq__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.46/5.70 = zero_zero_nat )
% 5.46/5.70 = ( M = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_0_iff
% 5.46/5.70 thf(fact_6863_of__nat__eq__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( ( semiri8010041392384452111omplex @ M )
% 5.46/5.70 = zero_zero_complex )
% 5.46/5.70 = ( M = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_0_iff
% 5.46/5.70 thf(fact_6864_of__nat__eq__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( ( semiri681578069525770553at_rat @ M )
% 5.46/5.70 = zero_zero_rat )
% 5.46/5.70 = ( M = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_0_iff
% 5.46/5.70 thf(fact_6865_of__nat__0__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( zero_zero_int
% 5.46/5.70 = ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( zero_zero_nat = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_eq_iff
% 5.46/5.70 thf(fact_6866_of__nat__0__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( zero_zero_real
% 5.46/5.70 = ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 = ( zero_zero_nat = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_eq_iff
% 5.46/5.70 thf(fact_6867_of__nat__0__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( zero_zero_nat
% 5.46/5.70 = ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.70 = ( zero_zero_nat = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_eq_iff
% 5.46/5.70 thf(fact_6868_of__nat__0__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( zero_zero_complex
% 5.46/5.70 = ( semiri8010041392384452111omplex @ N ) )
% 5.46/5.70 = ( zero_zero_nat = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_eq_iff
% 5.46/5.70 thf(fact_6869_of__nat__0__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( zero_zero_rat
% 5.46/5.70 = ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.70 = ( zero_zero_nat = N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_eq_iff
% 5.46/5.70 thf(fact_6870_of__nat__0,axiom,
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0
% 5.46/5.70 thf(fact_6871_of__nat__0,axiom,
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.46/5.70 = zero_zero_real ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0
% 5.46/5.70 thf(fact_6872_of__nat__0,axiom,
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0
% 5.46/5.70 thf(fact_6873_of__nat__0,axiom,
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.46/5.70 = zero_zero_complex ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0
% 5.46/5.70 thf(fact_6874_of__nat__0,axiom,
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.46/5.70 = zero_zero_rat ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0
% 5.46/5.70 thf(fact_6875_of__nat__less__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_iff
% 5.46/5.70 thf(fact_6876_of__nat__less__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_iff
% 5.46/5.70 thf(fact_6877_of__nat__less__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.70 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_iff
% 5.46/5.70 thf(fact_6878_of__nat__less__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.70 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_iff
% 5.46/5.70 thf(fact_6879_of__nat__numeral,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.46/5.70 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_numeral
% 5.46/5.70 thf(fact_6880_of__nat__numeral,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.46/5.70 = ( numeral_numeral_real @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_numeral
% 5.46/5.70 thf(fact_6881_of__nat__numeral,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.46/5.70 = ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_numeral
% 5.46/5.70 thf(fact_6882_of__nat__numeral,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.46/5.70 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_numeral
% 5.46/5.70 thf(fact_6883_of__nat__numeral,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.46/5.70 = ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_numeral
% 5.46/5.70 thf(fact_6884_of__nat__le__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_iff
% 5.46/5.70 thf(fact_6885_of__nat__le__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_iff
% 5.46/5.70 thf(fact_6886_of__nat__le__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_iff
% 5.46/5.70 thf(fact_6887_of__nat__le__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_iff
% 5.46/5.70 thf(fact_6888_of__nat__add,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.70 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_add
% 5.46/5.70 thf(fact_6889_of__nat__add,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.70 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_add
% 5.46/5.70 thf(fact_6890_of__nat__add,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.70 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_add
% 5.46/5.70 thf(fact_6891_of__nat__add,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.70 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_add
% 5.46/5.70 thf(fact_6892_of__nat__add,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.70 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_add
% 5.46/5.70 thf(fact_6893_of__nat__eq__1__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( semiri1314217659103216013at_int @ N )
% 5.46/5.70 = one_one_int )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_1_iff
% 5.46/5.70 thf(fact_6894_of__nat__eq__1__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( semiri5074537144036343181t_real @ N )
% 5.46/5.70 = one_one_real )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_1_iff
% 5.46/5.70 thf(fact_6895_of__nat__eq__1__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.46/5.70 = one_one_nat )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_1_iff
% 5.46/5.70 thf(fact_6896_of__nat__eq__1__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( semiri8010041392384452111omplex @ N )
% 5.46/5.70 = one_one_complex )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_1_iff
% 5.46/5.70 thf(fact_6897_of__nat__eq__1__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( semiri681578069525770553at_rat @ N )
% 5.46/5.70 = one_one_rat )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_1_iff
% 5.46/5.70 thf(fact_6898_of__nat__1__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( one_one_int
% 5.46/5.70 = ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1_eq_iff
% 5.46/5.70 thf(fact_6899_of__nat__1__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( one_one_real
% 5.46/5.70 = ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1_eq_iff
% 5.46/5.70 thf(fact_6900_of__nat__1__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( one_one_nat
% 5.46/5.70 = ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1_eq_iff
% 5.46/5.70 thf(fact_6901_of__nat__1__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( one_one_complex
% 5.46/5.70 = ( semiri8010041392384452111omplex @ N ) )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1_eq_iff
% 5.46/5.70 thf(fact_6902_of__nat__1__eq__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( one_one_rat
% 5.46/5.70 = ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.70 = ( N = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1_eq_iff
% 5.46/5.70 thf(fact_6903_of__nat__1,axiom,
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1
% 5.46/5.70 thf(fact_6904_of__nat__1,axiom,
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.46/5.70 = one_one_real ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1
% 5.46/5.70 thf(fact_6905_of__nat__1,axiom,
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.46/5.70 = one_one_nat ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1
% 5.46/5.70 thf(fact_6906_of__nat__1,axiom,
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.46/5.70 = one_one_complex ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1
% 5.46/5.70 thf(fact_6907_of__nat__1,axiom,
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.46/5.70 = one_one_rat ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_1
% 5.46/5.70 thf(fact_6908_of__nat__mult,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.46/5.70 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mult
% 5.46/5.70 thf(fact_6909_of__nat__mult,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.46/5.70 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mult
% 5.46/5.70 thf(fact_6910_of__nat__mult,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.46/5.70 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mult
% 5.46/5.70 thf(fact_6911_of__nat__mult,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 5.46/5.70 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mult
% 5.46/5.70 thf(fact_6912_of__nat__mult,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.46/5.70 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mult
% 5.46/5.70 thf(fact_6913_bit_Oconj__one__right,axiom,
% 5.46/5.70 ! [X2: code_integer] :
% 5.46/5.70 ( ( bit_se3949692690581998587nteger @ X2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.70 = X2 ) ).
% 5.46/5.70
% 5.46/5.70 % bit.conj_one_right
% 5.46/5.70 thf(fact_6914_bit_Oconj__one__right,axiom,
% 5.46/5.70 ! [X2: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ X2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 = X2 ) ).
% 5.46/5.70
% 5.46/5.70 % bit.conj_one_right
% 5.46/5.70 thf(fact_6915_and_Oright__neutral,axiom,
% 5.46/5.70 ! [A: code_integer] :
% 5.46/5.70 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.70 = A ) ).
% 5.46/5.70
% 5.46/5.70 % and.right_neutral
% 5.46/5.70 thf(fact_6916_and_Oright__neutral,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 = A ) ).
% 5.46/5.70
% 5.46/5.70 % and.right_neutral
% 5.46/5.70 thf(fact_6917_and_Oleft__neutral,axiom,
% 5.46/5.70 ! [A: code_integer] :
% 5.46/5.70 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.46/5.70 = A ) ).
% 5.46/5.70
% 5.46/5.70 % and.left_neutral
% 5.46/5.70 thf(fact_6918_and_Oleft__neutral,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.46/5.70 = A ) ).
% 5.46/5.70
% 5.46/5.70 % and.left_neutral
% 5.46/5.70 thf(fact_6919_of__nat__power,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.46/5.70 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power
% 5.46/5.70 thf(fact_6920_of__nat__power,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.46/5.70 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power
% 5.46/5.70 thf(fact_6921_of__nat__power,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.46/5.70 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power
% 5.46/5.70 thf(fact_6922_of__nat__power,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.46/5.70 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power
% 5.46/5.70 thf(fact_6923_of__nat__power,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 5.46/5.70 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power
% 5.46/5.70 thf(fact_6924_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.46/5.70 = ( semiri1314217659103216013at_int @ X2 ) )
% 5.46/5.70 = ( ( power_power_nat @ B @ W )
% 5.46/5.70 = X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_6925_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.46/5.70 = ( semiri5074537144036343181t_real @ X2 ) )
% 5.46/5.70 = ( ( power_power_nat @ B @ W )
% 5.46/5.70 = X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_6926_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.46/5.70 = ( semiri1316708129612266289at_nat @ X2 ) )
% 5.46/5.70 = ( ( power_power_nat @ B @ W )
% 5.46/5.70 = X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_6927_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.46/5.70 = ( semiri8010041392384452111omplex @ X2 ) )
% 5.46/5.70 = ( ( power_power_nat @ B @ W )
% 5.46/5.70 = X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_6928_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 5.46/5.70 = ( semiri681578069525770553at_rat @ X2 ) )
% 5.46/5.70 = ( ( power_power_nat @ B @ W )
% 5.46/5.70 = X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_6929_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ( semiri1314217659103216013at_int @ X2 )
% 5.46/5.70 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.46/5.70 = ( X2
% 5.46/5.70 = ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6930_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ( semiri5074537144036343181t_real @ X2 )
% 5.46/5.70 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.46/5.70 = ( X2
% 5.46/5.70 = ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6931_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ( semiri1316708129612266289at_nat @ X2 )
% 5.46/5.70 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.46/5.70 = ( X2
% 5.46/5.70 = ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6932_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ( semiri8010041392384452111omplex @ X2 )
% 5.46/5.70 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.46/5.70 = ( X2
% 5.46/5.70 = ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6933_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ( semiri681578069525770553at_rat @ X2 )
% 5.46/5.70 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.46/5.70 = ( X2
% 5.46/5.70 = ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6934_negative__zless,axiom,
% 5.46/5.70 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.46/5.70
% 5.46/5.70 % negative_zless
% 5.46/5.70 thf(fact_6935_log__one,axiom,
% 5.46/5.70 ! [A: real] :
% 5.46/5.70 ( ( log @ A @ one_one_real )
% 5.46/5.70 = zero_zero_real ) ).
% 5.46/5.70
% 5.46/5.70 % log_one
% 5.46/5.70 thf(fact_6936_and__nonnegative__int__iff,axiom,
% 5.46/5.70 ! [K: int,L2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.46/5.70 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.70 | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_nonnegative_int_iff
% 5.46/5.70 thf(fact_6937_and__negative__int__iff,axiom,
% 5.46/5.70 ! [K: int,L2: int] :
% 5.46/5.70 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.70 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.70 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_negative_int_iff
% 5.46/5.70 thf(fact_6938_pred__numeral__inc,axiom,
% 5.46/5.70 ! [K: num] :
% 5.46/5.70 ( ( pred_numeral @ ( inc @ K ) )
% 5.46/5.70 = ( numeral_numeral_nat @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % pred_numeral_inc
% 5.46/5.70 thf(fact_6939_of__nat__of__bool,axiom,
% 5.46/5.70 ! [P: $o] :
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.70 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_of_bool
% 5.46/5.70 thf(fact_6940_of__nat__of__bool,axiom,
% 5.46/5.70 ! [P: $o] :
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.70 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_of_bool
% 5.46/5.70 thf(fact_6941_of__nat__of__bool,axiom,
% 5.46/5.70 ! [P: $o] :
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.70 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_of_bool
% 5.46/5.70 thf(fact_6942_of__nat__of__bool,axiom,
% 5.46/5.70 ! [P: $o] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.70 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_of_bool
% 5.46/5.70 thf(fact_6943_of__nat__of__bool,axiom,
% 5.46/5.70 ! [P: $o] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.70 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_of_bool
% 5.46/5.70 thf(fact_6944_of__nat__of__bool,axiom,
% 5.46/5.70 ! [P: $o] :
% 5.46/5.70 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.70 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_of_bool
% 5.46/5.70 thf(fact_6945_of__nat__le__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.46/5.70 = ( M = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_0_iff
% 5.46/5.70 thf(fact_6946_of__nat__le__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.46/5.70 = ( M = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_0_iff
% 5.46/5.70 thf(fact_6947_of__nat__le__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.46/5.70 = ( M = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_0_iff
% 5.46/5.70 thf(fact_6948_of__nat__le__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.46/5.70 = ( M = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_0_iff
% 5.46/5.70 thf(fact_6949_of__nat__Suc,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.46/5.70 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_Suc
% 5.46/5.70 thf(fact_6950_of__nat__Suc,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.46/5.70 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_Suc
% 5.46/5.70 thf(fact_6951_of__nat__Suc,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.46/5.70 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_Suc
% 5.46/5.70 thf(fact_6952_of__nat__Suc,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.46/5.70 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_Suc
% 5.46/5.70 thf(fact_6953_of__nat__Suc,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.46/5.70 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_Suc
% 5.46/5.70 thf(fact_6954_and__numerals_I2_J,axiom,
% 5.46/5.70 ! [Y2: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(2)
% 5.46/5.70 thf(fact_6955_and__numerals_I2_J,axiom,
% 5.46/5.70 ! [Y2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.46/5.70 = one_one_nat ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(2)
% 5.46/5.70 thf(fact_6956_and__numerals_I8_J,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ one_one_int )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(8)
% 5.46/5.70 thf(fact_6957_and__numerals_I8_J,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ one_one_nat )
% 5.46/5.70 = one_one_nat ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(8)
% 5.46/5.70 thf(fact_6958_numeral__less__real__of__nat__iff,axiom,
% 5.46/5.70 ! [W: num,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_less_real_of_nat_iff
% 5.46/5.70 thf(fact_6959_real__of__nat__less__numeral__iff,axiom,
% 5.46/5.70 ! [N: nat,W: num] :
% 5.46/5.70 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.46/5.70 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_less_numeral_iff
% 5.46/5.70 thf(fact_6960_numeral__le__real__of__nat__iff,axiom,
% 5.46/5.70 ! [N: num,M: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_le_real_of_nat_iff
% 5.46/5.70 thf(fact_6961_log__eq__one,axiom,
% 5.46/5.70 ! [A: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.70 => ( ( A != one_one_real )
% 5.46/5.70 => ( ( log @ A @ A )
% 5.46/5.70 = one_one_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_eq_one
% 5.46/5.70 thf(fact_6962_log__less__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.70 => ( ( ord_less_real @ ( log @ A @ X2 ) @ ( log @ A @ Y2 ) )
% 5.46/5.70 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_less_cancel_iff
% 5.46/5.70 thf(fact_6963_log__less__one__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.46/5.70 = ( ord_less_real @ X2 @ A ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_less_one_cancel_iff
% 5.46/5.70 thf(fact_6964_one__less__log__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ A @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_less_log_cancel_iff
% 5.46/5.70 thf(fact_6965_log__less__zero__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.46/5.70 = ( ord_less_real @ X2 @ one_one_real ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_less_zero_cancel_iff
% 5.46/5.70 thf(fact_6966_zero__less__log__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ one_one_real @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_less_log_cancel_iff
% 5.46/5.70 thf(fact_6967_of__nat__0__less__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_less_iff
% 5.46/5.70 thf(fact_6968_of__nat__0__less__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_less_iff
% 5.46/5.70 thf(fact_6969_of__nat__0__less__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.70 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_less_iff
% 5.46/5.70 thf(fact_6970_of__nat__0__less__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.70 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_less_iff
% 5.46/5.70 thf(fact_6971_and__numerals_I1_J,axiom,
% 5.46/5.70 ! [Y2: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(1)
% 5.46/5.70 thf(fact_6972_and__numerals_I1_J,axiom,
% 5.46/5.70 ! [Y2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(1)
% 5.46/5.70 thf(fact_6973_and__numerals_I5_J,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ one_one_int )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(5)
% 5.46/5.70 thf(fact_6974_and__numerals_I5_J,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ one_one_nat )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(5)
% 5.46/5.70 thf(fact_6975_and__numerals_I3_J,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 5.46/5.70 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(3)
% 5.46/5.70 thf(fact_6976_and__numerals_I3_J,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.46/5.70 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(3)
% 5.46/5.70 thf(fact_6977_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.46/5.70 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_6978_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.46/5.70 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_6979_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.46/5.70 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_6980_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_6981_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.46/5.70 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_less_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6982_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.46/5.70 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_less_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6983_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.46/5.70 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_less_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6984_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.46/5.70 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_less_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6985_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [Y2: nat,X2: num,N: nat] :
% 5.46/5.70 ( ( ( semiri1314217659103216013at_int @ Y2 )
% 5.46/5.70 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.46/5.70 = ( Y2
% 5.46/5.70 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_6986_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [Y2: nat,X2: num,N: nat] :
% 5.46/5.70 ( ( ( semiri5074537144036343181t_real @ Y2 )
% 5.46/5.70 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.46/5.70 = ( Y2
% 5.46/5.70 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_6987_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [Y2: nat,X2: num,N: nat] :
% 5.46/5.70 ( ( ( semiri1316708129612266289at_nat @ Y2 )
% 5.46/5.70 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.46/5.70 = ( Y2
% 5.46/5.70 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_6988_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [Y2: nat,X2: num,N: nat] :
% 5.46/5.70 ( ( ( semiri8010041392384452111omplex @ Y2 )
% 5.46/5.70 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 5.46/5.70 = ( Y2
% 5.46/5.70 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_6989_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [Y2: nat,X2: num,N: nat] :
% 5.46/5.70 ( ( ( semiri681578069525770553at_rat @ Y2 )
% 5.46/5.70 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.46/5.70 = ( Y2
% 5.46/5.70 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_6990_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: num,N: nat,Y2: nat] :
% 5.46/5.70 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.46/5.70 = ( semiri1314217659103216013at_int @ Y2 ) )
% 5.46/5.70 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.46/5.70 = Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6991_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: num,N: nat,Y2: nat] :
% 5.46/5.70 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 5.46/5.70 = ( semiri5074537144036343181t_real @ Y2 ) )
% 5.46/5.70 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.46/5.70 = Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6992_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: num,N: nat,Y2: nat] :
% 5.46/5.70 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.46/5.70 = ( semiri1316708129612266289at_nat @ Y2 ) )
% 5.46/5.70 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.46/5.70 = Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6993_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: num,N: nat,Y2: nat] :
% 5.46/5.70 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 5.46/5.70 = ( semiri8010041392384452111omplex @ Y2 ) )
% 5.46/5.70 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.46/5.70 = Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6994_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: num,N: nat,Y2: nat] :
% 5.46/5.70 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 5.46/5.70 = ( semiri681578069525770553at_rat @ Y2 ) )
% 5.46/5.70 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.46/5.70 = Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6995_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.46/5.70 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_le_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6996_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.46/5.70 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_le_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6997_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.46/5.70 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_le_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6998_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,B: nat,W: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.46/5.70 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_power_le_of_nat_cancel_iff
% 5.46/5.70 thf(fact_6999_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_7000_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_7001_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_7002_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.46/5.70 ! [B: nat,W: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_of_nat_power_cancel_iff
% 5.46/5.70 thf(fact_7003_zero__le__log__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_le_log_cancel_iff
% 5.46/5.70 thf(fact_7004_log__le__zero__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_le_zero_cancel_iff
% 5.46/5.70 thf(fact_7005_one__le__log__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_real @ A @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_le_log_cancel_iff
% 5.46/5.70 thf(fact_7006_log__le__one__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ A ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_le_one_cancel_iff
% 5.46/5.70 thf(fact_7007_log__le__cancel__iff,axiom,
% 5.46/5.70 ! [A: real,X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ ( log @ A @ Y2 ) )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_le_cancel_iff
% 5.46/5.70 thf(fact_7008_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.70 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(5)
% 5.46/5.70 thf(fact_7009_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.70 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(5)
% 5.46/5.70 thf(fact_7010_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.70 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(5)
% 5.46/5.70 thf(fact_7011_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.70 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(5)
% 5.46/5.70 thf(fact_7012_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.70 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(5)
% 5.46/5.70 thf(fact_7013_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(6)
% 5.46/5.70 thf(fact_7014_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.70 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(6)
% 5.46/5.70 thf(fact_7015_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.70 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(6)
% 5.46/5.70 thf(fact_7016_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.70 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(6)
% 5.46/5.70 thf(fact_7017_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.70 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_neg_numeral_special(6)
% 5.46/5.70 thf(fact_7018_diff__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.70 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(5)
% 5.46/5.70 thf(fact_7019_diff__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.70 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(5)
% 5.46/5.70 thf(fact_7020_diff__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 5.46/5.70 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(5)
% 5.46/5.70 thf(fact_7021_diff__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.70 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(5)
% 5.46/5.70 thf(fact_7022_diff__numeral__special_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.70 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(5)
% 5.46/5.70 thf(fact_7023_diff__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(6)
% 5.46/5.70 thf(fact_7024_diff__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.70 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(6)
% 5.46/5.70 thf(fact_7025_diff__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.70 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(6)
% 5.46/5.70 thf(fact_7026_diff__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.70 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(6)
% 5.46/5.70 thf(fact_7027_diff__numeral__special_I6_J,axiom,
% 5.46/5.70 ! [M: num] :
% 5.46/5.70 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.70 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % diff_numeral_special(6)
% 5.46/5.70 thf(fact_7028_log__pow__cancel,axiom,
% 5.46/5.70 ! [A: real,B: nat] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.70 => ( ( A != one_one_real )
% 5.46/5.70 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.46/5.70 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_pow_cancel
% 5.46/5.70 thf(fact_7029_and__minus__numerals_I2_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % and_minus_numerals(2)
% 5.46/5.70 thf(fact_7030_and__minus__numerals_I6_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % and_minus_numerals(6)
% 5.46/5.70 thf(fact_7031_of__nat__zero__less__power__iff,axiom,
% 5.46/5.70 ! [X2: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X2 ) @ N ) )
% 5.46/5.70 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.46/5.70 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_zero_less_power_iff
% 5.46/5.70 thf(fact_7032_of__nat__zero__less__power__iff,axiom,
% 5.46/5.70 ! [X2: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X2 ) @ N ) )
% 5.46/5.70 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.46/5.70 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_zero_less_power_iff
% 5.46/5.70 thf(fact_7033_of__nat__zero__less__power__iff,axiom,
% 5.46/5.70 ! [X2: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N ) )
% 5.46/5.70 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.46/5.70 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_zero_less_power_iff
% 5.46/5.70 thf(fact_7034_of__nat__zero__less__power__iff,axiom,
% 5.46/5.70 ! [X2: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N ) )
% 5.46/5.70 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.46/5.70 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_zero_less_power_iff
% 5.46/5.70 thf(fact_7035_and__numerals_I4_J,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 5.46/5.70 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(4)
% 5.46/5.70 thf(fact_7036_and__numerals_I4_J,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.46/5.70 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(4)
% 5.46/5.70 thf(fact_7037_and__numerals_I6_J,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y2 ) ) )
% 5.46/5.70 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(6)
% 5.46/5.70 thf(fact_7038_and__numerals_I6_J,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.46/5.70 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(6)
% 5.46/5.70 thf(fact_7039_and__minus__numerals_I1_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % and_minus_numerals(1)
% 5.46/5.70 thf(fact_7040_and__minus__numerals_I5_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % and_minus_numerals(5)
% 5.46/5.70 thf(fact_7041_even__of__nat,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.46/5.70 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_of_nat
% 5.46/5.70 thf(fact_7042_even__of__nat,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_of_nat
% 5.46/5.70 thf(fact_7043_even__of__nat,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.70 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_of_nat
% 5.46/5.70 thf(fact_7044_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [I: num,N: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.46/5.70 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_less_of_nat_cancel_iff
% 5.46/5.70 thf(fact_7045_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [I: num,N: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.46/5.70 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_less_of_nat_cancel_iff
% 5.46/5.70 thf(fact_7046_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [I: num,N: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.46/5.70 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_less_of_nat_cancel_iff
% 5.46/5.70 thf(fact_7047_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [I: num,N: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_less_of_nat_cancel_iff
% 5.46/5.70 thf(fact_7048_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,I: num,N: nat] :
% 5.46/5.70 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.46/5.70 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_7049_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,I: num,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.46/5.70 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_7050_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,I: num,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.46/5.70 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_7051_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,I: num,N: nat] :
% 5.46/5.70 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.46/5.70 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_7052_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,I: num,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_7053_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,I: num,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_7054_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,I: num,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_7055_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.70 ! [X2: nat,I: num,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_le_numeral_power_cancel_iff
% 5.46/5.70 thf(fact_7056_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [I: num,N: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_le_of_nat_cancel_iff
% 5.46/5.70 thf(fact_7057_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [I: num,N: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_le_of_nat_cancel_iff
% 5.46/5.70 thf(fact_7058_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [I: num,N: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_le_of_nat_cancel_iff
% 5.46/5.70 thf(fact_7059_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.70 ! [I: num,N: nat,X2: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_power_le_of_nat_cancel_iff
% 5.46/5.70 thf(fact_7060_and__numerals_I7_J,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y2 ) ) )
% 5.46/5.70 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(7)
% 5.46/5.70 thf(fact_7061_and__numerals_I7_J,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.46/5.70 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_numerals(7)
% 5.46/5.70 thf(fact_7062_and_Oleft__commute,axiom,
% 5.46/5.70 ! [B: int,A: int,C: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.46/5.70 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.left_commute
% 5.46/5.70 thf(fact_7063_and_Oleft__commute,axiom,
% 5.46/5.70 ! [B: nat,A: nat,C: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.46/5.70 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.left_commute
% 5.46/5.70 thf(fact_7064_of__nat__and__eq,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.46/5.70 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_and_eq
% 5.46/5.70 thf(fact_7065_of__nat__and__eq,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.46/5.70 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_and_eq
% 5.46/5.70 thf(fact_7066_and_Ocommute,axiom,
% 5.46/5.70 ( bit_se725231765392027082nd_int
% 5.46/5.70 = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.commute
% 5.46/5.70 thf(fact_7067_and_Ocommute,axiom,
% 5.46/5.70 ( bit_se727722235901077358nd_nat
% 5.46/5.70 = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.commute
% 5.46/5.70 thf(fact_7068_and_Oassoc,axiom,
% 5.46/5.70 ! [A: int,B: int,C: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.46/5.70 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.assoc
% 5.46/5.70 thf(fact_7069_and_Oassoc,axiom,
% 5.46/5.70 ! [A: nat,B: nat,C: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.46/5.70 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and.assoc
% 5.46/5.70 thf(fact_7070_of__int__and__eq,axiom,
% 5.46/5.70 ! [K: int,L2: int] :
% 5.46/5.70 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.46/5.70 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_int_and_eq
% 5.46/5.70 thf(fact_7071_real__arch__simple,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ? [N3: nat] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_arch_simple
% 5.46/5.70 thf(fact_7072_real__arch__simple,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ? [N3: nat] : ( ord_less_eq_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_arch_simple
% 5.46/5.70 thf(fact_7073_reals__Archimedean2,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ? [N3: nat] : ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.46/5.70
% 5.46/5.70 % reals_Archimedean2
% 5.46/5.70 thf(fact_7074_reals__Archimedean2,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ? [N3: nat] : ( ord_less_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.46/5.70
% 5.46/5.70 % reals_Archimedean2
% 5.46/5.70 thf(fact_7075_mult__of__nat__commute,axiom,
% 5.46/5.70 ! [X2: nat,Y2: int] :
% 5.46/5.70 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X2 ) @ Y2 )
% 5.46/5.70 = ( times_times_int @ Y2 @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mult_of_nat_commute
% 5.46/5.70 thf(fact_7076_mult__of__nat__commute,axiom,
% 5.46/5.70 ! [X2: nat,Y2: real] :
% 5.46/5.70 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ Y2 )
% 5.46/5.70 = ( times_times_real @ Y2 @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mult_of_nat_commute
% 5.46/5.70 thf(fact_7077_mult__of__nat__commute,axiom,
% 5.46/5.70 ! [X2: nat,Y2: nat] :
% 5.46/5.70 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ Y2 )
% 5.46/5.70 = ( times_times_nat @ Y2 @ ( semiri1316708129612266289at_nat @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mult_of_nat_commute
% 5.46/5.70 thf(fact_7078_mult__of__nat__commute,axiom,
% 5.46/5.70 ! [X2: nat,Y2: complex] :
% 5.46/5.70 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X2 ) @ Y2 )
% 5.46/5.70 = ( times_times_complex @ Y2 @ ( semiri8010041392384452111omplex @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mult_of_nat_commute
% 5.46/5.70 thf(fact_7079_mult__of__nat__commute,axiom,
% 5.46/5.70 ! [X2: nat,Y2: rat] :
% 5.46/5.70 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X2 ) @ Y2 )
% 5.46/5.70 = ( times_times_rat @ Y2 @ ( semiri681578069525770553at_rat @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mult_of_nat_commute
% 5.46/5.70 thf(fact_7080_take__bit__of__nat,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.46/5.70 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_nat
% 5.46/5.70 thf(fact_7081_take__bit__of__nat,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.46/5.70 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_of_nat
% 5.46/5.70 thf(fact_7082_int__diff__cases,axiom,
% 5.46/5.70 ! [Z: int] :
% 5.46/5.70 ~ ! [M4: nat,N3: nat] :
% 5.46/5.70 ( Z
% 5.46/5.70 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_diff_cases
% 5.46/5.70 thf(fact_7083_of__nat__mask__eq,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.70 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mask_eq
% 5.46/5.70 thf(fact_7084_of__nat__mask__eq,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.70 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mask_eq
% 5.46/5.70 thf(fact_7085_less__log__of__power,axiom,
% 5.46/5.70 ! [B: real,N: nat,M: real] :
% 5.46/5.70 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 5.46/5.70 => ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.70 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_log_of_power
% 5.46/5.70 thf(fact_7086_log__of__power__eq,axiom,
% 5.46/5.70 ! [M: nat,B: real,N: nat] :
% 5.46/5.70 ( ( ( semiri5074537144036343181t_real @ M )
% 5.46/5.70 = ( power_power_real @ B @ N ) )
% 5.46/5.70 => ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.70 => ( ( semiri5074537144036343181t_real @ N )
% 5.46/5.70 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_of_power_eq
% 5.46/5.70 thf(fact_7087_of__nat__less__of__int__iff,axiom,
% 5.46/5.70 ! [N: nat,X2: int] :
% 5.46/5.70 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X2 ) )
% 5.46/5.70 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_of_int_iff
% 5.46/5.70 thf(fact_7088_of__nat__less__of__int__iff,axiom,
% 5.46/5.70 ! [N: nat,X2: int] :
% 5.46/5.70 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X2 ) )
% 5.46/5.70 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_of_int_iff
% 5.46/5.70 thf(fact_7089_of__nat__less__of__int__iff,axiom,
% 5.46/5.70 ! [N: nat,X2: int] :
% 5.46/5.70 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_of_int_iff
% 5.46/5.70 thf(fact_7090_num__induct,axiom,
% 5.46/5.70 ! [P: num > $o,X2: num] :
% 5.46/5.70 ( ( P @ one )
% 5.46/5.70 => ( ! [X3: num] :
% 5.46/5.70 ( ( P @ X3 )
% 5.46/5.70 => ( P @ ( inc @ X3 ) ) )
% 5.46/5.70 => ( P @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % num_induct
% 5.46/5.70 thf(fact_7091_add__inc,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( plus_plus_num @ X2 @ ( inc @ Y2 ) )
% 5.46/5.70 = ( inc @ ( plus_plus_num @ X2 @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_inc
% 5.46/5.70 thf(fact_7092_le__log__of__power,axiom,
% 5.46/5.70 ! [B: real,N: nat,M: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 5.46/5.70 => ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.70 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % le_log_of_power
% 5.46/5.70 thf(fact_7093_log__base__pow,axiom,
% 5.46/5.70 ! [A: real,N: nat,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.70 => ( ( log @ ( power_power_real @ A @ N ) @ X2 )
% 5.46/5.70 = ( divide_divide_real @ ( log @ A @ X2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_base_pow
% 5.46/5.70 thf(fact_7094_log__nat__power,axiom,
% 5.46/5.70 ! [X2: real,B: real,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( log @ B @ ( power_power_real @ X2 @ N ) )
% 5.46/5.70 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_nat_power
% 5.46/5.70 thf(fact_7095_and__eq__minus__1__iff,axiom,
% 5.46/5.70 ! [A: code_integer,B: code_integer] :
% 5.46/5.70 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.46/5.70 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.70 = ( ( A
% 5.46/5.70 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.70 & ( B
% 5.46/5.70 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_eq_minus_1_iff
% 5.46/5.70 thf(fact_7096_and__eq__minus__1__iff,axiom,
% 5.46/5.70 ! [A: int,B: int] :
% 5.46/5.70 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.46/5.70 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 = ( ( A
% 5.46/5.70 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.70 & ( B
% 5.46/5.70 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_eq_minus_1_iff
% 5.46/5.70 thf(fact_7097_of__nat__0__le__iff,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_le_iff
% 5.46/5.70 thf(fact_7098_of__nat__0__le__iff,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_le_iff
% 5.46/5.70 thf(fact_7099_of__nat__0__le__iff,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_le_iff
% 5.46/5.70 thf(fact_7100_of__nat__0__le__iff,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_0_le_iff
% 5.46/5.70 thf(fact_7101_of__nat__less__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_0_iff
% 5.46/5.70 thf(fact_7102_of__nat__less__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_0_iff
% 5.46/5.70 thf(fact_7103_of__nat__less__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_0_iff
% 5.46/5.70 thf(fact_7104_of__nat__less__0__iff,axiom,
% 5.46/5.70 ! [M: nat] :
% 5.46/5.70 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_0_iff
% 5.46/5.70 thf(fact_7105_of__nat__neq__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.46/5.70 != zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_neq_0
% 5.46/5.70 thf(fact_7106_of__nat__neq__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.46/5.70 != zero_zero_real ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_neq_0
% 5.46/5.70 thf(fact_7107_of__nat__neq__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.46/5.70 != zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_neq_0
% 5.46/5.70 thf(fact_7108_of__nat__neq__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.46/5.70 != zero_zero_complex ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_neq_0
% 5.46/5.70 thf(fact_7109_of__nat__neq__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.46/5.70 != zero_zero_rat ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_neq_0
% 5.46/5.70 thf(fact_7110_div__mult2__eq_H,axiom,
% 5.46/5.70 ! [A: int,M: nat,N: nat] :
% 5.46/5.70 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.70 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % div_mult2_eq'
% 5.46/5.70 thf(fact_7111_div__mult2__eq_H,axiom,
% 5.46/5.70 ! [A: nat,M: nat,N: nat] :
% 5.46/5.70 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.46/5.70 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % div_mult2_eq'
% 5.46/5.70 thf(fact_7112_less__imp__of__nat__less,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ M @ N )
% 5.46/5.70 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_imp_of_nat_less
% 5.46/5.70 thf(fact_7113_less__imp__of__nat__less,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ M @ N )
% 5.46/5.70 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_imp_of_nat_less
% 5.46/5.70 thf(fact_7114_less__imp__of__nat__less,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ M @ N )
% 5.46/5.70 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_imp_of_nat_less
% 5.46/5.70 thf(fact_7115_less__imp__of__nat__less,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ M @ N )
% 5.46/5.70 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_imp_of_nat_less
% 5.46/5.70 thf(fact_7116_of__nat__less__imp__less,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 => ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_imp_less
% 5.46/5.70 thf(fact_7117_of__nat__less__imp__less,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 => ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_imp_less
% 5.46/5.70 thf(fact_7118_of__nat__less__imp__less,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.70 => ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_imp_less
% 5.46/5.70 thf(fact_7119_of__nat__less__imp__less,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.70 => ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_imp_less
% 5.46/5.70 thf(fact_7120_of__nat__mono,axiom,
% 5.46/5.70 ! [I: nat,J: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.70 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mono
% 5.46/5.70 thf(fact_7121_of__nat__mono,axiom,
% 5.46/5.70 ! [I: nat,J: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.70 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mono
% 5.46/5.70 thf(fact_7122_of__nat__mono,axiom,
% 5.46/5.70 ! [I: nat,J: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.70 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mono
% 5.46/5.70 thf(fact_7123_of__nat__mono,axiom,
% 5.46/5.70 ! [I: nat,J: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.70 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mono
% 5.46/5.70 thf(fact_7124_AND__upper2_H,axiom,
% 5.46/5.70 ! [Y2: int,Z: int,X2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.70 => ( ( ord_less_eq_int @ Y2 @ Z )
% 5.46/5.70 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % AND_upper2'
% 5.46/5.70 thf(fact_7125_AND__upper1_H,axiom,
% 5.46/5.70 ! [Y2: int,Z: int,Ya: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.70 => ( ( ord_less_eq_int @ Y2 @ Z )
% 5.46/5.70 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % AND_upper1'
% 5.46/5.70 thf(fact_7126_AND__upper2,axiom,
% 5.46/5.70 ! [Y2: int,X2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.70 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % AND_upper2
% 5.46/5.70 thf(fact_7127_AND__upper1,axiom,
% 5.46/5.70 ! [X2: int,Y2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.70 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % AND_upper1
% 5.46/5.70 thf(fact_7128_AND__lower,axiom,
% 5.46/5.70 ! [X2: int,Y2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % AND_lower
% 5.46/5.70 thf(fact_7129_log__def,axiom,
% 5.46/5.70 ( log
% 5.46/5.70 = ( ^ [A3: real,X: real] : ( divide_divide_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ A3 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_def
% 5.46/5.70 thf(fact_7130_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.46/5.70 thf(fact_7131_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.46/5.70 thf(fact_7132_of__nat__dvd__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.46/5.70 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_dvd_iff
% 5.46/5.70 thf(fact_7133_of__nat__dvd__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_dvd_iff
% 5.46/5.70 thf(fact_7134_of__nat__dvd__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.70 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_dvd_iff
% 5.46/5.70 thf(fact_7135_take__bit__eq__mask,axiom,
% 5.46/5.70 ( bit_se2923211474154528505it_int
% 5.46/5.70 = ( ^ [N2: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_mask
% 5.46/5.70 thf(fact_7136_take__bit__eq__mask,axiom,
% 5.46/5.70 ( bit_se2925701944663578781it_nat
% 5.46/5.70 = ( ^ [N2: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % take_bit_eq_mask
% 5.46/5.70 thf(fact_7137_int__ops_I3_J,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.46/5.70 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_ops(3)
% 5.46/5.70 thf(fact_7138_int__cases,axiom,
% 5.46/5.70 ! [Z: int] :
% 5.46/5.70 ( ! [N3: nat] :
% 5.46/5.70 ( Z
% 5.46/5.70 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.46/5.70 => ~ ! [N3: nat] :
% 5.46/5.70 ( Z
% 5.46/5.70 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_cases
% 5.46/5.70 thf(fact_7139_int__of__nat__induct,axiom,
% 5.46/5.70 ! [P: int > $o,Z: int] :
% 5.46/5.70 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.46/5.70 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.46/5.70 => ( P @ Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_of_nat_induct
% 5.46/5.70 thf(fact_7140_nat__int__comparison_I2_J,axiom,
% 5.46/5.70 ( ord_less_nat
% 5.46/5.70 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_int_comparison(2)
% 5.46/5.70 thf(fact_7141_nat__int__comparison_I3_J,axiom,
% 5.46/5.70 ( ord_less_eq_nat
% 5.46/5.70 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_int_comparison(3)
% 5.46/5.70 thf(fact_7142_zle__int,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % zle_int
% 5.46/5.70 thf(fact_7143_of__nat__mod,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.70 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mod
% 5.46/5.70 thf(fact_7144_of__nat__mod,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.70 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mod
% 5.46/5.70 thf(fact_7145_of__nat__mod,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.70 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_mod
% 5.46/5.70 thf(fact_7146_int__ops_I2_J,axiom,
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % int_ops(2)
% 5.46/5.70 thf(fact_7147_int__ops_I5_J,axiom,
% 5.46/5.70 ! [A: nat,B: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.46/5.70 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_ops(5)
% 5.46/5.70 thf(fact_7148_int__plus,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.70 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_plus
% 5.46/5.70 thf(fact_7149_zadd__int__left,axiom,
% 5.46/5.70 ! [M: nat,N: nat,Z: int] :
% 5.46/5.70 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.46/5.70 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % zadd_int_left
% 5.46/5.70 thf(fact_7150_int__ops_I7_J,axiom,
% 5.46/5.70 ! [A: nat,B: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.46/5.70 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_ops(7)
% 5.46/5.70 thf(fact_7151_not__int__zless__negative,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % not_int_zless_negative
% 5.46/5.70 thf(fact_7152_zdiv__int,axiom,
% 5.46/5.70 ! [A: nat,B: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.46/5.70 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdiv_int
% 5.46/5.70 thf(fact_7153_of__nat__max,axiom,
% 5.46/5.70 ! [X2: nat,Y2: nat] :
% 5.46/5.70 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.46/5.70 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X2 ) @ ( semiri4216267220026989637d_enat @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_max
% 5.46/5.70 thf(fact_7154_of__nat__max,axiom,
% 5.46/5.70 ! [X2: nat,Y2: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.46/5.70 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_max
% 5.46/5.70 thf(fact_7155_of__nat__max,axiom,
% 5.46/5.70 ! [X2: nat,Y2: nat] :
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.46/5.70 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_max
% 5.46/5.70 thf(fact_7156_of__nat__max,axiom,
% 5.46/5.70 ! [X2: nat,Y2: nat] :
% 5.46/5.70 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.46/5.70 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( semiri1316708129612266289at_nat @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_max
% 5.46/5.70 thf(fact_7157_of__nat__max,axiom,
% 5.46/5.70 ! [X2: nat,Y2: nat] :
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X2 @ Y2 ) )
% 5.46/5.70 = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( semiri681578069525770553at_rat @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_max
% 5.46/5.70 thf(fact_7158_log2__of__power__eq,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( M
% 5.46/5.70 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 => ( ( semiri5074537144036343181t_real @ N )
% 5.46/5.70 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log2_of_power_eq
% 5.46/5.70 thf(fact_7159_log__of__power__less,axiom,
% 5.46/5.70 ! [M: nat,B: real,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.46/5.70 => ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.70 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_of_power_less
% 5.46/5.70 thf(fact_7160_zmod__int,axiom,
% 5.46/5.70 ! [A: nat,B: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.46/5.70 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zmod_int
% 5.46/5.70 thf(fact_7161_nat__less__as__int,axiom,
% 5.46/5.70 ( ord_less_nat
% 5.46/5.70 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_less_as_int
% 5.46/5.70 thf(fact_7162_nat__leq__as__int,axiom,
% 5.46/5.70 ( ord_less_eq_nat
% 5.46/5.70 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_leq_as_int
% 5.46/5.70 thf(fact_7163_inc_Osimps_I1_J,axiom,
% 5.46/5.70 ( ( inc @ one )
% 5.46/5.70 = ( bit0 @ one ) ) ).
% 5.46/5.70
% 5.46/5.70 % inc.simps(1)
% 5.46/5.70 thf(fact_7164_inc_Osimps_I2_J,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( inc @ ( bit0 @ X2 ) )
% 5.46/5.70 = ( bit1 @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % inc.simps(2)
% 5.46/5.70 thf(fact_7165_inc_Osimps_I3_J,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( inc @ ( bit1 @ X2 ) )
% 5.46/5.70 = ( bit0 @ ( inc @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inc.simps(3)
% 5.46/5.70 thf(fact_7166_log__of__power__le,axiom,
% 5.46/5.70 ! [M: nat,B: real,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.46/5.70 => ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.70 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_of_power_le
% 5.46/5.70 thf(fact_7167_ex__less__of__nat__mult,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ? [N3: nat] : ( ord_less_real @ Y2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ex_less_of_nat_mult
% 5.46/5.70 thf(fact_7168_ex__less__of__nat__mult,axiom,
% 5.46/5.70 ! [X2: rat,Y2: rat] :
% 5.46/5.70 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.46/5.70 => ? [N3: nat] : ( ord_less_rat @ Y2 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ex_less_of_nat_mult
% 5.46/5.70 thf(fact_7169_add__One,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( plus_plus_num @ X2 @ one )
% 5.46/5.70 = ( inc @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_One
% 5.46/5.70 thf(fact_7170_AND__upper2_H_H,axiom,
% 5.46/5.70 ! [Y2: int,Z: int,X2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.70 => ( ( ord_less_int @ Y2 @ Z )
% 5.46/5.70 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % AND_upper2''
% 5.46/5.70 thf(fact_7171_AND__upper1_H_H,axiom,
% 5.46/5.70 ! [Y2: int,Z: int,Ya: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.70 => ( ( ord_less_int @ Y2 @ Z )
% 5.46/5.70 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % AND_upper1''
% 5.46/5.70 thf(fact_7172_and__less__eq,axiom,
% 5.46/5.70 ! [L2: int,K: int] :
% 5.46/5.70 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.70 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_less_eq
% 5.46/5.70 thf(fact_7173_inc__BitM__eq,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( inc @ ( bitM @ N ) )
% 5.46/5.70 = ( bit0 @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % inc_BitM_eq
% 5.46/5.70 thf(fact_7174_of__nat__diff,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_diff
% 5.46/5.70 thf(fact_7175_of__nat__diff,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_diff
% 5.46/5.70 thf(fact_7176_of__nat__diff,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_diff
% 5.46/5.70 thf(fact_7177_of__nat__diff,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_diff
% 5.46/5.70 thf(fact_7178_of__nat__diff,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_diff
% 5.46/5.70 thf(fact_7179_BitM__inc__eq,axiom,
% 5.46/5.70 ! [N: num] :
% 5.46/5.70 ( ( bitM @ ( inc @ N ) )
% 5.46/5.70 = ( bit1 @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % BitM_inc_eq
% 5.46/5.70 thf(fact_7180_exp__of__nat2__mult,axiom,
% 5.46/5.70 ! [X2: real,N: nat] :
% 5.46/5.70 ( ( exp_real @ ( times_times_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.70 = ( power_power_real @ ( exp_real @ X2 ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_of_nat2_mult
% 5.46/5.70 thf(fact_7181_exp__of__nat2__mult,axiom,
% 5.46/5.70 ! [X2: complex,N: nat] :
% 5.46/5.70 ( ( exp_complex @ ( times_times_complex @ X2 @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.46/5.70 = ( power_power_complex @ ( exp_complex @ X2 ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_of_nat2_mult
% 5.46/5.70 thf(fact_7182_exp__of__nat__mult,axiom,
% 5.46/5.70 ! [N: nat,X2: real] :
% 5.46/5.70 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) )
% 5.46/5.70 = ( power_power_real @ ( exp_real @ X2 ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_of_nat_mult
% 5.46/5.70 thf(fact_7183_exp__of__nat__mult,axiom,
% 5.46/5.70 ! [N: nat,X2: complex] :
% 5.46/5.70 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X2 ) )
% 5.46/5.70 = ( power_power_complex @ ( exp_complex @ X2 ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_of_nat_mult
% 5.46/5.70 thf(fact_7184_log__ln,axiom,
% 5.46/5.70 ( ln_ln_real
% 5.46/5.70 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_ln
% 5.46/5.70 thf(fact_7185_reals__Archimedean3,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ! [Y4: real] :
% 5.46/5.70 ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % reals_Archimedean3
% 5.46/5.70 thf(fact_7186_int__cases4,axiom,
% 5.46/5.70 ! [M: int] :
% 5.46/5.70 ( ! [N3: nat] :
% 5.46/5.70 ( M
% 5.46/5.70 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.46/5.70 => ~ ! [N3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.46/5.70 => ( M
% 5.46/5.70 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_cases4
% 5.46/5.70 thf(fact_7187_real__of__nat__div4,axiom,
% 5.46/5.70 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_div4
% 5.46/5.70 thf(fact_7188_int__ops_I4_J,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.46/5.70 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_ops(4)
% 5.46/5.70 thf(fact_7189_int__Suc,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.46/5.70 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_Suc
% 5.46/5.70 thf(fact_7190_zless__iff__Suc__zadd,axiom,
% 5.46/5.70 ( ord_less_int
% 5.46/5.70 = ( ^ [W2: int,Z4: int] :
% 5.46/5.70 ? [N2: nat] :
% 5.46/5.70 ( Z4
% 5.46/5.70 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zless_iff_Suc_zadd
% 5.46/5.70 thf(fact_7191_real__of__nat__div,axiom,
% 5.46/5.70 ! [D2: nat,N: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ D2 @ N )
% 5.46/5.70 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D2 ) )
% 5.46/5.70 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_div
% 5.46/5.70 thf(fact_7192_mult__inc,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( times_times_num @ X2 @ ( inc @ Y2 ) )
% 5.46/5.70 = ( plus_plus_num @ ( times_times_num @ X2 @ Y2 ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % mult_inc
% 5.46/5.70 thf(fact_7193_less__log2__of__power,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.46/5.70 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_log2_of_power
% 5.46/5.70 thf(fact_7194_le__log2__of__power,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.46/5.70 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % le_log2_of_power
% 5.46/5.70 thf(fact_7195_even__and__iff,axiom,
% 5.46/5.70 ! [A: code_integer,B: code_integer] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.46/5.70 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_and_iff
% 5.46/5.70 thf(fact_7196_even__and__iff,axiom,
% 5.46/5.70 ! [A: int,B: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.46/5.70 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_and_iff
% 5.46/5.70 thf(fact_7197_even__and__iff,axiom,
% 5.46/5.70 ! [A: nat,B: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.46/5.70 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_and_iff
% 5.46/5.70 thf(fact_7198_log2__of__power__less,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.70 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log2_of_power_less
% 5.46/5.70 thf(fact_7199_log__base__change,axiom,
% 5.46/5.70 ! [A: real,B: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.70 => ( ( A != one_one_real )
% 5.46/5.70 => ( ( log @ B @ X2 )
% 5.46/5.70 = ( divide_divide_real @ ( log @ A @ X2 ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_base_change
% 5.46/5.70 thf(fact_7200_even__and__iff__int,axiom,
% 5.46/5.70 ! [K: int,L2: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.46/5.70 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.46/5.70 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_and_iff_int
% 5.46/5.70 thf(fact_7201_numeral__inc,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( numera6690914467698888265omplex @ ( inc @ X2 ) )
% 5.46/5.70 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_inc
% 5.46/5.70 thf(fact_7202_numeral__inc,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( numeral_numeral_real @ ( inc @ X2 ) )
% 5.46/5.70 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_inc
% 5.46/5.70 thf(fact_7203_numeral__inc,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( numeral_numeral_rat @ ( inc @ X2 ) )
% 5.46/5.70 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_inc
% 5.46/5.70 thf(fact_7204_numeral__inc,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( numeral_numeral_nat @ ( inc @ X2 ) )
% 5.46/5.70 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_inc
% 5.46/5.70 thf(fact_7205_numeral__inc,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( numeral_numeral_int @ ( inc @ X2 ) )
% 5.46/5.70 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_inc
% 5.46/5.70 thf(fact_7206_mod__mult2__eq_H,axiom,
% 5.46/5.70 ! [A: code_integer,M: nat,N: nat] :
% 5.46/5.70 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.46/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_mult2_eq'
% 5.46/5.70 thf(fact_7207_mod__mult2__eq_H,axiom,
% 5.46/5.70 ! [A: int,M: nat,N: nat] :
% 5.46/5.70 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_mult2_eq'
% 5.46/5.70 thf(fact_7208_mod__mult2__eq_H,axiom,
% 5.46/5.70 ! [A: nat,M: nat,N: nat] :
% 5.46/5.70 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_mult2_eq'
% 5.46/5.70 thf(fact_7209_field__char__0__class_Oof__nat__div,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % field_char_0_class.of_nat_div
% 5.46/5.70 thf(fact_7210_field__char__0__class_Oof__nat__div,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % field_char_0_class.of_nat_div
% 5.46/5.70 thf(fact_7211_field__char__0__class_Oof__nat__div,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % field_char_0_class.of_nat_div
% 5.46/5.70 thf(fact_7212_pos__int__cases,axiom,
% 5.46/5.70 ! [K: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.70 => ~ ! [N3: nat] :
% 5.46/5.70 ( ( K
% 5.46/5.70 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.46/5.70 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pos_int_cases
% 5.46/5.70 thf(fact_7213_zero__less__imp__eq__int,axiom,
% 5.46/5.70 ! [K: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.70 => ? [N3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.46/5.70 & ( K
% 5.46/5.70 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_less_imp_eq_int
% 5.46/5.70 thf(fact_7214_int__cases3,axiom,
% 5.46/5.70 ! [K: int] :
% 5.46/5.70 ( ( K != zero_zero_int )
% 5.46/5.70 => ( ! [N3: nat] :
% 5.46/5.70 ( ( K
% 5.46/5.70 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.46/5.70 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.46/5.70 => ~ ! [N3: nat] :
% 5.46/5.70 ( ( K
% 5.46/5.70 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.46/5.70 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_cases3
% 5.46/5.70 thf(fact_7215_nat__less__real__le,axiom,
% 5.46/5.70 ( ord_less_nat
% 5.46/5.70 = ( ^ [N2: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_less_real_le
% 5.46/5.70 thf(fact_7216_nat__le__real__less,axiom,
% 5.46/5.70 ( ord_less_eq_nat
% 5.46/5.70 = ( ^ [N2: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_le_real_less
% 5.46/5.70 thf(fact_7217_zmult__zless__mono2__lemma,axiom,
% 5.46/5.70 ! [I: int,J: int,K: nat] :
% 5.46/5.70 ( ( ord_less_int @ I @ J )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.70 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zmult_zless_mono2_lemma
% 5.46/5.70 thf(fact_7218_not__zle__0__negative,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % not_zle_0_negative
% 5.46/5.70 thf(fact_7219_negD,axiom,
% 5.46/5.70 ! [X2: int] :
% 5.46/5.70 ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.46/5.70 => ? [N3: nat] :
% 5.46/5.70 ( X2
% 5.46/5.70 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % negD
% 5.46/5.70 thf(fact_7220_negative__zless__0,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % negative_zless_0
% 5.46/5.70 thf(fact_7221_log2__of__power__le,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.70 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log2_of_power_le
% 5.46/5.70 thf(fact_7222_int__ops_I6_J,axiom,
% 5.46/5.70 ! [A: nat,B: nat] :
% 5.46/5.70 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.46/5.70 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.46/5.70 = zero_zero_int ) )
% 5.46/5.70 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.46/5.70 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.46/5.70 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_ops(6)
% 5.46/5.70 thf(fact_7223_real__of__nat__div__aux,axiom,
% 5.46/5.70 ! [X2: nat,D2: nat] :
% 5.46/5.70 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ D2 ) )
% 5.46/5.70 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X2 @ D2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X2 @ D2 ) ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_div_aux
% 5.46/5.70 thf(fact_7224_one__and__eq,axiom,
% 5.46/5.70 ! [A: code_integer] :
% 5.46/5.70 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.46/5.70 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_and_eq
% 5.46/5.70 thf(fact_7225_one__and__eq,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.46/5.70 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_and_eq
% 5.46/5.70 thf(fact_7226_one__and__eq,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.46/5.70 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_and_eq
% 5.46/5.70 thf(fact_7227_and__one__eq,axiom,
% 5.46/5.70 ! [A: code_integer] :
% 5.46/5.70 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.46/5.70 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_one_eq
% 5.46/5.70 thf(fact_7228_and__one__eq,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.46/5.70 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_one_eq
% 5.46/5.70 thf(fact_7229_and__one__eq,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.46/5.70 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_one_eq
% 5.46/5.70 thf(fact_7230_log__mult,axiom,
% 5.46/5.70 ! [A: real,X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.70 => ( ( A != one_one_real )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.70 => ( ( log @ A @ ( times_times_real @ X2 @ Y2 ) )
% 5.46/5.70 = ( plus_plus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_mult
% 5.46/5.70 thf(fact_7231_log__divide,axiom,
% 5.46/5.70 ! [A: real,X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.70 => ( ( A != one_one_real )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.70 => ( ( log @ A @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.46/5.70 = ( minus_minus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_divide
% 5.46/5.70 thf(fact_7232_nat__approx__posE,axiom,
% 5.46/5.70 ! [E: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.70 => ~ ! [N3: nat] :
% 5.46/5.70 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_approx_posE
% 5.46/5.70 thf(fact_7233_nat__approx__posE,axiom,
% 5.46/5.70 ! [E: rat] :
% 5.46/5.70 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.46/5.70 => ~ ! [N3: nat] :
% 5.46/5.70 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_approx_posE
% 5.46/5.70 thf(fact_7234_of__nat__less__two__power,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_two_power
% 5.46/5.70 thf(fact_7235_of__nat__less__two__power,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_two_power
% 5.46/5.70 thf(fact_7236_of__nat__less__two__power,axiom,
% 5.46/5.70 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_less_two_power
% 5.46/5.70 thf(fact_7237_inverse__of__nat__le,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( N != zero_zero_nat )
% 5.46/5.70 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inverse_of_nat_le
% 5.46/5.70 thf(fact_7238_inverse__of__nat__le,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( N != zero_zero_nat )
% 5.46/5.70 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inverse_of_nat_le
% 5.46/5.70 thf(fact_7239_member__bound__size__univ,axiom,
% 5.46/5.70 ! [T: vEBT_VEBT,N: nat,U: real,X2: nat] :
% 5.46/5.70 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.70 => ( ( U
% 5.46/5.70 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.70 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X2 ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % member_bound_size_univ
% 5.46/5.70 thf(fact_7240_exp__divide__power__eq,axiom,
% 5.46/5.70 ! [N: nat,X2: real] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.46/5.70 = ( exp_real @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_divide_power_eq
% 5.46/5.70 thf(fact_7241_exp__divide__power__eq,axiom,
% 5.46/5.70 ! [N: nat,X2: complex] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X2 @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.46/5.70 = ( exp_complex @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_divide_power_eq
% 5.46/5.70 thf(fact_7242_real__archimedian__rdiv__eq__0,axiom,
% 5.46/5.70 ! [X2: real,C: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.70 => ( ! [M4: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 5.46/5.70 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X2 ) @ C ) )
% 5.46/5.70 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_archimedian_rdiv_eq_0
% 5.46/5.70 thf(fact_7243_neg__int__cases,axiom,
% 5.46/5.70 ! [K: int] :
% 5.46/5.70 ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.70 => ~ ! [N3: nat] :
% 5.46/5.70 ( ( K
% 5.46/5.70 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.46/5.70 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % neg_int_cases
% 5.46/5.70 thf(fact_7244_zdiff__int__split,axiom,
% 5.46/5.70 ! [P: int > $o,X2: nat,Y2: nat] :
% 5.46/5.70 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X2 @ Y2 ) ) )
% 5.46/5.70 = ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 5.46/5.70 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) )
% 5.46/5.70 & ( ( ord_less_nat @ X2 @ Y2 )
% 5.46/5.70 => ( P @ zero_zero_int ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdiff_int_split
% 5.46/5.70 thf(fact_7245_real__of__nat__div2,axiom,
% 5.46/5.70 ! [N: nat,X2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_div2
% 5.46/5.70 thf(fact_7246_real__of__nat__div3,axiom,
% 5.46/5.70 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) @ one_one_real ) ).
% 5.46/5.70
% 5.46/5.70 % real_of_nat_div3
% 5.46/5.70 thf(fact_7247_ln__realpow,axiom,
% 5.46/5.70 ! [X2: real,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ln_ln_real @ ( power_power_real @ X2 @ N ) )
% 5.46/5.70 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ln_realpow
% 5.46/5.70 thf(fact_7248_log__eq__div__ln__mult__log,axiom,
% 5.46/5.70 ! [A: real,B: real,X2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.70 => ( ( A != one_one_real )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.70 => ( ( B != one_one_real )
% 5.46/5.70 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( log @ A @ X2 )
% 5.46/5.70 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X2 ) ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_eq_div_ln_mult_log
% 5.46/5.70 thf(fact_7249_linear__plus__1__le__power,axiom,
% 5.46/5.70 ! [X2: real,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X2 @ one_one_real ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % linear_plus_1_le_power
% 5.46/5.70 thf(fact_7250_Bernoulli__inequality,axiom,
% 5.46/5.70 ! [X2: real,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.70 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % Bernoulli_inequality
% 5.46/5.70 thf(fact_7251_and__int__rec,axiom,
% 5.46/5.70 ( bit_se725231765392027082nd_int
% 5.46/5.70 = ( ^ [K2: int,L: int] :
% 5.46/5.70 ( plus_plus_int
% 5.46/5.70 @ ( zero_n2684676970156552555ol_int
% 5.46/5.70 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.46/5.70 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.46/5.70 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_int_rec
% 5.46/5.70 thf(fact_7252_double__arith__series,axiom,
% 5.46/5.70 ! [A: int,D2: int,N: nat] :
% 5.46/5.70 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.46/5.70 @ ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D2 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_arith_series
% 5.46/5.70 thf(fact_7253_double__arith__series,axiom,
% 5.46/5.70 ! [A: complex,D2: complex,N: nat] :
% 5.46/5.70 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.46/5.70 @ ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I4 ) @ D2 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_arith_series
% 5.46/5.70 thf(fact_7254_double__arith__series,axiom,
% 5.46/5.70 ! [A: rat,D2: rat,N: nat] :
% 5.46/5.70 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.46/5.70 @ ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I4 ) @ D2 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_arith_series
% 5.46/5.70 thf(fact_7255_double__arith__series,axiom,
% 5.46/5.70 ! [A: nat,D2: nat,N: nat] :
% 5.46/5.70 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.46/5.70 @ ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D2 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_arith_series
% 5.46/5.70 thf(fact_7256_double__arith__series,axiom,
% 5.46/5.70 ! [A: real,D2: real,N: nat] :
% 5.46/5.70 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.46/5.70 @ ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I4 ) @ D2 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_arith_series
% 5.46/5.70 thf(fact_7257_double__gauss__sum,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum
% 5.46/5.70 thf(fact_7258_double__gauss__sum,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum
% 5.46/5.70 thf(fact_7259_double__gauss__sum,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum
% 5.46/5.70 thf(fact_7260_double__gauss__sum,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum
% 5.46/5.70 thf(fact_7261_double__gauss__sum,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.70 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum
% 5.46/5.70 thf(fact_7262_arith__series,axiom,
% 5.46/5.70 ! [A: int,D2: int,N: nat] :
% 5.46/5.70 ( ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D2 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.70 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % arith_series
% 5.46/5.70 thf(fact_7263_arith__series,axiom,
% 5.46/5.70 ! [A: nat,D2: nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D2 ) )
% 5.46/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.70 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % arith_series
% 5.46/5.70 thf(fact_7264_gauss__sum,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.70 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % gauss_sum
% 5.46/5.70 thf(fact_7265_gauss__sum,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.70 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % gauss_sum
% 5.46/5.70 thf(fact_7266_double__gauss__sum__from__Suc__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.46/5.70 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum_from_Suc_0
% 5.46/5.70 thf(fact_7267_double__gauss__sum__from__Suc__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.46/5.70 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum_from_Suc_0
% 5.46/5.70 thf(fact_7268_double__gauss__sum__from__Suc__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.46/5.70 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum_from_Suc_0
% 5.46/5.70 thf(fact_7269_double__gauss__sum__from__Suc__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.46/5.70 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum_from_Suc_0
% 5.46/5.70 thf(fact_7270_double__gauss__sum__from__Suc__0,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.46/5.70 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_gauss_sum_from_Suc_0
% 5.46/5.70 thf(fact_7271_sum__gp__offset,axiom,
% 5.46/5.70 ! [X2: complex,M: nat,N: nat] :
% 5.46/5.70 ( ( ( X2 = one_one_complex )
% 5.46/5.70 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.46/5.70 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.46/5.70 & ( ( X2 != one_one_complex )
% 5.46/5.70 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.46/5.70 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp_offset
% 5.46/5.70 thf(fact_7272_sum__gp__offset,axiom,
% 5.46/5.70 ! [X2: rat,M: nat,N: nat] :
% 5.46/5.70 ( ( ( X2 = one_one_rat )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.46/5.70 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.46/5.70 & ( ( X2 != one_one_rat )
% 5.46/5.70 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.46/5.70 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp_offset
% 5.46/5.70 thf(fact_7273_sum__gp__offset,axiom,
% 5.46/5.70 ! [X2: real,M: nat,N: nat] :
% 5.46/5.70 ( ( ( X2 = one_one_real )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.46/5.70 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.46/5.70 & ( ( X2 != one_one_real )
% 5.46/5.70 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.46/5.70 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_gp_offset
% 5.46/5.70 thf(fact_7274_Bernoulli__inequality__even,axiom,
% 5.46/5.70 ! [N: nat,X2: real] :
% 5.46/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % Bernoulli_inequality_even
% 5.46/5.70 thf(fact_7275_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.46/5.70 ! [N: nat,X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X2 )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_ge_one_plus_x_over_n_power_n
% 5.46/5.70 thf(fact_7276_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.46/5.70 ! [X2: real,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_ge_one_minus_x_over_n_power_n
% 5.46/5.70 thf(fact_7277_log__base__10__eq2,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.70 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_base_10_eq2
% 5.46/5.70 thf(fact_7278_of__nat__code__if,axiom,
% 5.46/5.70 ( semiri1314217659103216013at_int
% 5.46/5.70 = ( ^ [N2: nat] :
% 5.46/5.70 ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 5.46/5.70 @ ( produc6840382203811409530at_int
% 5.46/5.70 @ ^ [M3: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ one_one_int ) )
% 5.46/5.70 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_code_if
% 5.46/5.70 thf(fact_7279_of__nat__code__if,axiom,
% 5.46/5.70 ( semiri5074537144036343181t_real
% 5.46/5.70 = ( ^ [N2: nat] :
% 5.46/5.70 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.46/5.70 @ ( produc1703576794950452218t_real
% 5.46/5.70 @ ^ [M3: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ one_one_real ) )
% 5.46/5.70 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_code_if
% 5.46/5.70 thf(fact_7280_of__nat__code__if,axiom,
% 5.46/5.70 ( semiri1316708129612266289at_nat
% 5.46/5.70 = ( ^ [N2: nat] :
% 5.46/5.70 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.46/5.70 @ ( produc6842872674320459806at_nat
% 5.46/5.70 @ ^ [M3: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ one_one_nat ) )
% 5.46/5.70 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_code_if
% 5.46/5.70 thf(fact_7281_of__nat__code__if,axiom,
% 5.46/5.70 ( semiri8010041392384452111omplex
% 5.46/5.70 = ( ^ [N2: nat] :
% 5.46/5.70 ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 5.46/5.70 @ ( produc1917071388513777916omplex
% 5.46/5.70 @ ^ [M3: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ one_one_complex ) )
% 5.46/5.70 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_code_if
% 5.46/5.70 thf(fact_7282_of__nat__code__if,axiom,
% 5.46/5.70 ( semiri681578069525770553at_rat
% 5.46/5.70 = ( ^ [N2: nat] :
% 5.46/5.70 ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 5.46/5.70 @ ( produc6207742614233964070at_rat
% 5.46/5.70 @ ^ [M3: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ one_one_rat ) )
% 5.46/5.70 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_nat_code_if
% 5.46/5.70 thf(fact_7283_monoseq__arctan__series,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.70 => ( topolo6980174941875973593q_real
% 5.46/5.70 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % monoseq_arctan_series
% 5.46/5.70 thf(fact_7284_lemma__termdiff3,axiom,
% 5.46/5.70 ! [H2: real,Z: real,K5: real,N: nat] :
% 5.46/5.70 ( ( H2 != zero_zero_real )
% 5.46/5.70 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.46/5.70 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.46/5.70 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lemma_termdiff3
% 5.46/5.70 thf(fact_7285_lemma__termdiff3,axiom,
% 5.46/5.70 ! [H2: complex,Z: complex,K5: real,N: nat] :
% 5.46/5.70 ( ( H2 != zero_zero_complex )
% 5.46/5.70 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.46/5.70 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.46/5.70 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lemma_termdiff3
% 5.46/5.70 thf(fact_7286_log__ceil__idem,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.46/5.70 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.46/5.70 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % log_ceil_idem
% 5.46/5.70 thf(fact_7287_ln__series,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.70 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.70 => ( ( ln_ln_real @ X2 )
% 5.46/5.70 = ( suminf_real
% 5.46/5.70 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ln_series
% 5.46/5.70 thf(fact_7288_lemma__termdiff2,axiom,
% 5.46/5.70 ! [H2: complex,Z: complex,N: nat] :
% 5.46/5.70 ( ( H2 != zero_zero_complex )
% 5.46/5.70 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.46/5.70 = ( times_times_complex @ H2
% 5.46/5.70 @ ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [P5: nat] :
% 5.46/5.70 ( groups2073611262835488442omplex
% 5.46/5.70 @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lemma_termdiff2
% 5.46/5.70 thf(fact_7289_lemma__termdiff2,axiom,
% 5.46/5.70 ! [H2: rat,Z: rat,N: nat] :
% 5.46/5.70 ( ( H2 != zero_zero_rat )
% 5.46/5.70 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.46/5.70 = ( times_times_rat @ H2
% 5.46/5.70 @ ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [P5: nat] :
% 5.46/5.70 ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q4 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lemma_termdiff2
% 5.46/5.70 thf(fact_7290_lemma__termdiff2,axiom,
% 5.46/5.70 ! [H2: real,Z: real,N: nat] :
% 5.46/5.70 ( ( H2 != zero_zero_real )
% 5.46/5.70 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.46/5.70 = ( times_times_real @ H2
% 5.46/5.70 @ ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [P5: nat] :
% 5.46/5.70 ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lemma_termdiff2
% 5.46/5.70 thf(fact_7291_lessThan__iff,axiom,
% 5.46/5.70 ! [I: rat,K: rat] :
% 5.46/5.70 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 5.46/5.70 = ( ord_less_rat @ I @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_iff
% 5.46/5.70 thf(fact_7292_lessThan__iff,axiom,
% 5.46/5.70 ! [I: num,K: num] :
% 5.46/5.70 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 5.46/5.70 = ( ord_less_num @ I @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_iff
% 5.46/5.70 thf(fact_7293_lessThan__iff,axiom,
% 5.46/5.70 ! [I: int,K: int] :
% 5.46/5.70 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 5.46/5.70 = ( ord_less_int @ I @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_iff
% 5.46/5.70 thf(fact_7294_lessThan__iff,axiom,
% 5.46/5.70 ! [I: nat,K: nat] :
% 5.46/5.70 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 5.46/5.70 = ( ord_less_nat @ I @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_iff
% 5.46/5.70 thf(fact_7295_lessThan__iff,axiom,
% 5.46/5.70 ! [I: real,K: real] :
% 5.46/5.70 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 5.46/5.70 = ( ord_less_real @ I @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_iff
% 5.46/5.70 thf(fact_7296_of__int__ceiling__cancel,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = X2 )
% 5.46/5.70 = ( ? [N2: int] :
% 5.46/5.70 ( X2
% 5.46/5.70 = ( ring_1_of_int_rat @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_int_ceiling_cancel
% 5.46/5.70 thf(fact_7297_of__int__ceiling__cancel,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = X2 )
% 5.46/5.70 = ( ? [N2: int] :
% 5.46/5.70 ( X2
% 5.46/5.70 = ( ring_1_of_int_real @ N2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_int_ceiling_cancel
% 5.46/5.70 thf(fact_7298_heigt__uplog__rel,axiom,
% 5.46/5.70 ! [T: vEBT_VEBT,N: nat] :
% 5.46/5.70 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.70 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 5.46/5.70 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % heigt_uplog_rel
% 5.46/5.70 thf(fact_7299_lessThan__subset__iff,axiom,
% 5.46/5.70 ! [X2: rat,Y2: rat] :
% 5.46/5.70 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X2 ) @ ( set_ord_lessThan_rat @ Y2 ) )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_subset_iff
% 5.46/5.70 thf(fact_7300_lessThan__subset__iff,axiom,
% 5.46/5.70 ! [X2: num,Y2: num] :
% 5.46/5.70 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X2 ) @ ( set_ord_lessThan_num @ Y2 ) )
% 5.46/5.70 = ( ord_less_eq_num @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_subset_iff
% 5.46/5.70 thf(fact_7301_lessThan__subset__iff,axiom,
% 5.46/5.70 ! [X2: int,Y2: int] :
% 5.46/5.70 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X2 ) @ ( set_ord_lessThan_int @ Y2 ) )
% 5.46/5.70 = ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_subset_iff
% 5.46/5.70 thf(fact_7302_lessThan__subset__iff,axiom,
% 5.46/5.70 ! [X2: nat,Y2: nat] :
% 5.46/5.70 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X2 ) @ ( set_ord_lessThan_nat @ Y2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_subset_iff
% 5.46/5.70 thf(fact_7303_lessThan__subset__iff,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X2 ) @ ( set_or5984915006950818249n_real @ Y2 ) )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_subset_iff
% 5.46/5.70 thf(fact_7304_ceiling__numeral,axiom,
% 5.46/5.70 ! [V: num] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.46/5.70 = ( numeral_numeral_int @ V ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_numeral
% 5.46/5.70 thf(fact_7305_ceiling__numeral,axiom,
% 5.46/5.70 ! [V: num] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.46/5.70 = ( numeral_numeral_int @ V ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_numeral
% 5.46/5.70 thf(fact_7306_ceiling__one,axiom,
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_one
% 5.46/5.70 thf(fact_7307_ceiling__one,axiom,
% 5.46/5.70 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.46/5.70 = one_one_int ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_one
% 5.46/5.70 thf(fact_7308_sum_OlessThan__Suc,axiom,
% 5.46/5.70 ! [G: nat > rat,N: nat] :
% 5.46/5.70 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.lessThan_Suc
% 5.46/5.70 thf(fact_7309_sum_OlessThan__Suc,axiom,
% 5.46/5.70 ! [G: nat > int,N: nat] :
% 5.46/5.70 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.lessThan_Suc
% 5.46/5.70 thf(fact_7310_sum_OlessThan__Suc,axiom,
% 5.46/5.70 ! [G: nat > nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.lessThan_Suc
% 5.46/5.70 thf(fact_7311_sum_OlessThan__Suc,axiom,
% 5.46/5.70 ! [G: nat > real,N: nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.lessThan_Suc
% 5.46/5.70 thf(fact_7312_ceiling__add__of__int,axiom,
% 5.46/5.70 ! [X2: rat,Z: int] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_add_of_int
% 5.46/5.70 thf(fact_7313_ceiling__add__of__int,axiom,
% 5.46/5.70 ! [X2: real,Z: int] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_add_of_int
% 5.46/5.70 thf(fact_7314_ceiling__diff__of__int,axiom,
% 5.46/5.70 ! [X2: rat,Z: int] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.46/5.70 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_diff_of_int
% 5.46/5.70 thf(fact_7315_ceiling__diff__of__int,axiom,
% 5.46/5.70 ! [X2: real,Z: int] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.46/5.70 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_diff_of_int
% 5.46/5.70 thf(fact_7316_ceiling__le__zero,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_zero
% 5.46/5.70 thf(fact_7317_ceiling__le__zero,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_zero
% 5.46/5.70 thf(fact_7318_zero__less__ceiling,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_less_ceiling
% 5.46/5.70 thf(fact_7319_zero__less__ceiling,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_less_ceiling
% 5.46/5.70 thf(fact_7320_ceiling__le__numeral,axiom,
% 5.46/5.70 ! [X2: real,V: num] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_numeral
% 5.46/5.70 thf(fact_7321_ceiling__le__numeral,axiom,
% 5.46/5.70 ! [X2: rat,V: num] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_numeral
% 5.46/5.70 thf(fact_7322_ceiling__less__one,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_one
% 5.46/5.70 thf(fact_7323_ceiling__less__one,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_one
% 5.46/5.70 thf(fact_7324_one__le__ceiling,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_le_ceiling
% 5.46/5.70 thf(fact_7325_one__le__ceiling,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_le_ceiling
% 5.46/5.70 thf(fact_7326_numeral__less__ceiling,axiom,
% 5.46/5.70 ! [V: num,X2: real] :
% 5.46/5.70 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_less_ceiling
% 5.46/5.70 thf(fact_7327_numeral__less__ceiling,axiom,
% 5.46/5.70 ! [V: num,X2: rat] :
% 5.46/5.70 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_less_ceiling
% 5.46/5.70 thf(fact_7328_ceiling__le__one,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_one
% 5.46/5.70 thf(fact_7329_ceiling__le__one,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_one
% 5.46/5.70 thf(fact_7330_one__less__ceiling,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_rat @ one_one_rat @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_less_ceiling
% 5.46/5.70 thf(fact_7331_one__less__ceiling,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ one_one_real @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_less_ceiling
% 5.46/5.70 thf(fact_7332_ceiling__add__numeral,axiom,
% 5.46/5.70 ! [X2: real,V: num] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_add_numeral
% 5.46/5.70 thf(fact_7333_ceiling__add__numeral,axiom,
% 5.46/5.70 ! [X2: rat,V: num] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_add_numeral
% 5.46/5.70 thf(fact_7334_ceiling__neg__numeral,axiom,
% 5.46/5.70 ! [V: num] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.70 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_neg_numeral
% 5.46/5.70 thf(fact_7335_ceiling__neg__numeral,axiom,
% 5.46/5.70 ! [V: num] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.70 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_neg_numeral
% 5.46/5.70 thf(fact_7336_ceiling__add__one,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 5.46/5.70 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_add_one
% 5.46/5.70 thf(fact_7337_ceiling__add__one,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ one_one_real ) )
% 5.46/5.70 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_add_one
% 5.46/5.70 thf(fact_7338_ceiling__diff__numeral,axiom,
% 5.46/5.70 ! [X2: real,V: num] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.70 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_diff_numeral
% 5.46/5.70 thf(fact_7339_ceiling__diff__numeral,axiom,
% 5.46/5.70 ! [X2: rat,V: num] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.70 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_diff_numeral
% 5.46/5.70 thf(fact_7340_ceiling__diff__one,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.46/5.70 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_diff_one
% 5.46/5.70 thf(fact_7341_ceiling__diff__one,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.46/5.70 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_diff_one
% 5.46/5.70 thf(fact_7342_ceiling__numeral__power,axiom,
% 5.46/5.70 ! [X2: num,N: nat] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.46/5.70 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_numeral_power
% 5.46/5.70 thf(fact_7343_ceiling__numeral__power,axiom,
% 5.46/5.70 ! [X2: num,N: nat] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.46/5.70 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_numeral_power
% 5.46/5.70 thf(fact_7344_and__nat__numerals_I3_J,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % and_nat_numerals(3)
% 5.46/5.70 thf(fact_7345_and__nat__numerals_I1_J,axiom,
% 5.46/5.70 ! [Y2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % and_nat_numerals(1)
% 5.46/5.70 thf(fact_7346_powser__zero,axiom,
% 5.46/5.70 ! [F: nat > complex] :
% 5.46/5.70 ( ( suminf_complex
% 5.46/5.70 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 5.46/5.70 = ( F @ zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % powser_zero
% 5.46/5.70 thf(fact_7347_powser__zero,axiom,
% 5.46/5.70 ! [F: nat > real] :
% 5.46/5.70 ( ( suminf_real
% 5.46/5.70 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 5.46/5.70 = ( F @ zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % powser_zero
% 5.46/5.70 thf(fact_7348_ceiling__less__zero,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_zero
% 5.46/5.70 thf(fact_7349_ceiling__less__zero,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_zero
% 5.46/5.70 thf(fact_7350_zero__le__ceiling,axiom,
% 5.46/5.70 ! [X2: real] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_le_ceiling
% 5.46/5.70 thf(fact_7351_zero__le__ceiling,axiom,
% 5.46/5.70 ! [X2: rat] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_le_ceiling
% 5.46/5.70 thf(fact_7352_and__nat__numerals_I4_J,axiom,
% 5.46/5.70 ! [X2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.70 = one_one_nat ) ).
% 5.46/5.70
% 5.46/5.70 % and_nat_numerals(4)
% 5.46/5.70 thf(fact_7353_and__nat__numerals_I2_J,axiom,
% 5.46/5.70 ! [Y2: num] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.46/5.70 = one_one_nat ) ).
% 5.46/5.70
% 5.46/5.70 % and_nat_numerals(2)
% 5.46/5.70 thf(fact_7354_ceiling__divide__eq__div__numeral,axiom,
% 5.46/5.70 ! [A: num,B: num] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.46/5.70 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_divide_eq_div_numeral
% 5.46/5.70 thf(fact_7355_ceiling__less__numeral,axiom,
% 5.46/5.70 ! [X2: real,V: num] :
% 5.46/5.70 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_numeral
% 5.46/5.70 thf(fact_7356_ceiling__less__numeral,axiom,
% 5.46/5.70 ! [X2: rat,V: num] :
% 5.46/5.70 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_numeral
% 5.46/5.70 thf(fact_7357_numeral__le__ceiling,axiom,
% 5.46/5.70 ! [V: num,X2: real] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_le_ceiling
% 5.46/5.70 thf(fact_7358_numeral__le__ceiling,axiom,
% 5.46/5.70 ! [V: num,X2: rat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_le_ceiling
% 5.46/5.70 thf(fact_7359_ceiling__le__neg__numeral,axiom,
% 5.46/5.70 ! [X2: real,V: num] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_neg_numeral
% 5.46/5.70 thf(fact_7360_ceiling__le__neg__numeral,axiom,
% 5.46/5.70 ! [X2: rat,V: num] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_neg_numeral
% 5.46/5.70 thf(fact_7361_neg__numeral__less__ceiling,axiom,
% 5.46/5.70 ! [V: num,X2: real] :
% 5.46/5.70 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % neg_numeral_less_ceiling
% 5.46/5.70 thf(fact_7362_neg__numeral__less__ceiling,axiom,
% 5.46/5.70 ! [V: num,X2: rat] :
% 5.46/5.70 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % neg_numeral_less_ceiling
% 5.46/5.70 thf(fact_7363_Suc__0__and__eq,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.70 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % Suc_0_and_eq
% 5.46/5.70 thf(fact_7364_and__Suc__0__eq,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.70 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % and_Suc_0_eq
% 5.46/5.70 thf(fact_7365_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.46/5.70 ! [A: num,B: num] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.46/5.70 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_minus_divide_eq_div_numeral
% 5.46/5.70 thf(fact_7366_ceiling__less__neg__numeral,axiom,
% 5.46/5.70 ! [X2: real,V: num] :
% 5.46/5.70 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_neg_numeral
% 5.46/5.70 thf(fact_7367_ceiling__less__neg__numeral,axiom,
% 5.46/5.70 ! [X2: rat,V: num] :
% 5.46/5.70 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_neg_numeral
% 5.46/5.70 thf(fact_7368_neg__numeral__le__ceiling,axiom,
% 5.46/5.70 ! [V: num,X2: real] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % neg_numeral_le_ceiling
% 5.46/5.70 thf(fact_7369_neg__numeral__le__ceiling,axiom,
% 5.46/5.70 ! [V: num,X2: rat] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % neg_numeral_le_ceiling
% 5.46/5.70 thf(fact_7370_lessThan__def,axiom,
% 5.46/5.70 ( set_ord_lessThan_rat
% 5.46/5.70 = ( ^ [U2: rat] :
% 5.46/5.70 ( collect_rat
% 5.46/5.70 @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_def
% 5.46/5.70 thf(fact_7371_lessThan__def,axiom,
% 5.46/5.70 ( set_ord_lessThan_num
% 5.46/5.70 = ( ^ [U2: num] :
% 5.46/5.70 ( collect_num
% 5.46/5.70 @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_def
% 5.46/5.70 thf(fact_7372_lessThan__def,axiom,
% 5.46/5.70 ( set_ord_lessThan_int
% 5.46/5.70 = ( ^ [U2: int] :
% 5.46/5.70 ( collect_int
% 5.46/5.70 @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_def
% 5.46/5.70 thf(fact_7373_lessThan__def,axiom,
% 5.46/5.70 ( set_ord_lessThan_nat
% 5.46/5.70 = ( ^ [U2: nat] :
% 5.46/5.70 ( collect_nat
% 5.46/5.70 @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_def
% 5.46/5.70 thf(fact_7374_lessThan__def,axiom,
% 5.46/5.70 ( set_or5984915006950818249n_real
% 5.46/5.70 = ( ^ [U2: real] :
% 5.46/5.70 ( collect_real
% 5.46/5.70 @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_def
% 5.46/5.70 thf(fact_7375_ceiling__mono,axiom,
% 5.46/5.70 ! [Y2: real,X2: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ Y2 @ X2 )
% 5.46/5.70 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y2 ) @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_mono
% 5.46/5.70 thf(fact_7376_ceiling__mono,axiom,
% 5.46/5.70 ! [Y2: rat,X2: rat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ Y2 @ X2 )
% 5.46/5.70 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y2 ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_mono
% 5.46/5.70 thf(fact_7377_le__of__int__ceiling,axiom,
% 5.46/5.70 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % le_of_int_ceiling
% 5.46/5.70 thf(fact_7378_le__of__int__ceiling,axiom,
% 5.46/5.70 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % le_of_int_ceiling
% 5.46/5.70 thf(fact_7379_ceiling__less__cancel,axiom,
% 5.46/5.70 ! [X2: rat,Y2: rat] :
% 5.46/5.70 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y2 ) )
% 5.46/5.70 => ( ord_less_rat @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_cancel
% 5.46/5.70 thf(fact_7380_ceiling__less__cancel,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] :
% 5.46/5.70 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y2 ) )
% 5.46/5.70 => ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_less_cancel
% 5.46/5.70 thf(fact_7381_lessThan__strict__subset__iff,axiom,
% 5.46/5.70 ! [M: rat,N: rat] :
% 5.46/5.70 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 5.46/5.70 = ( ord_less_rat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_strict_subset_iff
% 5.46/5.70 thf(fact_7382_lessThan__strict__subset__iff,axiom,
% 5.46/5.70 ! [M: num,N: num] :
% 5.46/5.70 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 5.46/5.70 = ( ord_less_num @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_strict_subset_iff
% 5.46/5.70 thf(fact_7383_lessThan__strict__subset__iff,axiom,
% 5.46/5.70 ! [M: int,N: int] :
% 5.46/5.70 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 5.46/5.70 = ( ord_less_int @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_strict_subset_iff
% 5.46/5.70 thf(fact_7384_lessThan__strict__subset__iff,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.70 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_strict_subset_iff
% 5.46/5.70 thf(fact_7385_lessThan__strict__subset__iff,axiom,
% 5.46/5.70 ! [M: real,N: real] :
% 5.46/5.70 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.46/5.70 = ( ord_less_real @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % lessThan_strict_subset_iff
% 5.46/5.70 thf(fact_7386_complex__mod__minus__le__complex__mod,axiom,
% 5.46/5.70 ! [X2: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % complex_mod_minus_le_complex_mod
% 5.46/5.70 thf(fact_7387_complex__mod__triangle__ineq2,axiom,
% 5.46/5.70 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % complex_mod_triangle_ineq2
% 5.46/5.70 thf(fact_7388_ceiling__le,axiom,
% 5.46/5.70 ! [X2: real,A: int] :
% 5.46/5.70 ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A ) )
% 5.46/5.70 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le
% 5.46/5.70 thf(fact_7389_ceiling__le,axiom,
% 5.46/5.70 ! [X2: rat,A: int] :
% 5.46/5.70 ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.70 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le
% 5.46/5.70 thf(fact_7390_ceiling__le__iff,axiom,
% 5.46/5.70 ! [X2: real,Z: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.46/5.70 = ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_iff
% 5.46/5.70 thf(fact_7391_ceiling__le__iff,axiom,
% 5.46/5.70 ! [X2: rat,Z: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.46/5.70 = ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_le_iff
% 5.46/5.70 thf(fact_7392_less__ceiling__iff,axiom,
% 5.46/5.70 ! [Z: int,X2: rat] :
% 5.46/5.70 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.70 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_ceiling_iff
% 5.46/5.70 thf(fact_7393_less__ceiling__iff,axiom,
% 5.46/5.70 ! [Z: int,X2: real] :
% 5.46/5.70 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.70 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_ceiling_iff
% 5.46/5.70 thf(fact_7394_ceiling__add__le,axiom,
% 5.46/5.70 ! [X2: rat,Y2: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ Y2 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_add_le
% 5.46/5.70 thf(fact_7395_ceiling__add__le,axiom,
% 5.46/5.70 ! [X2: real,Y2: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_add_le
% 5.46/5.70 thf(fact_7396_norm__exp,axiom,
% 5.46/5.70 ! [X2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X2 ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % norm_exp
% 5.46/5.70 thf(fact_7397_norm__exp,axiom,
% 5.46/5.70 ! [X2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X2 ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % norm_exp
% 5.46/5.70 thf(fact_7398_sum_Onat__diff__reindex,axiom,
% 5.46/5.70 ! [G: nat > nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.70 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.nat_diff_reindex
% 5.46/5.70 thf(fact_7399_sum_Onat__diff__reindex,axiom,
% 5.46/5.70 ! [G: nat > real,N: nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.70 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.nat_diff_reindex
% 5.46/5.70 thf(fact_7400_sum__diff__distrib,axiom,
% 5.46/5.70 ! [Q: real > nat,P: real > nat,N: real] :
% 5.46/5.70 ( ! [X3: real] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.46/5.70 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 5.46/5.70 = ( groups1935376822645274424al_nat
% 5.46/5.70 @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.46/5.70 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff_distrib
% 5.46/5.70 thf(fact_7401_sum__diff__distrib,axiom,
% 5.46/5.70 ! [Q: nat > nat,P: nat > nat,N: nat] :
% 5.46/5.70 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.46/5.70 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.46/5.70 = ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_diff_distrib
% 5.46/5.70 thf(fact_7402_of__int__ceiling__le__add__one,axiom,
% 5.46/5.70 ! [R: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ ( plus_plus_real @ R @ one_one_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_int_ceiling_le_add_one
% 5.46/5.70 thf(fact_7403_of__int__ceiling__le__add__one,axiom,
% 5.46/5.70 ! [R: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ ( plus_plus_rat @ R @ one_one_rat ) ) ).
% 5.46/5.70
% 5.46/5.70 % of_int_ceiling_le_add_one
% 5.46/5.70 thf(fact_7404_of__int__ceiling__diff__one__le,axiom,
% 5.46/5.70 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ one_one_real ) @ R ) ).
% 5.46/5.70
% 5.46/5.70 % of_int_ceiling_diff_one_le
% 5.46/5.70 thf(fact_7405_of__int__ceiling__diff__one__le,axiom,
% 5.46/5.70 ! [R: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ one_one_rat ) @ R ) ).
% 5.46/5.70
% 5.46/5.70 % of_int_ceiling_diff_one_le
% 5.46/5.70 thf(fact_7406_ceiling__divide__eq__div,axiom,
% 5.46/5.70 ! [A: int,B: int] :
% 5.46/5.70 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 5.46/5.70 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_divide_eq_div
% 5.46/5.70 thf(fact_7407_ceiling__divide__eq__div,axiom,
% 5.46/5.70 ! [A: int,B: int] :
% 5.46/5.70 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 5.46/5.70 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % ceiling_divide_eq_div
% 5.46/5.70 thf(fact_7408_sum_OlessThan__Suc__shift,axiom,
% 5.46/5.70 ! [G: nat > rat,N: nat] :
% 5.46/5.70 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.46/5.70 @ ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.lessThan_Suc_shift
% 5.46/5.70 thf(fact_7409_sum_OlessThan__Suc__shift,axiom,
% 5.46/5.70 ! [G: nat > int,N: nat] :
% 5.46/5.70 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.46/5.70 @ ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.lessThan_Suc_shift
% 5.46/5.70 thf(fact_7410_sum_OlessThan__Suc__shift,axiom,
% 5.46/5.70 ! [G: nat > nat,N: nat] :
% 5.46/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.46/5.70 @ ( groups3542108847815614940at_nat
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.lessThan_Suc_shift
% 5.46/5.70 thf(fact_7411_sum_OlessThan__Suc__shift,axiom,
% 5.46/5.70 ! [G: nat > real,N: nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.70 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.46/5.70 @ ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum.lessThan_Suc_shift
% 5.46/5.70 thf(fact_7412_sum__lessThan__telescope_H,axiom,
% 5.46/5.70 ! [F: nat > rat,M: nat] :
% 5.46/5.70 ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.70 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_lessThan_telescope'
% 5.46/5.70 thf(fact_7413_sum__lessThan__telescope_H,axiom,
% 5.46/5.70 ! [F: nat > int,M: nat] :
% 5.46/5.70 ( ( groups3539618377306564664at_int
% 5.46/5.70 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.70 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_lessThan_telescope'
% 5.46/5.70 thf(fact_7414_sum__lessThan__telescope_H,axiom,
% 5.46/5.70 ! [F: nat > real,M: nat] :
% 5.46/5.70 ( ( groups6591440286371151544t_real
% 5.46/5.70 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.46/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.70 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_lessThan_telescope'
% 5.46/5.70 thf(fact_7415_sum__lessThan__telescope,axiom,
% 5.46/5.70 ! [F: nat > rat,M: nat] :
% 5.46/5.70 ( ( groups2906978787729119204at_rat
% 5.46/5.70 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.71 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_lessThan_telescope
% 5.46/5.71 thf(fact_7416_sum__lessThan__telescope,axiom,
% 5.46/5.71 ! [F: nat > int,M: nat] :
% 5.46/5.71 ( ( groups3539618377306564664at_int
% 5.46/5.71 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.71 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_lessThan_telescope
% 5.46/5.71 thf(fact_7417_sum__lessThan__telescope,axiom,
% 5.46/5.71 ! [F: nat > real,M: nat] :
% 5.46/5.71 ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.71 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_lessThan_telescope
% 5.46/5.71 thf(fact_7418_sumr__diff__mult__const2,axiom,
% 5.46/5.71 ! [F: nat > int,N: nat,R: int] :
% 5.46/5.71 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R ) )
% 5.46/5.71 = ( groups3539618377306564664at_int
% 5.46/5.71 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ R )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sumr_diff_mult_const2
% 5.46/5.71 thf(fact_7419_sumr__diff__mult__const2,axiom,
% 5.46/5.71 ! [F: nat > complex,N: nat,R: complex] :
% 5.46/5.71 ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R ) )
% 5.46/5.71 = ( groups2073611262835488442omplex
% 5.46/5.71 @ ^ [I4: nat] : ( minus_minus_complex @ ( F @ I4 ) @ R )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sumr_diff_mult_const2
% 5.46/5.71 thf(fact_7420_sumr__diff__mult__const2,axiom,
% 5.46/5.71 ! [F: nat > rat,N: nat,R: rat] :
% 5.46/5.71 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R ) )
% 5.46/5.71 = ( groups2906978787729119204at_rat
% 5.46/5.71 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ R )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sumr_diff_mult_const2
% 5.46/5.71 thf(fact_7421_sumr__diff__mult__const2,axiom,
% 5.46/5.71 ! [F: nat > real,N: nat,R: real] :
% 5.46/5.71 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R ) )
% 5.46/5.71 = ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ R )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sumr_diff_mult_const2
% 5.46/5.71 thf(fact_7422_sum_OatLeast1__atMost__eq,axiom,
% 5.46/5.71 ! [G: nat > nat,N: nat] :
% 5.46/5.71 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.46/5.71 = ( groups3542108847815614940at_nat
% 5.46/5.71 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.atLeast1_atMost_eq
% 5.46/5.71 thf(fact_7423_sum_OatLeast1__atMost__eq,axiom,
% 5.46/5.71 ! [G: nat > real,N: nat] :
% 5.46/5.71 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.46/5.71 = ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.atLeast1_atMost_eq
% 5.46/5.71 thf(fact_7424_ceiling__correct,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) @ one_one_real ) @ X2 )
% 5.46/5.71 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_correct
% 5.46/5.71 thf(fact_7425_ceiling__correct,axiom,
% 5.46/5.71 ! [X2: rat] :
% 5.46/5.71 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) @ one_one_rat ) @ X2 )
% 5.46/5.71 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_correct
% 5.46/5.71 thf(fact_7426_ceiling__unique,axiom,
% 5.46/5.71 ! [Z: int,X2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.71 => ( ( archim7802044766580827645g_real @ X2 )
% 5.46/5.71 = Z ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_unique
% 5.46/5.71 thf(fact_7427_ceiling__unique,axiom,
% 5.46/5.71 ! [Z: int,X2: rat] :
% 5.46/5.71 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.71 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.46/5.71 = Z ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_unique
% 5.46/5.71 thf(fact_7428_ceiling__eq__iff,axiom,
% 5.46/5.71 ! [X2: real,A: int] :
% 5.46/5.71 ( ( ( archim7802044766580827645g_real @ X2 )
% 5.46/5.71 = A )
% 5.46/5.71 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X2 )
% 5.46/5.71 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_eq_iff
% 5.46/5.71 thf(fact_7429_ceiling__eq__iff,axiom,
% 5.46/5.71 ! [X2: rat,A: int] :
% 5.46/5.71 ( ( ( archim2889992004027027881ng_rat @ X2 )
% 5.46/5.71 = A )
% 5.46/5.71 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X2 )
% 5.46/5.71 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_eq_iff
% 5.46/5.71 thf(fact_7430_ceiling__split,axiom,
% 5.46/5.71 ! [P: int > $o,T: real] :
% 5.46/5.71 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.46/5.71 = ( ! [I4: int] :
% 5.46/5.71 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) @ T )
% 5.46/5.71 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I4 ) ) )
% 5.46/5.71 => ( P @ I4 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_split
% 5.46/5.71 thf(fact_7431_ceiling__split,axiom,
% 5.46/5.71 ! [P: int > $o,T: rat] :
% 5.46/5.71 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.46/5.71 = ( ! [I4: int] :
% 5.46/5.71 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T )
% 5.46/5.71 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I4 ) ) )
% 5.46/5.71 => ( P @ I4 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_split
% 5.46/5.71 thf(fact_7432_mult__ceiling__le,axiom,
% 5.46/5.71 ! [A: real,B: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.46/5.71 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_ceiling_le
% 5.46/5.71 thf(fact_7433_mult__ceiling__le,axiom,
% 5.46/5.71 ! [A: rat,B: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.46/5.71 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_ceiling_le
% 5.46/5.71 thf(fact_7434_ceiling__less__iff,axiom,
% 5.46/5.71 ! [X2: real,Z: int] :
% 5.46/5.71 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.46/5.71 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_less_iff
% 5.46/5.71 thf(fact_7435_ceiling__less__iff,axiom,
% 5.46/5.71 ! [X2: rat,Z: int] :
% 5.46/5.71 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.46/5.71 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_less_iff
% 5.46/5.71 thf(fact_7436_le__ceiling__iff,axiom,
% 5.46/5.71 ! [Z: int,X2: rat] :
% 5.46/5.71 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.46/5.71 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_ceiling_iff
% 5.46/5.71 thf(fact_7437_le__ceiling__iff,axiom,
% 5.46/5.71 ! [Z: int,X2: real] :
% 5.46/5.71 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.46/5.71 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_ceiling_iff
% 5.46/5.71 thf(fact_7438_power__diff__1__eq,axiom,
% 5.46/5.71 ! [X2: complex,N: nat] :
% 5.46/5.71 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex )
% 5.46/5.71 = ( times_times_complex @ ( minus_minus_complex @ X2 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_diff_1_eq
% 5.46/5.71 thf(fact_7439_power__diff__1__eq,axiom,
% 5.46/5.71 ! [X2: rat,N: nat] :
% 5.46/5.71 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat )
% 5.46/5.71 = ( times_times_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_diff_1_eq
% 5.46/5.71 thf(fact_7440_power__diff__1__eq,axiom,
% 5.46/5.71 ! [X2: int,N: nat] :
% 5.46/5.71 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ one_one_int )
% 5.46/5.71 = ( times_times_int @ ( minus_minus_int @ X2 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_diff_1_eq
% 5.46/5.71 thf(fact_7441_power__diff__1__eq,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real )
% 5.46/5.71 = ( times_times_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_diff_1_eq
% 5.46/5.71 thf(fact_7442_one__diff__power__eq,axiom,
% 5.46/5.71 ! [X2: complex,N: nat] :
% 5.46/5.71 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.46/5.71 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % one_diff_power_eq
% 5.46/5.71 thf(fact_7443_one__diff__power__eq,axiom,
% 5.46/5.71 ! [X2: rat,N: nat] :
% 5.46/5.71 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.46/5.71 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % one_diff_power_eq
% 5.46/5.71 thf(fact_7444_one__diff__power__eq,axiom,
% 5.46/5.71 ! [X2: int,N: nat] :
% 5.46/5.71 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.46/5.71 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % one_diff_power_eq
% 5.46/5.71 thf(fact_7445_one__diff__power__eq,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.46/5.71 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % one_diff_power_eq
% 5.46/5.71 thf(fact_7446_geometric__sum,axiom,
% 5.46/5.71 ! [X2: complex,N: nat] :
% 5.46/5.71 ( ( X2 != one_one_complex )
% 5.46/5.71 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % geometric_sum
% 5.46/5.71 thf(fact_7447_geometric__sum,axiom,
% 5.46/5.71 ! [X2: rat,N: nat] :
% 5.46/5.71 ( ( X2 != one_one_rat )
% 5.46/5.71 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % geometric_sum
% 5.46/5.71 thf(fact_7448_geometric__sum,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( X2 != one_one_real )
% 5.46/5.71 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % geometric_sum
% 5.46/5.71 thf(fact_7449_ceiling__divide__upper,axiom,
% 5.46/5.71 ! [Q2: real,P2: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.46/5.71 => ( ord_less_eq_real @ P2 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_divide_upper
% 5.46/5.71 thf(fact_7450_ceiling__divide__upper,axiom,
% 5.46/5.71 ! [Q2: rat,P2: rat] :
% 5.46/5.71 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.46/5.71 => ( ord_less_eq_rat @ P2 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_divide_upper
% 5.46/5.71 thf(fact_7451_monoseq__realpow,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.71 => ( topolo6980174941875973593q_real @ ( power_power_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % monoseq_realpow
% 5.46/5.71 thf(fact_7452_sum__gp__strict,axiom,
% 5.46/5.71 ! [X2: complex,N: nat] :
% 5.46/5.71 ( ( ( X2 = one_one_complex )
% 5.46/5.71 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.46/5.71 & ( ( X2 != one_one_complex )
% 5.46/5.71 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_gp_strict
% 5.46/5.71 thf(fact_7453_sum__gp__strict,axiom,
% 5.46/5.71 ! [X2: rat,N: nat] :
% 5.46/5.71 ( ( ( X2 = one_one_rat )
% 5.46/5.71 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.46/5.71 & ( ( X2 != one_one_rat )
% 5.46/5.71 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_gp_strict
% 5.46/5.71 thf(fact_7454_sum__gp__strict,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( ( X2 = one_one_real )
% 5.46/5.71 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.71 & ( ( X2 != one_one_real )
% 5.46/5.71 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_gp_strict
% 5.46/5.71 thf(fact_7455_lemma__termdiff1,axiom,
% 5.46/5.71 ! [Z: complex,H2: complex,M: nat] :
% 5.46/5.71 ( ( groups2073611262835488442omplex
% 5.46/5.71 @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ P5 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.71 = ( groups2073611262835488442omplex
% 5.46/5.71 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % lemma_termdiff1
% 5.46/5.71 thf(fact_7456_lemma__termdiff1,axiom,
% 5.46/5.71 ! [Z: rat,H2: rat,M: nat] :
% 5.46/5.71 ( ( groups2906978787729119204at_rat
% 5.46/5.71 @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ P5 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.71 = ( groups2906978787729119204at_rat
% 5.46/5.71 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % lemma_termdiff1
% 5.46/5.71 thf(fact_7457_lemma__termdiff1,axiom,
% 5.46/5.71 ! [Z: int,H2: int,M: nat] :
% 5.46/5.71 ( ( groups3539618377306564664at_int
% 5.46/5.71 @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ P5 ) ) @ ( power_power_int @ Z @ M ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.71 = ( groups3539618377306564664at_int
% 5.46/5.71 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % lemma_termdiff1
% 5.46/5.71 thf(fact_7458_lemma__termdiff1,axiom,
% 5.46/5.71 ! [Z: real,H2: real,M: nat] :
% 5.46/5.71 ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ P5 ) ) @ ( power_power_real @ Z @ M ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) )
% 5.46/5.71 = ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % lemma_termdiff1
% 5.46/5.71 thf(fact_7459_power__diff__sumr2,axiom,
% 5.46/5.71 ! [X2: complex,N: nat,Y2: complex] :
% 5.46/5.71 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 5.46/5.71 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y2 )
% 5.46/5.71 @ ( groups2073611262835488442omplex
% 5.46/5.71 @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_diff_sumr2
% 5.46/5.71 thf(fact_7460_power__diff__sumr2,axiom,
% 5.46/5.71 ! [X2: rat,N: nat,Y2: rat] :
% 5.46/5.71 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 5.46/5.71 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y2 )
% 5.46/5.71 @ ( groups2906978787729119204at_rat
% 5.46/5.71 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_rat @ X2 @ I4 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_diff_sumr2
% 5.46/5.71 thf(fact_7461_power__diff__sumr2,axiom,
% 5.46/5.71 ! [X2: int,N: nat,Y2: int] :
% 5.46/5.71 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y2 @ N ) )
% 5.46/5.71 = ( times_times_int @ ( minus_minus_int @ X2 @ Y2 )
% 5.46/5.71 @ ( groups3539618377306564664at_int
% 5.46/5.71 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_int @ X2 @ I4 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_diff_sumr2
% 5.46/5.71 thf(fact_7462_power__diff__sumr2,axiom,
% 5.46/5.71 ! [X2: real,N: nat,Y2: real] :
% 5.46/5.71 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y2 @ N ) )
% 5.46/5.71 = ( times_times_real @ ( minus_minus_real @ X2 @ Y2 )
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_real @ X2 @ I4 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_diff_sumr2
% 5.46/5.71 thf(fact_7463_diff__power__eq__sum,axiom,
% 5.46/5.71 ! [X2: complex,N: nat,Y2: complex] :
% 5.46/5.71 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) @ ( power_power_complex @ Y2 @ ( suc @ N ) ) )
% 5.46/5.71 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y2 )
% 5.46/5.71 @ ( groups2073611262835488442omplex
% 5.46/5.71 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X2 @ P5 ) @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_power_eq_sum
% 5.46/5.71 thf(fact_7464_diff__power__eq__sum,axiom,
% 5.46/5.71 ! [X2: rat,N: nat,Y2: rat] :
% 5.46/5.71 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) @ ( power_power_rat @ Y2 @ ( suc @ N ) ) )
% 5.46/5.71 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y2 )
% 5.46/5.71 @ ( groups2906978787729119204at_rat
% 5.46/5.71 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X2 @ P5 ) @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_power_eq_sum
% 5.46/5.71 thf(fact_7465_diff__power__eq__sum,axiom,
% 5.46/5.71 ! [X2: int,N: nat,Y2: int] :
% 5.46/5.71 ( ( minus_minus_int @ ( power_power_int @ X2 @ ( suc @ N ) ) @ ( power_power_int @ Y2 @ ( suc @ N ) ) )
% 5.46/5.71 = ( times_times_int @ ( minus_minus_int @ X2 @ Y2 )
% 5.46/5.71 @ ( groups3539618377306564664at_int
% 5.46/5.71 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X2 @ P5 ) @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_power_eq_sum
% 5.46/5.71 thf(fact_7466_diff__power__eq__sum,axiom,
% 5.46/5.71 ! [X2: real,N: nat,Y2: real] :
% 5.46/5.71 ( ( minus_minus_real @ ( power_power_real @ X2 @ ( suc @ N ) ) @ ( power_power_real @ Y2 @ ( suc @ N ) ) )
% 5.46/5.71 = ( times_times_real @ ( minus_minus_real @ X2 @ Y2 )
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X2 @ P5 ) @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_power_eq_sum
% 5.46/5.71 thf(fact_7467_ceiling__divide__lower,axiom,
% 5.46/5.71 ! [Q2: real,P2: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.46/5.71 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) @ P2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_divide_lower
% 5.46/5.71 thf(fact_7468_ceiling__divide__lower,axiom,
% 5.46/5.71 ! [Q2: rat,P2: rat] :
% 5.46/5.71 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.46/5.71 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) @ P2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_divide_lower
% 5.46/5.71 thf(fact_7469_ceiling__eq,axiom,
% 5.46/5.71 ! [N: int,X2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.46/5.71 => ( ( archim7802044766580827645g_real @ X2 )
% 5.46/5.71 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_eq
% 5.46/5.71 thf(fact_7470_ceiling__eq,axiom,
% 5.46/5.71 ! [N: int,X2: rat] :
% 5.46/5.71 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 5.46/5.71 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.46/5.71 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_eq
% 5.46/5.71 thf(fact_7471_real__sum__nat__ivl__bounded2,axiom,
% 5.46/5.71 ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 5.46/5.71 ( ! [P7: nat] :
% 5.46/5.71 ( ( ord_less_nat @ P7 @ N )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.46/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % real_sum_nat_ivl_bounded2
% 5.46/5.71 thf(fact_7472_real__sum__nat__ivl__bounded2,axiom,
% 5.46/5.71 ! [N: nat,F: nat > int,K5: int,K: nat] :
% 5.46/5.71 ( ! [P7: nat] :
% 5.46/5.71 ( ( ord_less_nat @ P7 @ N )
% 5.46/5.71 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.46/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.46/5.71 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % real_sum_nat_ivl_bounded2
% 5.46/5.71 thf(fact_7473_real__sum__nat__ivl__bounded2,axiom,
% 5.46/5.71 ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 5.46/5.71 ( ! [P7: nat] :
% 5.46/5.71 ( ( ord_less_nat @ P7 @ N )
% 5.46/5.71 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.46/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.46/5.71 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % real_sum_nat_ivl_bounded2
% 5.46/5.71 thf(fact_7474_real__sum__nat__ivl__bounded2,axiom,
% 5.46/5.71 ! [N: nat,F: nat > real,K5: real,K: nat] :
% 5.46/5.71 ( ! [P7: nat] :
% 5.46/5.71 ( ( ord_less_nat @ P7 @ N )
% 5.46/5.71 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.46/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.46/5.71 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % real_sum_nat_ivl_bounded2
% 5.46/5.71 thf(fact_7475_exp__bound__half,axiom,
% 5.46/5.71 ! [Z: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % exp_bound_half
% 5.46/5.71 thf(fact_7476_exp__bound__half,axiom,
% 5.46/5.71 ! [Z: complex] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % exp_bound_half
% 5.46/5.71 thf(fact_7477_one__diff__power__eq_H,axiom,
% 5.46/5.71 ! [X2: complex,N: nat] :
% 5.46/5.71 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.46/5.71 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 )
% 5.46/5.71 @ ( groups2073611262835488442omplex
% 5.46/5.71 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % one_diff_power_eq'
% 5.46/5.71 thf(fact_7478_one__diff__power__eq_H,axiom,
% 5.46/5.71 ! [X2: rat,N: nat] :
% 5.46/5.71 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.46/5.71 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 )
% 5.46/5.71 @ ( groups2906978787729119204at_rat
% 5.46/5.71 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % one_diff_power_eq'
% 5.46/5.71 thf(fact_7479_one__diff__power__eq_H,axiom,
% 5.46/5.71 ! [X2: int,N: nat] :
% 5.46/5.71 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.46/5.71 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 )
% 5.46/5.71 @ ( groups3539618377306564664at_int
% 5.46/5.71 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % one_diff_power_eq'
% 5.46/5.71 thf(fact_7480_one__diff__power__eq_H,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.46/5.71 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 )
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % one_diff_power_eq'
% 5.46/5.71 thf(fact_7481_and__nat__unfold,axiom,
% 5.46/5.71 ( bit_se727722235901077358nd_nat
% 5.46/5.71 = ( ^ [M3: nat,N2: nat] :
% 5.46/5.71 ( if_nat
% 5.46/5.71 @ ( ( M3 = zero_zero_nat )
% 5.46/5.71 | ( N2 = zero_zero_nat ) )
% 5.46/5.71 @ zero_zero_nat
% 5.46/5.71 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % and_nat_unfold
% 5.46/5.71 thf(fact_7482_and__nat__rec,axiom,
% 5.46/5.71 ( bit_se727722235901077358nd_nat
% 5.46/5.71 = ( ^ [M3: nat,N2: nat] :
% 5.46/5.71 ( plus_plus_nat
% 5.46/5.71 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.71 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 5.46/5.71 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.71 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % and_nat_rec
% 5.46/5.71 thf(fact_7483_sum__split__even__odd,axiom,
% 5.46/5.71 ! [F: nat > real,G: nat > real,N: nat] :
% 5.46/5.71 ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G @ I4 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_split_even_odd
% 5.46/5.71 thf(fact_7484_exp__bound__lemma,axiom,
% 5.46/5.71 ! [Z: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % exp_bound_lemma
% 5.46/5.71 thf(fact_7485_exp__bound__lemma,axiom,
% 5.46/5.71 ! [Z: complex] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % exp_bound_lemma
% 5.46/5.71 thf(fact_7486_ceiling__log__nat__eq__if,axiom,
% 5.46/5.71 ! [B: nat,N: nat,K: nat] :
% 5.46/5.71 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.46/5.71 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.46/5.71 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.46/5.71 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.46/5.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_log_nat_eq_if
% 5.46/5.71 thf(fact_7487_ceiling__log__nat__eq__powr__iff,axiom,
% 5.46/5.71 ! [B: nat,K: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.46/5.71 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.71 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.46/5.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.46/5.71 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.46/5.71 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_log_nat_eq_powr_iff
% 5.46/5.71 thf(fact_7488_ceiling__log2__div2,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.71 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % ceiling_log2_div2
% 5.46/5.71 thf(fact_7489_arctan__series,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.71 => ( ( arctan @ X2 )
% 5.46/5.71 = ( suminf_real
% 5.46/5.71 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % arctan_series
% 5.46/5.71 thf(fact_7490_norm__divide__numeral,axiom,
% 5.46/5.71 ! [A: real,W: num] :
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.71 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_divide_numeral
% 5.46/5.71 thf(fact_7491_norm__divide__numeral,axiom,
% 5.46/5.71 ! [A: complex,W: num] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.71 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_divide_numeral
% 5.46/5.71 thf(fact_7492_norm__mult__numeral1,axiom,
% 5.46/5.71 ! [W: num,A: real] :
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.46/5.71 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult_numeral1
% 5.46/5.71 thf(fact_7493_norm__mult__numeral1,axiom,
% 5.46/5.71 ! [W: num,A: complex] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.46/5.71 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult_numeral1
% 5.46/5.71 thf(fact_7494_norm__mult__numeral2,axiom,
% 5.46/5.71 ! [A: real,W: num] :
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.71 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult_numeral2
% 5.46/5.71 thf(fact_7495_norm__mult__numeral2,axiom,
% 5.46/5.71 ! [A: complex,W: num] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.71 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult_numeral2
% 5.46/5.71 thf(fact_7496_norm__neg__numeral,axiom,
% 5.46/5.71 ! [W: num] :
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.71 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_neg_numeral
% 5.46/5.71 thf(fact_7497_norm__neg__numeral,axiom,
% 5.46/5.71 ! [W: num] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.71 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_neg_numeral
% 5.46/5.71 thf(fact_7498_norm__le__zero__iff,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X2 ) @ zero_zero_real )
% 5.46/5.71 = ( X2 = zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_le_zero_iff
% 5.46/5.71 thf(fact_7499_norm__le__zero__iff,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real )
% 5.46/5.71 = ( X2 = zero_zero_complex ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_le_zero_iff
% 5.46/5.71 thf(fact_7500_norm__one,axiom,
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % norm_one
% 5.46/5.71 thf(fact_7501_norm__one,axiom,
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % norm_one
% 5.46/5.71 thf(fact_7502_norm__numeral,axiom,
% 5.46/5.71 ! [W: num] :
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.71 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_numeral
% 5.46/5.71 thf(fact_7503_norm__numeral,axiom,
% 5.46/5.71 ! [W: num] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.71 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_numeral
% 5.46/5.71 thf(fact_7504_zero__less__norm__iff,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.46/5.71 = ( X2 != zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % zero_less_norm_iff
% 5.46/5.71 thf(fact_7505_zero__less__norm__iff,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.46/5.71 = ( X2 != zero_zero_complex ) ) ).
% 5.46/5.71
% 5.46/5.71 % zero_less_norm_iff
% 5.46/5.71 thf(fact_7506_norm__minus__commute,axiom,
% 5.46/5.71 ! [A: complex,B: complex] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 5.46/5.71 = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_minus_commute
% 5.46/5.71 thf(fact_7507_norm__not__less__zero,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % norm_not_less_zero
% 5.46/5.71 thf(fact_7508_norm__ge__zero,axiom,
% 5.46/5.71 ! [X2: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_ge_zero
% 5.46/5.71 thf(fact_7509_norm__mult,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y2 ) )
% 5.46/5.71 = ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult
% 5.46/5.71 thf(fact_7510_norm__mult,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y2 ) )
% 5.46/5.71 = ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult
% 5.46/5.71 thf(fact_7511_norm__divide,axiom,
% 5.46/5.71 ! [A: real,B: real] :
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.71 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_divide
% 5.46/5.71 thf(fact_7512_norm__divide,axiom,
% 5.46/5.71 ! [A: complex,B: complex] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.46/5.71 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_divide
% 5.46/5.71 thf(fact_7513_sum__norm__le,axiom,
% 5.46/5.71 ! [S2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > complex,G: product_prod_nat_nat > real] :
% 5.46/5.71 ( ! [X3: product_prod_nat_nat] :
% 5.46/5.71 ( ( member8440522571783428010at_nat @ X3 @ S2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6381953495645901045omplex @ F @ S2 ) ) @ ( groups4567486121110086003t_real @ G @ S2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_norm_le
% 5.46/5.71 thf(fact_7514_sum__norm__le,axiom,
% 5.46/5.71 ! [S2: set_real,F: real > complex,G: real > real] :
% 5.46/5.71 ( ! [X3: real] :
% 5.46/5.71 ( ( member_real @ X3 @ S2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_norm_le
% 5.46/5.71 thf(fact_7515_sum__norm__le,axiom,
% 5.46/5.71 ! [S2: set_int,F: int > complex,G: int > real] :
% 5.46/5.71 ( ! [X3: int] :
% 5.46/5.71 ( ( member_int @ X3 @ S2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_norm_le
% 5.46/5.71 thf(fact_7516_sum__norm__le,axiom,
% 5.46/5.71 ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 5.46/5.71 ( ! [X3: nat] :
% 5.46/5.71 ( ( member_nat @ X3 @ S2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_norm_le
% 5.46/5.71 thf(fact_7517_sum__norm__le,axiom,
% 5.46/5.71 ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 5.46/5.71 ( ! [X3: complex] :
% 5.46/5.71 ( ( member_complex @ X3 @ S2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_norm_le
% 5.46/5.71 thf(fact_7518_sum__norm__le,axiom,
% 5.46/5.71 ! [S2: set_nat,F: nat > real,G: nat > real] :
% 5.46/5.71 ( ! [X3: nat] :
% 5.46/5.71 ( ( member_nat @ X3 @ S2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_norm_le
% 5.46/5.71 thf(fact_7519_norm__power,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) )
% 5.46/5.71 = ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_power
% 5.46/5.71 thf(fact_7520_norm__power,axiom,
% 5.46/5.71 ! [X2: complex,N: nat] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) )
% 5.46/5.71 = ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_power
% 5.46/5.71 thf(fact_7521_norm__sum,axiom,
% 5.46/5.71 ! [F: nat > complex,A2: set_nat] :
% 5.46/5.71 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 5.46/5.71 @ A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_sum
% 5.46/5.71 thf(fact_7522_norm__sum,axiom,
% 5.46/5.71 ! [F: complex > complex,A2: set_complex] :
% 5.46/5.71 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.46/5.71 @ ( groups5808333547571424918x_real
% 5.46/5.71 @ ^ [I4: complex] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 5.46/5.71 @ A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_sum
% 5.46/5.71 thf(fact_7523_norm__sum,axiom,
% 5.46/5.71 ! [F: nat > real,A2: set_nat] :
% 5.46/5.71 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( F @ I4 ) )
% 5.46/5.71 @ A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_sum
% 5.46/5.71 thf(fact_7524_norm__uminus__minus,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ Y2 ) )
% 5.46/5.71 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_uminus_minus
% 5.46/5.71 thf(fact_7525_norm__uminus__minus,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ Y2 ) )
% 5.46/5.71 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_uminus_minus
% 5.46/5.71 thf(fact_7526_nonzero__norm__divide,axiom,
% 5.46/5.71 ! [B: real,A: real] :
% 5.46/5.71 ( ( B != zero_zero_real )
% 5.46/5.71 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.46/5.71 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % nonzero_norm_divide
% 5.46/5.71 thf(fact_7527_nonzero__norm__divide,axiom,
% 5.46/5.71 ! [B: complex,A: complex] :
% 5.46/5.71 ( ( B != zero_zero_complex )
% 5.46/5.71 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.46/5.71 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % nonzero_norm_divide
% 5.46/5.71 thf(fact_7528_power__eq__imp__eq__norm,axiom,
% 5.46/5.71 ! [W: real,N: nat,Z: real] :
% 5.46/5.71 ( ( ( power_power_real @ W @ N )
% 5.46/5.71 = ( power_power_real @ Z @ N ) )
% 5.46/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ( ( real_V7735802525324610683m_real @ W )
% 5.46/5.71 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_eq_imp_eq_norm
% 5.46/5.71 thf(fact_7529_power__eq__imp__eq__norm,axiom,
% 5.46/5.71 ! [W: complex,N: nat,Z: complex] :
% 5.46/5.71 ( ( ( power_power_complex @ W @ N )
% 5.46/5.71 = ( power_power_complex @ Z @ N ) )
% 5.46/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ( ( real_V1022390504157884413omplex @ W )
% 5.46/5.71 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_eq_imp_eq_norm
% 5.46/5.71 thf(fact_7530_norm__mult__less,axiom,
% 5.46/5.71 ! [X2: real,R: real,Y2: real,S: real] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R )
% 5.46/5.71 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S )
% 5.46/5.71 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y2 ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult_less
% 5.46/5.71 thf(fact_7531_norm__mult__less,axiom,
% 5.46/5.71 ! [X2: complex,R: real,Y2: complex,S: real] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R )
% 5.46/5.71 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S )
% 5.46/5.71 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y2 ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult_less
% 5.46/5.71 thf(fact_7532_norm__mult__ineq,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y2 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult_ineq
% 5.46/5.71 thf(fact_7533_norm__mult__ineq,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y2 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_mult_ineq
% 5.46/5.71 thf(fact_7534_norm__triangle__lt,axiom,
% 5.46/5.71 ! [X2: real,Y2: real,E: real] :
% 5.46/5.71 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 5.46/5.71 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ E ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_lt
% 5.46/5.71 thf(fact_7535_norm__triangle__lt,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex,E: real] :
% 5.46/5.71 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 5.46/5.71 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ E ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_lt
% 5.46/5.71 thf(fact_7536_norm__add__less,axiom,
% 5.46/5.71 ! [X2: real,R: real,Y2: real,S: real] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R )
% 5.46/5.71 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S )
% 5.46/5.71 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_add_less
% 5.46/5.71 thf(fact_7537_norm__add__less,axiom,
% 5.46/5.71 ! [X2: complex,R: real,Y2: complex,S: real] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R )
% 5.46/5.71 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S )
% 5.46/5.71 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_add_less
% 5.46/5.71 thf(fact_7538_norm__add__leD,axiom,
% 5.46/5.71 ! [A: real,B: real,C: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_add_leD
% 5.46/5.71 thf(fact_7539_norm__add__leD,axiom,
% 5.46/5.71 ! [A: complex,B: complex,C: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_add_leD
% 5.46/5.71 thf(fact_7540_norm__triangle__le,axiom,
% 5.46/5.71 ! [X2: real,Y2: real,E: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ E ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_le
% 5.46/5.71 thf(fact_7541_norm__triangle__le,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex,E: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ E ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_le
% 5.46/5.71 thf(fact_7542_norm__triangle__ineq,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_ineq
% 5.46/5.71 thf(fact_7543_norm__triangle__ineq,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_ineq
% 5.46/5.71 thf(fact_7544_norm__triangle__mono,axiom,
% 5.46/5.71 ! [A: real,R: real,B: real,S: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_mono
% 5.46/5.71 thf(fact_7545_norm__triangle__mono,axiom,
% 5.46/5.71 ! [A: complex,R: real,B: complex,S: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_mono
% 5.46/5.71 thf(fact_7546_norm__power__ineq,axiom,
% 5.46/5.71 ! [X2: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_power_ineq
% 5.46/5.71 thf(fact_7547_norm__power__ineq,axiom,
% 5.46/5.71 ! [X2: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_power_ineq
% 5.46/5.71 thf(fact_7548_norm__diff__triangle__less,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex,E1: real,Z: complex,E22: real] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y2 ) ) @ E1 )
% 5.46/5.71 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y2 @ Z ) ) @ E22 )
% 5.46/5.71 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_diff_triangle_less
% 5.46/5.71 thf(fact_7549_norm__triangle__sub,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y2 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_sub
% 5.46/5.71 thf(fact_7550_norm__triangle__ineq4,axiom,
% 5.46/5.71 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_ineq4
% 5.46/5.71 thf(fact_7551_norm__diff__triangle__le,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex,E1: real,Z: complex,E22: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y2 ) ) @ E1 )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y2 @ Z ) ) @ E22 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_diff_triangle_le
% 5.46/5.71 thf(fact_7552_norm__triangle__le__diff,axiom,
% 5.46/5.71 ! [X2: complex,Y2: complex,E: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y2 ) ) @ E ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_le_diff
% 5.46/5.71 thf(fact_7553_norm__diff__ineq,axiom,
% 5.46/5.71 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_diff_ineq
% 5.46/5.71 thf(fact_7554_norm__diff__ineq,axiom,
% 5.46/5.71 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_diff_ineq
% 5.46/5.71 thf(fact_7555_norm__triangle__ineq2,axiom,
% 5.46/5.71 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_ineq2
% 5.46/5.71 thf(fact_7556_power__eq__1__iff,axiom,
% 5.46/5.71 ! [W: real,N: nat] :
% 5.46/5.71 ( ( ( power_power_real @ W @ N )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_eq_1_iff
% 5.46/5.71 thf(fact_7557_power__eq__1__iff,axiom,
% 5.46/5.71 ! [W: complex,N: nat] :
% 5.46/5.71 ( ( ( power_power_complex @ W @ N )
% 5.46/5.71 = one_one_complex )
% 5.46/5.71 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_eq_1_iff
% 5.46/5.71 thf(fact_7558_norm__diff__triangle__ineq,axiom,
% 5.46/5.71 ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_diff_triangle_ineq
% 5.46/5.71 thf(fact_7559_norm__diff__triangle__ineq,axiom,
% 5.46/5.71 ! [A: complex,B: complex,C: complex,D2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_diff_triangle_ineq
% 5.46/5.71 thf(fact_7560_norm__triangle__ineq3,axiom,
% 5.46/5.71 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_triangle_ineq3
% 5.46/5.71 thf(fact_7561_square__norm__one,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 => ( ( real_V7735802525324610683m_real @ X2 )
% 5.46/5.71 = one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % square_norm_one
% 5.46/5.71 thf(fact_7562_square__norm__one,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = one_one_complex )
% 5.46/5.71 => ( ( real_V1022390504157884413omplex @ X2 )
% 5.46/5.71 = one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % square_norm_one
% 5.46/5.71 thf(fact_7563_norm__power__diff,axiom,
% 5.46/5.71 ! [Z: real,W: real,M: nat] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_power_diff
% 5.46/5.71 thf(fact_7564_norm__power__diff,axiom,
% 5.46/5.71 ! [Z: complex,W: complex,M: nat] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % norm_power_diff
% 5.46/5.71 thf(fact_7565_suminf__geometric,axiom,
% 5.46/5.71 ! [C: real] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.46/5.71 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.46/5.71 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_geometric
% 5.46/5.71 thf(fact_7566_suminf__geometric,axiom,
% 5.46/5.71 ! [C: complex] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.46/5.71 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.46/5.71 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_geometric
% 5.46/5.71 thf(fact_7567_sum__bounds__lt__plus1,axiom,
% 5.46/5.71 ! [F: nat > nat,Mm: nat] :
% 5.46/5.71 ( ( groups3542108847815614940at_nat
% 5.46/5.71 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.46/5.71 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_bounds_lt_plus1
% 5.46/5.71 thf(fact_7568_sum__bounds__lt__plus1,axiom,
% 5.46/5.71 ! [F: nat > real,Mm: nat] :
% 5.46/5.71 ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.46/5.71 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_bounds_lt_plus1
% 5.46/5.71 thf(fact_7569_sumr__cos__zero__one,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ zero_zero_real @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % sumr_cos_zero_one
% 5.46/5.71 thf(fact_7570_pi__series,axiom,
% 5.46/5.71 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = ( suminf_real
% 5.46/5.71 @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pi_series
% 5.46/5.71 thf(fact_7571_summable__arctan__series,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_arctan_series
% 5.46/5.71 thf(fact_7572_summable__iff__shift,axiom,
% 5.46/5.71 ! [F: nat > real,K: nat] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.46/5.71 = ( summable_real @ F ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_iff_shift
% 5.46/5.71 thf(fact_7573_cos__coeff__0,axiom,
% 5.46/5.71 ( ( cos_coeff @ zero_zero_nat )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_coeff_0
% 5.46/5.71 thf(fact_7574_summable__cmult__iff,axiom,
% 5.46/5.71 ! [C: complex,F: nat > complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.46/5.71 = ( ( C = zero_zero_complex )
% 5.46/5.71 | ( summable_complex @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_cmult_iff
% 5.46/5.71 thf(fact_7575_summable__cmult__iff,axiom,
% 5.46/5.71 ! [C: real,F: nat > real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.46/5.71 = ( ( C = zero_zero_real )
% 5.46/5.71 | ( summable_real @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_cmult_iff
% 5.46/5.71 thf(fact_7576_summable__divide__iff,axiom,
% 5.46/5.71 ! [F: nat > complex,C: complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.46/5.71 = ( ( C = zero_zero_complex )
% 5.46/5.71 | ( summable_complex @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_divide_iff
% 5.46/5.71 thf(fact_7577_summable__divide__iff,axiom,
% 5.46/5.71 ! [F: nat > real,C: real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.46/5.71 = ( ( C = zero_zero_real )
% 5.46/5.71 | ( summable_real @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_divide_iff
% 5.46/5.71 thf(fact_7578_summable__geometric__iff,axiom,
% 5.46/5.71 ! [C: real] :
% 5.46/5.71 ( ( summable_real @ ( power_power_real @ C ) )
% 5.46/5.71 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_geometric_iff
% 5.46/5.71 thf(fact_7579_summable__geometric__iff,axiom,
% 5.46/5.71 ! [C: complex] :
% 5.46/5.71 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.46/5.71 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_geometric_iff
% 5.46/5.71 thf(fact_7580_summable__comparison__test,axiom,
% 5.46/5.71 ! [F: nat > real,G: nat > real] :
% 5.46/5.71 ( ? [N8: nat] :
% 5.46/5.71 ! [N3: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.46/5.71 => ( ( summable_real @ G )
% 5.46/5.71 => ( summable_real @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_comparison_test
% 5.46/5.71 thf(fact_7581_summable__comparison__test,axiom,
% 5.46/5.71 ! [F: nat > complex,G: nat > real] :
% 5.46/5.71 ( ? [N8: nat] :
% 5.46/5.71 ! [N3: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.46/5.71 => ( ( summable_real @ G )
% 5.46/5.71 => ( summable_complex @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_comparison_test
% 5.46/5.71 thf(fact_7582_summable__comparison__test_H,axiom,
% 5.46/5.71 ! [G: nat > real,N4: nat,F: nat > real] :
% 5.46/5.71 ( ( summable_real @ G )
% 5.46/5.71 => ( ! [N3: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.46/5.71 => ( summable_real @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_comparison_test'
% 5.46/5.71 thf(fact_7583_summable__comparison__test_H,axiom,
% 5.46/5.71 ! [G: nat > real,N4: nat,F: nat > complex] :
% 5.46/5.71 ( ( summable_real @ G )
% 5.46/5.71 => ( ! [N3: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.46/5.71 => ( summable_complex @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_comparison_test'
% 5.46/5.71 thf(fact_7584_summable__ignore__initial__segment,axiom,
% 5.46/5.71 ! [F: nat > real,K: nat] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_ignore_initial_segment
% 5.46/5.71 thf(fact_7585_summable__add,axiom,
% 5.46/5.71 ! [F: nat > real,G: nat > real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( summable_real @ G )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_add
% 5.46/5.71 thf(fact_7586_summable__add,axiom,
% 5.46/5.71 ! [F: nat > nat,G: nat > nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ( summable_nat @ G )
% 5.46/5.71 => ( summable_nat
% 5.46/5.71 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_add
% 5.46/5.71 thf(fact_7587_summable__add,axiom,
% 5.46/5.71 ! [F: nat > int,G: nat > int] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ( summable_int @ G )
% 5.46/5.71 => ( summable_int
% 5.46/5.71 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_add
% 5.46/5.71 thf(fact_7588_summable__mult,axiom,
% 5.46/5.71 ! [F: nat > real,C: real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_mult
% 5.46/5.71 thf(fact_7589_summable__mult2,axiom,
% 5.46/5.71 ! [F: nat > real,C: real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_mult2
% 5.46/5.71 thf(fact_7590_summable__diff,axiom,
% 5.46/5.71 ! [F: nat > real,G: nat > real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( summable_real @ G )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_diff
% 5.46/5.71 thf(fact_7591_summable__divide,axiom,
% 5.46/5.71 ! [F: nat > complex,C: complex] :
% 5.46/5.71 ( ( summable_complex @ F )
% 5.46/5.71 => ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_divide
% 5.46/5.71 thf(fact_7592_summable__divide,axiom,
% 5.46/5.71 ! [F: nat > real,C: real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_divide
% 5.46/5.71 thf(fact_7593_summable__Suc__iff,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.46/5.71 = ( summable_real @ F ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_Suc_iff
% 5.46/5.71 thf(fact_7594_suminf__le,axiom,
% 5.46/5.71 ! [F: nat > real,G: nat > real] :
% 5.46/5.71 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.46/5.71 => ( ( summable_real @ F )
% 5.46/5.71 => ( ( summable_real @ G )
% 5.46/5.71 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_le
% 5.46/5.71 thf(fact_7595_suminf__le,axiom,
% 5.46/5.71 ! [F: nat > nat,G: nat > nat] :
% 5.46/5.71 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.46/5.71 => ( ( summable_nat @ F )
% 5.46/5.71 => ( ( summable_nat @ G )
% 5.46/5.71 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_le
% 5.46/5.71 thf(fact_7596_suminf__le,axiom,
% 5.46/5.71 ! [F: nat > int,G: nat > int] :
% 5.46/5.71 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.46/5.71 => ( ( summable_int @ F )
% 5.46/5.71 => ( ( summable_int @ G )
% 5.46/5.71 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_le
% 5.46/5.71 thf(fact_7597_summable__mult__D,axiom,
% 5.46/5.71 ! [C: complex,F: nat > complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.46/5.71 => ( ( C != zero_zero_complex )
% 5.46/5.71 => ( summable_complex @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_mult_D
% 5.46/5.71 thf(fact_7598_summable__mult__D,axiom,
% 5.46/5.71 ! [C: real,F: nat > real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.46/5.71 => ( ( C != zero_zero_real )
% 5.46/5.71 => ( summable_real @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_mult_D
% 5.46/5.71 thf(fact_7599_summable__zero__power,axiom,
% 5.46/5.71 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % summable_zero_power
% 5.46/5.71 thf(fact_7600_summable__zero__power,axiom,
% 5.46/5.71 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.46/5.71
% 5.46/5.71 % summable_zero_power
% 5.46/5.71 thf(fact_7601_summable__zero__power,axiom,
% 5.46/5.71 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.46/5.71
% 5.46/5.71 % summable_zero_power
% 5.46/5.71 thf(fact_7602_suminf__mult2,axiom,
% 5.46/5.71 ! [F: nat > real,C: real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.46/5.71 = ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_mult2
% 5.46/5.71 thf(fact_7603_suminf__mult,axiom,
% 5.46/5.71 ! [F: nat > real,C: real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.46/5.71 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_mult
% 5.46/5.71 thf(fact_7604_suminf__add,axiom,
% 5.46/5.71 ! [F: nat > real,G: nat > real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( summable_real @ G )
% 5.46/5.71 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.46/5.71 = ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_add
% 5.46/5.71 thf(fact_7605_suminf__add,axiom,
% 5.46/5.71 ! [F: nat > nat,G: nat > nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ( summable_nat @ G )
% 5.46/5.71 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.46/5.71 = ( suminf_nat
% 5.46/5.71 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_add
% 5.46/5.71 thf(fact_7606_suminf__add,axiom,
% 5.46/5.71 ! [F: nat > int,G: nat > int] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ( summable_int @ G )
% 5.46/5.71 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.46/5.71 = ( suminf_int
% 5.46/5.71 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_add
% 5.46/5.71 thf(fact_7607_suminf__diff,axiom,
% 5.46/5.71 ! [F: nat > real,G: nat > real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( summable_real @ G )
% 5.46/5.71 => ( ( minus_minus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.46/5.71 = ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_diff
% 5.46/5.71 thf(fact_7608_suminf__divide,axiom,
% 5.46/5.71 ! [F: nat > complex,C: complex] :
% 5.46/5.71 ( ( summable_complex @ F )
% 5.46/5.71 => ( ( suminf_complex
% 5.46/5.71 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.46/5.71 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_divide
% 5.46/5.71 thf(fact_7609_suminf__divide,axiom,
% 5.46/5.71 ! [F: nat > real,C: real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.46/5.71 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_divide
% 5.46/5.71 thf(fact_7610_powser__insidea,axiom,
% 5.46/5.71 ! [F: nat > real,X2: real,Z: real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) )
% 5.46/5.71 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_insidea
% 5.46/5.71 thf(fact_7611_powser__insidea,axiom,
% 5.46/5.71 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) )
% 5.46/5.71 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_insidea
% 5.46/5.71 thf(fact_7612_suminf__nonneg,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_nonneg
% 5.46/5.71 thf(fact_7613_suminf__nonneg,axiom,
% 5.46/5.71 ! [F: nat > nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.46/5.71 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_nonneg
% 5.46/5.71 thf(fact_7614_suminf__nonneg,axiom,
% 5.46/5.71 ! [F: nat > int] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.46/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_nonneg
% 5.46/5.71 thf(fact_7615_suminf__eq__zero__iff,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.46/5.71 => ( ( ( suminf_real @ F )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 = ( ! [N2: nat] :
% 5.46/5.71 ( ( F @ N2 )
% 5.46/5.71 = zero_zero_real ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_eq_zero_iff
% 5.46/5.71 thf(fact_7616_suminf__eq__zero__iff,axiom,
% 5.46/5.71 ! [F: nat > nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.46/5.71 => ( ( ( suminf_nat @ F )
% 5.46/5.71 = zero_zero_nat )
% 5.46/5.71 = ( ! [N2: nat] :
% 5.46/5.71 ( ( F @ N2 )
% 5.46/5.71 = zero_zero_nat ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_eq_zero_iff
% 5.46/5.71 thf(fact_7617_suminf__eq__zero__iff,axiom,
% 5.46/5.71 ! [F: nat > int] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.46/5.71 => ( ( ( suminf_int @ F )
% 5.46/5.71 = zero_zero_int )
% 5.46/5.71 = ( ! [N2: nat] :
% 5.46/5.71 ( ( F @ N2 )
% 5.46/5.71 = zero_zero_int ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_eq_zero_iff
% 5.46/5.71 thf(fact_7618_suminf__pos,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 5.46/5.71 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_pos
% 5.46/5.71 thf(fact_7619_suminf__pos,axiom,
% 5.46/5.71 ! [F: nat > nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.46/5.71 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_pos
% 5.46/5.71 thf(fact_7620_suminf__pos,axiom,
% 5.46/5.71 ! [F: nat > int] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 5.46/5.71 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_pos
% 5.46/5.71 thf(fact_7621_summable__zero__power_H,axiom,
% 5.46/5.71 ! [F: nat > complex] :
% 5.46/5.71 ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_zero_power'
% 5.46/5.71 thf(fact_7622_summable__zero__power_H,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_zero_power'
% 5.46/5.71 thf(fact_7623_summable__zero__power_H,axiom,
% 5.46/5.71 ! [F: nat > int] :
% 5.46/5.71 ( summable_int
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_int @ ( F @ N2 ) @ ( power_power_int @ zero_zero_int @ N2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_zero_power'
% 5.46/5.71 thf(fact_7624_summable__0__powser,axiom,
% 5.46/5.71 ! [F: nat > complex] :
% 5.46/5.71 ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_0_powser
% 5.46/5.71 thf(fact_7625_summable__0__powser,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_0_powser
% 5.46/5.71 thf(fact_7626_powser__split__head_I3_J,axiom,
% 5.46/5.71 ! [F: nat > complex,Z: complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.46/5.71 => ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_split_head(3)
% 5.46/5.71 thf(fact_7627_powser__split__head_I3_J,axiom,
% 5.46/5.71 ! [F: nat > real,Z: real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_split_head(3)
% 5.46/5.71 thf(fact_7628_summable__powser__split__head,axiom,
% 5.46/5.71 ! [F: nat > complex,Z: complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.46/5.71 = ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_powser_split_head
% 5.46/5.71 thf(fact_7629_summable__powser__split__head,axiom,
% 5.46/5.71 ! [F: nat > real,Z: real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.46/5.71 = ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_powser_split_head
% 5.46/5.71 thf(fact_7630_summable__powser__ignore__initial__segment,axiom,
% 5.46/5.71 ! [F: nat > complex,M: nat,Z: complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.46/5.71 = ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_powser_ignore_initial_segment
% 5.46/5.71 thf(fact_7631_summable__powser__ignore__initial__segment,axiom,
% 5.46/5.71 ! [F: nat > real,M: nat,Z: real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.46/5.71 = ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_powser_ignore_initial_segment
% 5.46/5.71 thf(fact_7632_pi__gt__zero,axiom,
% 5.46/5.71 ord_less_real @ zero_zero_real @ pi ).
% 5.46/5.71
% 5.46/5.71 % pi_gt_zero
% 5.46/5.71 thf(fact_7633_pi__not__less__zero,axiom,
% 5.46/5.71 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % pi_not_less_zero
% 5.46/5.71 thf(fact_7634_pi__ge__zero,axiom,
% 5.46/5.71 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.46/5.71
% 5.46/5.71 % pi_ge_zero
% 5.46/5.71 thf(fact_7635_summable__norm__comparison__test,axiom,
% 5.46/5.71 ! [F: nat > complex,G: nat > real] :
% 5.46/5.71 ( ? [N8: nat] :
% 5.46/5.71 ! [N3: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.46/5.71 => ( ( summable_real @ G )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_norm_comparison_test
% 5.46/5.71 thf(fact_7636_summable__rabs__comparison__test,axiom,
% 5.46/5.71 ! [F: nat > real,G: nat > real] :
% 5.46/5.71 ( ? [N8: nat] :
% 5.46/5.71 ! [N3: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.46/5.71 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.46/5.71 => ( ( summable_real @ G )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_rabs_comparison_test
% 5.46/5.71 thf(fact_7637_summable__rabs,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.46/5.71 @ ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_rabs
% 5.46/5.71 thf(fact_7638_suminf__pos2,axiom,
% 5.46/5.71 ! [F: nat > real,I: nat] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.46/5.71 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.46/5.71 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_pos2
% 5.46/5.71 thf(fact_7639_suminf__pos2,axiom,
% 5.46/5.71 ! [F: nat > nat,I: nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.46/5.71 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.46/5.71 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_pos2
% 5.46/5.71 thf(fact_7640_suminf__pos2,axiom,
% 5.46/5.71 ! [F: nat > int,I: nat] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.46/5.71 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.46/5.71 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_pos2
% 5.46/5.71 thf(fact_7641_suminf__pos__iff,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.46/5.71 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.46/5.71 = ( ? [I4: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_pos_iff
% 5.46/5.71 thf(fact_7642_suminf__pos__iff,axiom,
% 5.46/5.71 ! [F: nat > nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.46/5.71 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.46/5.71 = ( ? [I4: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_pos_iff
% 5.46/5.71 thf(fact_7643_suminf__pos__iff,axiom,
% 5.46/5.71 ! [F: nat > int] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.46/5.71 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.46/5.71 = ( ? [I4: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I4 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_pos_iff
% 5.46/5.71 thf(fact_7644_suminf__le__const,axiom,
% 5.46/5.71 ! [F: nat > int,X2: int] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.46/5.71 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_le_const
% 5.46/5.71 thf(fact_7645_suminf__le__const,axiom,
% 5.46/5.71 ! [F: nat > nat,X2: nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.46/5.71 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_le_const
% 5.46/5.71 thf(fact_7646_suminf__le__const,axiom,
% 5.46/5.71 ! [F: nat > real,X2: real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_le_const
% 5.46/5.71 thf(fact_7647_summableI__nonneg__bounded,axiom,
% 5.46/5.71 ! [F: nat > int,X2: int] :
% 5.46/5.71 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.46/5.71 => ( summable_int @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summableI_nonneg_bounded
% 5.46/5.71 thf(fact_7648_summableI__nonneg__bounded,axiom,
% 5.46/5.71 ! [F: nat > nat,X2: nat] :
% 5.46/5.71 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.46/5.71 => ( summable_nat @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summableI_nonneg_bounded
% 5.46/5.71 thf(fact_7649_summableI__nonneg__bounded,axiom,
% 5.46/5.71 ! [F: nat > real,X2: real] :
% 5.46/5.71 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.46/5.71 => ( summable_real @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summableI_nonneg_bounded
% 5.46/5.71 thf(fact_7650_summable__geometric,axiom,
% 5.46/5.71 ! [C: real] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.46/5.71 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_geometric
% 5.46/5.71 thf(fact_7651_summable__geometric,axiom,
% 5.46/5.71 ! [C: complex] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.46/5.71 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_geometric
% 5.46/5.71 thf(fact_7652_complete__algebra__summable__geometric,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ one_one_real )
% 5.46/5.71 => ( summable_real @ ( power_power_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % complete_algebra_summable_geometric
% 5.46/5.71 thf(fact_7653_complete__algebra__summable__geometric,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ one_one_real )
% 5.46/5.71 => ( summable_complex @ ( power_power_complex @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % complete_algebra_summable_geometric
% 5.46/5.71 thf(fact_7654_suminf__split__head,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.46/5.71 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_split_head
% 5.46/5.71 thf(fact_7655_summable__norm,axiom,
% 5.46/5.71 ! [F: nat > real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 5.46/5.71 @ ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_norm
% 5.46/5.71 thf(fact_7656_summable__norm,axiom,
% 5.46/5.71 ! [F: nat > complex] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 5.46/5.71 @ ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_norm
% 5.46/5.71 thf(fact_7657_sum__le__suminf,axiom,
% 5.46/5.71 ! [F: nat > int,I5: set_nat] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ( finite_finite_nat @ I5 )
% 5.46/5.71 => ( ! [N3: nat] :
% 5.46/5.71 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.46/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 5.46/5.71 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I5 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_le_suminf
% 5.46/5.71 thf(fact_7658_sum__le__suminf,axiom,
% 5.46/5.71 ! [F: nat > nat,I5: set_nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ( finite_finite_nat @ I5 )
% 5.46/5.71 => ( ! [N3: nat] :
% 5.46/5.71 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.46/5.71 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 5.46/5.71 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I5 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_le_suminf
% 5.46/5.71 thf(fact_7659_sum__le__suminf,axiom,
% 5.46/5.71 ! [F: nat > real,I5: set_nat] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( finite_finite_nat @ I5 )
% 5.46/5.71 => ( ! [N3: nat] :
% 5.46/5.71 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I5 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_le_suminf
% 5.46/5.71 thf(fact_7660_suminf__split__initial__segment,axiom,
% 5.46/5.71 ! [F: nat > real,K: nat] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( suminf_real @ F )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.46/5.71 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_split_initial_segment
% 5.46/5.71 thf(fact_7661_suminf__minus__initial__segment,axiom,
% 5.46/5.71 ! [F: nat > real,K: nat] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.46/5.71 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_minus_initial_segment
% 5.46/5.71 thf(fact_7662_powser__inside,axiom,
% 5.46/5.71 ! [F: nat > real,X2: real,Z: real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) )
% 5.46/5.71 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_inside
% 5.46/5.71 thf(fact_7663_powser__inside,axiom,
% 5.46/5.71 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) )
% 5.46/5.71 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.46/5.71 => ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_inside
% 5.46/5.71 thf(fact_7664_sum__less__suminf,axiom,
% 5.46/5.71 ! [F: nat > int,N: nat] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ! [M4: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M4 )
% 5.46/5.71 => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.46/5.71 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_less_suminf
% 5.46/5.71 thf(fact_7665_sum__less__suminf,axiom,
% 5.46/5.71 ! [F: nat > nat,N: nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ! [M4: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M4 )
% 5.46/5.71 => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.46/5.71 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_less_suminf
% 5.46/5.71 thf(fact_7666_sum__less__suminf,axiom,
% 5.46/5.71 ! [F: nat > real,N: nat] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ! [M4: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M4 )
% 5.46/5.71 => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.46/5.71 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_less_suminf
% 5.46/5.71 thf(fact_7667_pi__less__4,axiom,
% 5.46/5.71 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pi_less_4
% 5.46/5.71 thf(fact_7668_pi__ge__two,axiom,
% 5.46/5.71 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.46/5.71
% 5.46/5.71 % pi_ge_two
% 5.46/5.71 thf(fact_7669_pi__half__neq__two,axiom,
% 5.46/5.71 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.71 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pi_half_neq_two
% 5.46/5.71 thf(fact_7670_powser__split__head_I1_J,axiom,
% 5.46/5.71 ! [F: nat > complex,Z: complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.46/5.71 => ( ( suminf_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.46/5.71 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.46/5.71 @ ( times_times_complex
% 5.46/5.71 @ ( suminf_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.46/5.71 @ Z ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_split_head(1)
% 5.46/5.71 thf(fact_7671_powser__split__head_I1_J,axiom,
% 5.46/5.71 ! [F: nat > real,Z: real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.46/5.71 => ( ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.46/5.71 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.46/5.71 @ ( times_times_real
% 5.46/5.71 @ ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.46/5.71 @ Z ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_split_head(1)
% 5.46/5.71 thf(fact_7672_powser__split__head_I2_J,axiom,
% 5.46/5.71 ! [F: nat > complex,Z: complex] :
% 5.46/5.71 ( ( summable_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.46/5.71 => ( ( times_times_complex
% 5.46/5.71 @ ( suminf_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.46/5.71 @ Z )
% 5.46/5.71 = ( minus_minus_complex
% 5.46/5.71 @ ( suminf_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.46/5.71 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_split_head(2)
% 5.46/5.71 thf(fact_7673_powser__split__head_I2_J,axiom,
% 5.46/5.71 ! [F: nat > real,Z: real] :
% 5.46/5.71 ( ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.46/5.71 => ( ( times_times_real
% 5.46/5.71 @ ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.46/5.71 @ Z )
% 5.46/5.71 = ( minus_minus_real
% 5.46/5.71 @ ( suminf_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.46/5.71 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_split_head(2)
% 5.46/5.71 thf(fact_7674_summable__partial__sum__bound,axiom,
% 5.46/5.71 ! [F: nat > complex,E: real] :
% 5.46/5.71 ( ( summable_complex @ F )
% 5.46/5.71 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.71 => ~ ! [N9: nat] :
% 5.46/5.71 ~ ! [M2: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N9 @ M2 )
% 5.46/5.71 => ! [N7: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N7 ) ) ) @ E ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_partial_sum_bound
% 5.46/5.71 thf(fact_7675_summable__partial__sum__bound,axiom,
% 5.46/5.71 ! [F: nat > real,E: real] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.71 => ~ ! [N9: nat] :
% 5.46/5.71 ~ ! [M2: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N9 @ M2 )
% 5.46/5.71 => ! [N7: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N7 ) ) ) @ E ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_partial_sum_bound
% 5.46/5.71 thf(fact_7676_suminf__exist__split,axiom,
% 5.46/5.71 ! [R: real,F: nat > real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ R )
% 5.46/5.71 => ( ( summable_real @ F )
% 5.46/5.71 => ? [N9: nat] :
% 5.46/5.71 ! [N7: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N9 @ N7 )
% 5.46/5.71 => ( ord_less_real
% 5.46/5.71 @ ( real_V7735802525324610683m_real
% 5.46/5.71 @ ( suminf_real
% 5.46/5.71 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N7 ) ) ) )
% 5.46/5.71 @ R ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_exist_split
% 5.46/5.71 thf(fact_7677_suminf__exist__split,axiom,
% 5.46/5.71 ! [R: real,F: nat > complex] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ R )
% 5.46/5.71 => ( ( summable_complex @ F )
% 5.46/5.71 => ? [N9: nat] :
% 5.46/5.71 ! [N7: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N9 @ N7 )
% 5.46/5.71 => ( ord_less_real
% 5.46/5.71 @ ( real_V1022390504157884413omplex
% 5.46/5.71 @ ( suminf_complex
% 5.46/5.71 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N7 ) ) ) )
% 5.46/5.71 @ R ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % suminf_exist_split
% 5.46/5.71 thf(fact_7678_summable__power__series,axiom,
% 5.46/5.71 ! [F: nat > real,Z: real] :
% 5.46/5.71 ( ! [I2: nat] : ( ord_less_eq_real @ ( F @ I2 ) @ one_one_real )
% 5.46/5.71 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.46/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.46/5.71 => ( ( ord_less_real @ Z @ one_one_real )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_power_series
% 5.46/5.71 thf(fact_7679_Abel__lemma,axiom,
% 5.46/5.71 ! [R: real,R0: real,A: nat > complex,M7: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ R )
% 5.46/5.71 => ( ( ord_less_real @ R @ R0 )
% 5.46/5.71 => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 5.46/5.71 => ( summable_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R @ N2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Abel_lemma
% 5.46/5.71 thf(fact_7680_summable__ratio__test,axiom,
% 5.46/5.71 ! [C: real,N4: nat,F: nat > real] :
% 5.46/5.71 ( ( ord_less_real @ C @ one_one_real )
% 5.46/5.71 => ( ! [N3: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 5.46/5.71 => ( summable_real @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_ratio_test
% 5.46/5.71 thf(fact_7681_summable__ratio__test,axiom,
% 5.46/5.71 ! [C: real,N4: nat,F: nat > complex] :
% 5.46/5.71 ( ( ord_less_real @ C @ one_one_real )
% 5.46/5.71 => ( ! [N3: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.46/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 5.46/5.71 => ( summable_complex @ F ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % summable_ratio_test
% 5.46/5.71 thf(fact_7682_sum__less__suminf2,axiom,
% 5.46/5.71 ! [F: nat > int,N: nat,I: nat] :
% 5.46/5.71 ( ( summable_int @ F )
% 5.46/5.71 => ( ! [M4: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M4 )
% 5.46/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.46/5.71 => ( ( ord_less_eq_nat @ N @ I )
% 5.46/5.71 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.46/5.71 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_less_suminf2
% 5.46/5.71 thf(fact_7683_sum__less__suminf2,axiom,
% 5.46/5.71 ! [F: nat > nat,N: nat,I: nat] :
% 5.46/5.71 ( ( summable_nat @ F )
% 5.46/5.71 => ( ! [M4: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M4 )
% 5.46/5.71 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.46/5.71 => ( ( ord_less_eq_nat @ N @ I )
% 5.46/5.71 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.46/5.71 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_less_suminf2
% 5.46/5.71 thf(fact_7684_sum__less__suminf2,axiom,
% 5.46/5.71 ! [F: nat > real,N: nat,I: nat] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ! [M4: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M4 )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.46/5.71 => ( ( ord_less_eq_nat @ N @ I )
% 5.46/5.71 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.46/5.71 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_less_suminf2
% 5.46/5.71 thf(fact_7685_pi__half__neq__zero,axiom,
% 5.46/5.71 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.71 != zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % pi_half_neq_zero
% 5.46/5.71 thf(fact_7686_pi__half__less__two,axiom,
% 5.46/5.71 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.46/5.71
% 5.46/5.71 % pi_half_less_two
% 5.46/5.71 thf(fact_7687_pi__half__le__two,axiom,
% 5.46/5.71 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.46/5.71
% 5.46/5.71 % pi_half_le_two
% 5.46/5.71 thf(fact_7688_pi__half__gt__zero,axiom,
% 5.46/5.71 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pi_half_gt_zero
% 5.46/5.71 thf(fact_7689_pi__half__ge__zero,axiom,
% 5.46/5.71 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pi_half_ge_zero
% 5.46/5.71 thf(fact_7690_m2pi__less__pi,axiom,
% 5.46/5.71 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.46/5.71
% 5.46/5.71 % m2pi_less_pi
% 5.46/5.71 thf(fact_7691_arctan__ubound,axiom,
% 5.46/5.71 ! [Y2: real] : ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % arctan_ubound
% 5.46/5.71 thf(fact_7692_arctan__one,axiom,
% 5.46/5.71 ( ( arctan @ one_one_real )
% 5.46/5.71 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % arctan_one
% 5.46/5.71 thf(fact_7693_minus__pi__half__less__zero,axiom,
% 5.46/5.71 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.46/5.71
% 5.46/5.71 % minus_pi_half_less_zero
% 5.46/5.71 thf(fact_7694_arctan__bounded,axiom,
% 5.46/5.71 ! [Y2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 5.46/5.71 & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % arctan_bounded
% 5.46/5.71 thf(fact_7695_arctan__lbound,axiom,
% 5.46/5.71 ! [Y2: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % arctan_lbound
% 5.46/5.71 thf(fact_7696_machin__Euler,axiom,
% 5.46/5.71 ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.71 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % machin_Euler
% 5.46/5.71 thf(fact_7697_machin,axiom,
% 5.46/5.71 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % machin
% 5.46/5.71 thf(fact_7698_sum__pos__lt__pair,axiom,
% 5.46/5.71 ! [F: nat > real,K: nat] :
% 5.46/5.71 ( ( summable_real @ F )
% 5.46/5.71 => ( ! [D3: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) @ one_one_nat ) ) ) ) )
% 5.46/5.71 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_pos_lt_pair
% 5.46/5.71 thf(fact_7699_sin__cos__npi,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_cos_npi
% 5.46/5.71 thf(fact_7700_and__int_Oelims,axiom,
% 5.46/5.71 ! [X2: int,Xa2: int,Y2: int] :
% 5.46/5.71 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.46/5.71 = Y2 )
% 5.46/5.71 => ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.71 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.71 => ( Y2
% 5.46/5.71 = ( uminus_uminus_int
% 5.46/5.71 @ ( zero_n2684676970156552555ol_int
% 5.46/5.71 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.46/5.71 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.71 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.71 => ( Y2
% 5.46/5.71 = ( plus_plus_int
% 5.46/5.71 @ ( zero_n2684676970156552555ol_int
% 5.46/5.71 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.46/5.71 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.46/5.71 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % and_int.elims
% 5.46/5.71 thf(fact_7701_and__int_Osimps,axiom,
% 5.46/5.71 ( bit_se725231765392027082nd_int
% 5.46/5.71 = ( ^ [K2: int,L: int] :
% 5.46/5.71 ( if_int
% 5.46/5.71 @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.71 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.71 @ ( uminus_uminus_int
% 5.46/5.71 @ ( zero_n2684676970156552555ol_int
% 5.46/5.71 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.46/5.71 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.46/5.71 @ ( plus_plus_int
% 5.46/5.71 @ ( zero_n2684676970156552555ol_int
% 5.46/5.71 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.46/5.71 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.46/5.71 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % and_int.simps
% 5.46/5.71 thf(fact_7702_cos__pi__eq__zero,axiom,
% 5.46/5.71 ! [M: nat] :
% 5.46/5.71 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_pi_eq_zero
% 5.46/5.71 thf(fact_7703_Maclaurin__exp__lt,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( X2 != zero_zero_real )
% 5.46/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ? [T5: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T5 ) )
% 5.46/5.71 & ( ord_less_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X2 ) )
% 5.46/5.71 & ( ( exp_real @ X2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_exp_lt
% 5.46/5.71 thf(fact_7704_Diff__insert0,axiom,
% 5.46/5.71 ! [X2: vEBT_VEBT,A2: set_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.46/5.71 ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ B3 ) )
% 5.46/5.71 = ( minus_5127226145743854075T_VEBT @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert0
% 5.46/5.71 thf(fact_7705_Diff__insert0,axiom,
% 5.46/5.71 ! [X2: complex,A2: set_complex,B3: set_complex] :
% 5.46/5.71 ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ B3 ) )
% 5.46/5.71 = ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert0
% 5.46/5.71 thf(fact_7706_Diff__insert0,axiom,
% 5.46/5.71 ! [X2: real,A2: set_real,B3: set_real] :
% 5.46/5.71 ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ B3 ) )
% 5.46/5.71 = ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert0
% 5.46/5.71 thf(fact_7707_Diff__insert0,axiom,
% 5.46/5.71 ! [X2: int,A2: set_int,B3: set_int] :
% 5.46/5.71 ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ B3 ) )
% 5.46/5.71 = ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert0
% 5.46/5.71 thf(fact_7708_Diff__insert0,axiom,
% 5.46/5.71 ! [X2: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ~ ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X2 @ B3 ) )
% 5.46/5.71 = ( minus_1356011639430497352at_nat @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert0
% 5.46/5.71 thf(fact_7709_Diff__insert0,axiom,
% 5.46/5.71 ! [X2: nat,A2: set_nat,B3: set_nat] :
% 5.46/5.71 ( ~ ( member_nat @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ B3 ) )
% 5.46/5.71 = ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert0
% 5.46/5.71 thf(fact_7710_insert__Diff1,axiom,
% 5.46/5.71 ! [X2: vEBT_VEBT,B3: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_5127226145743854075T_VEBT @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff1
% 5.46/5.71 thf(fact_7711_insert__Diff1,axiom,
% 5.46/5.71 ! [X2: complex,B3: set_complex,A2: set_complex] :
% 5.46/5.71 ( ( member_complex @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff1
% 5.46/5.71 thf(fact_7712_insert__Diff1,axiom,
% 5.46/5.71 ! [X2: real,B3: set_real,A2: set_real] :
% 5.46/5.71 ( ( member_real @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff1
% 5.46/5.71 thf(fact_7713_insert__Diff1,axiom,
% 5.46/5.71 ! [X2: int,B3: set_int,A2: set_int] :
% 5.46/5.71 ( ( member_int @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff1
% 5.46/5.71 thf(fact_7714_insert__Diff1,axiom,
% 5.46/5.71 ! [X2: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( member8440522571783428010at_nat @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_1356011639430497352at_nat @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff1
% 5.46/5.71 thf(fact_7715_insert__Diff1,axiom,
% 5.46/5.71 ! [X2: nat,B3: set_nat,A2: set_nat] :
% 5.46/5.71 ( ( member_nat @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff1
% 5.46/5.71 thf(fact_7716_cos__zero,axiom,
% 5.46/5.71 ( ( cos_complex @ zero_zero_complex )
% 5.46/5.71 = one_one_complex ) ).
% 5.46/5.71
% 5.46/5.71 % cos_zero
% 5.46/5.71 thf(fact_7717_cos__zero,axiom,
% 5.46/5.71 ( ( cos_real @ zero_zero_real )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_zero
% 5.46/5.71 thf(fact_7718_insert__Diff__single,axiom,
% 5.46/5.71 ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 5.46/5.71 ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 = ( insert_VEBT_VEBT @ A @ A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_single
% 5.46/5.71 thf(fact_7719_insert__Diff__single,axiom,
% 5.46/5.71 ! [A: int,A2: set_int] :
% 5.46/5.71 ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.46/5.71 = ( insert_int @ A @ A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_single
% 5.46/5.71 thf(fact_7720_insert__Diff__single,axiom,
% 5.46/5.71 ! [A: real,A2: set_real] :
% 5.46/5.71 ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.46/5.71 = ( insert_real @ A @ A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_single
% 5.46/5.71 thf(fact_7721_insert__Diff__single,axiom,
% 5.46/5.71 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 5.46/5.71 = ( insert8211810215607154385at_nat @ A @ A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_single
% 5.46/5.71 thf(fact_7722_insert__Diff__single,axiom,
% 5.46/5.71 ! [A: nat,A2: set_nat] :
% 5.46/5.71 ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.46/5.71 = ( insert_nat @ A @ A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_single
% 5.46/5.71 thf(fact_7723_finite__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ B3 ) ) )
% 5.46/5.71 = ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_Diff_insert
% 5.46/5.71 thf(fact_7724_finite__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_real,A: real,B3: set_real] :
% 5.46/5.71 ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) ) )
% 5.46/5.71 = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_Diff_insert
% 5.46/5.71 thf(fact_7725_finite__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_int,A: int,B3: set_int] :
% 5.46/5.71 ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) ) )
% 5.46/5.71 = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_Diff_insert
% 5.46/5.71 thf(fact_7726_finite__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_complex,A: complex,B3: set_complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B3 ) ) )
% 5.46/5.71 = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_Diff_insert
% 5.46/5.71 thf(fact_7727_finite__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B3 ) ) )
% 5.46/5.71 = ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_Diff_insert
% 5.46/5.71 thf(fact_7728_finite__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_nat,A: nat,B3: set_nat] :
% 5.46/5.71 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) ) )
% 5.46/5.71 = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_Diff_insert
% 5.46/5.71 thf(fact_7729_fact__0,axiom,
% 5.46/5.71 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.46/5.71 = one_one_complex ) ).
% 5.46/5.71
% 5.46/5.71 % fact_0
% 5.46/5.71 thf(fact_7730_fact__0,axiom,
% 5.46/5.71 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.46/5.71 = one_one_rat ) ).
% 5.46/5.71
% 5.46/5.71 % fact_0
% 5.46/5.71 thf(fact_7731_fact__0,axiom,
% 5.46/5.71 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.46/5.71 = one_one_int ) ).
% 5.46/5.71
% 5.46/5.71 % fact_0
% 5.46/5.71 thf(fact_7732_fact__0,axiom,
% 5.46/5.71 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % fact_0
% 5.46/5.71 thf(fact_7733_fact__0,axiom,
% 5.46/5.71 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.46/5.71 = one_one_nat ) ).
% 5.46/5.71
% 5.46/5.71 % fact_0
% 5.46/5.71 thf(fact_7734_fact__1,axiom,
% 5.46/5.71 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.46/5.71 = one_one_complex ) ).
% 5.46/5.71
% 5.46/5.71 % fact_1
% 5.46/5.71 thf(fact_7735_fact__1,axiom,
% 5.46/5.71 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.46/5.71 = one_one_rat ) ).
% 5.46/5.71
% 5.46/5.71 % fact_1
% 5.46/5.71 thf(fact_7736_fact__1,axiom,
% 5.46/5.71 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.46/5.71 = one_one_int ) ).
% 5.46/5.71
% 5.46/5.71 % fact_1
% 5.46/5.71 thf(fact_7737_fact__1,axiom,
% 5.46/5.71 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % fact_1
% 5.46/5.71 thf(fact_7738_fact__1,axiom,
% 5.46/5.71 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.46/5.71 = one_one_nat ) ).
% 5.46/5.71
% 5.46/5.71 % fact_1
% 5.46/5.71 thf(fact_7739_sin__pi__minus,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( sin_real @ ( minus_minus_real @ pi @ X2 ) )
% 5.46/5.71 = ( sin_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_pi_minus
% 5.46/5.71 thf(fact_7740_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7741_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_real,X2: real,G: real > real] :
% 5.46/5.71 ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7742_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_int,X2: int,G: int > real] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7743_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7744_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7745_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_real,X2: real,G: real > rat] :
% 5.46/5.71 ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7746_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_nat,X2: nat,G: nat > rat] :
% 5.46/5.71 ( ( finite_finite_nat @ A2 )
% 5.46/5.71 => ( ~ ( member_nat @ X2 @ A2 )
% 5.46/5.71 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7747_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_int,X2: int,G: int > rat] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7748_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,G: complex > rat] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7749_sum_Oinsert,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert
% 5.46/5.71 thf(fact_7750_fact__Suc__0,axiom,
% 5.46/5.71 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.46/5.71 = one_one_complex ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc_0
% 5.46/5.71 thf(fact_7751_fact__Suc__0,axiom,
% 5.46/5.71 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.46/5.71 = one_one_rat ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc_0
% 5.46/5.71 thf(fact_7752_fact__Suc__0,axiom,
% 5.46/5.71 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.46/5.71 = one_one_int ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc_0
% 5.46/5.71 thf(fact_7753_fact__Suc__0,axiom,
% 5.46/5.71 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc_0
% 5.46/5.71 thf(fact_7754_fact__Suc__0,axiom,
% 5.46/5.71 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.46/5.71 = one_one_nat ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc_0
% 5.46/5.71 thf(fact_7755_fact__Suc,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.46/5.71 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc
% 5.46/5.71 thf(fact_7756_fact__Suc,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( semiri5044797733671781792omplex @ ( suc @ N ) )
% 5.46/5.71 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc
% 5.46/5.71 thf(fact_7757_fact__Suc,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.46/5.71 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc
% 5.46/5.71 thf(fact_7758_fact__Suc,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.46/5.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc
% 5.46/5.71 thf(fact_7759_fact__Suc,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.46/5.71 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_Suc
% 5.46/5.71 thf(fact_7760_single__Diff__lessThan,axiom,
% 5.46/5.71 ! [K: int] :
% 5.46/5.71 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 5.46/5.71 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % single_Diff_lessThan
% 5.46/5.71 thf(fact_7761_single__Diff__lessThan,axiom,
% 5.46/5.71 ! [K: nat] :
% 5.46/5.71 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 5.46/5.71 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 5.46/5.71
% 5.46/5.71 % single_Diff_lessThan
% 5.46/5.71 thf(fact_7762_single__Diff__lessThan,axiom,
% 5.46/5.71 ! [K: real] :
% 5.46/5.71 ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 5.46/5.71 = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % single_Diff_lessThan
% 5.46/5.71 thf(fact_7763_cos__pi,axiom,
% 5.46/5.71 ( ( cos_real @ pi )
% 5.46/5.71 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_pi
% 5.46/5.71 thf(fact_7764_cos__periodic__pi2,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( cos_real @ ( plus_plus_real @ pi @ X2 ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_periodic_pi2
% 5.46/5.71 thf(fact_7765_cos__periodic__pi,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( cos_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_periodic_pi
% 5.46/5.71 thf(fact_7766_sin__periodic__pi2,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( sin_real @ ( plus_plus_real @ pi @ X2 ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_periodic_pi2
% 5.46/5.71 thf(fact_7767_sin__periodic__pi,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( sin_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_periodic_pi
% 5.46/5.71 thf(fact_7768_cos__pi__minus,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( cos_real @ ( minus_minus_real @ pi @ X2 ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_pi_minus
% 5.46/5.71 thf(fact_7769_cos__minus__pi,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( cos_real @ ( minus_minus_real @ X2 @ pi ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_minus_pi
% 5.46/5.71 thf(fact_7770_sin__minus__pi,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( sin_real @ ( minus_minus_real @ X2 @ pi ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_minus_pi
% 5.46/5.71 thf(fact_7771_fact__2,axiom,
% 5.46/5.71 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_2
% 5.46/5.71 thf(fact_7772_fact__2,axiom,
% 5.46/5.71 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_2
% 5.46/5.71 thf(fact_7773_fact__2,axiom,
% 5.46/5.71 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_2
% 5.46/5.71 thf(fact_7774_fact__2,axiom,
% 5.46/5.71 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_2
% 5.46/5.71 thf(fact_7775_fact__2,axiom,
% 5.46/5.71 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_2
% 5.46/5.71 thf(fact_7776_sin__cos__squared__add3,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ X2 ) ) @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( sin_complex @ X2 ) ) )
% 5.46/5.71 = one_one_complex ) ).
% 5.46/5.71
% 5.46/5.71 % sin_cos_squared_add3
% 5.46/5.71 thf(fact_7777_sin__cos__squared__add3,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ X2 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ X2 ) ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_cos_squared_add3
% 5.46/5.71 thf(fact_7778_set__replicate,axiom,
% 5.46/5.71 ! [N: nat,X2: vEBT_VEBT] :
% 5.46/5.71 ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.46/5.71 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate
% 5.46/5.71 thf(fact_7779_set__replicate,axiom,
% 5.46/5.71 ! [N: nat,X2: nat] :
% 5.46/5.71 ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( set_nat2 @ ( replicate_nat @ N @ X2 ) )
% 5.46/5.71 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate
% 5.46/5.71 thf(fact_7780_set__replicate,axiom,
% 5.46/5.71 ! [N: nat,X2: int] :
% 5.46/5.71 ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( set_int2 @ ( replicate_int @ N @ X2 ) )
% 5.46/5.71 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate
% 5.46/5.71 thf(fact_7781_set__replicate,axiom,
% 5.46/5.71 ! [N: nat,X2: real] :
% 5.46/5.71 ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( set_real2 @ ( replicate_real @ N @ X2 ) )
% 5.46/5.71 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate
% 5.46/5.71 thf(fact_7782_sin__npi,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_npi
% 5.46/5.71 thf(fact_7783_sin__npi2,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_npi2
% 5.46/5.71 thf(fact_7784_sin__npi__int,axiom,
% 5.46/5.71 ! [N: int] :
% 5.46/5.71 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_npi_int
% 5.46/5.71 thf(fact_7785_cos__pi__half,axiom,
% 5.46/5.71 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_pi_half
% 5.46/5.71 thf(fact_7786_sin__two__pi,axiom,
% 5.46/5.71 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_two_pi
% 5.46/5.71 thf(fact_7787_sin__pi__half,axiom,
% 5.46/5.71 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_pi_half
% 5.46/5.71 thf(fact_7788_cos__two__pi,axiom,
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_two_pi
% 5.46/5.71 thf(fact_7789_cos__periodic,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( cos_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.71 = ( cos_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_periodic
% 5.46/5.71 thf(fact_7790_sin__periodic,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( sin_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.71 = ( sin_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_periodic
% 5.46/5.71 thf(fact_7791_cos__2pi__minus,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.46/5.71 = ( cos_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_2pi_minus
% 5.46/5.71 thf(fact_7792_cos__npi2,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.71 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_npi2
% 5.46/5.71 thf(fact_7793_cos__npi,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.46/5.71 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_npi
% 5.46/5.71 thf(fact_7794_sin__cos__squared__add2,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_cos_squared_add2
% 5.46/5.71 thf(fact_7795_sin__cos__squared__add2,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = one_one_complex ) ).
% 5.46/5.71
% 5.46/5.71 % sin_cos_squared_add2
% 5.46/5.71 thf(fact_7796_sin__cos__squared__add,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_cos_squared_add
% 5.46/5.71 thf(fact_7797_sin__cos__squared__add,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = one_one_complex ) ).
% 5.46/5.71
% 5.46/5.71 % sin_cos_squared_add
% 5.46/5.71 thf(fact_7798_sin__2npi,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_2npi
% 5.46/5.71 thf(fact_7799_cos__2npi,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_2npi
% 5.46/5.71 thf(fact_7800_sin__2pi__minus,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_2pi_minus
% 5.46/5.71 thf(fact_7801_sin__int__2pin,axiom,
% 5.46/5.71 ! [N: int] :
% 5.46/5.71 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_int_2pin
% 5.46/5.71 thf(fact_7802_cos__int__2pin,axiom,
% 5.46/5.71 ! [N: int] :
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_int_2pin
% 5.46/5.71 thf(fact_7803_cos__3over2__pi,axiom,
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_3over2_pi
% 5.46/5.71 thf(fact_7804_sin__3over2__pi,axiom,
% 5.46/5.71 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.46/5.71 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_3over2_pi
% 5.46/5.71 thf(fact_7805_cos__npi__int,axiom,
% 5.46/5.71 ! [N: int] :
% 5.46/5.71 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.71 = one_one_real ) )
% 5.46/5.71 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.71 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_npi_int
% 5.46/5.71 thf(fact_7806_polar__Ex,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ? [R3: real,A5: real] :
% 5.46/5.71 ( ( X2
% 5.46/5.71 = ( times_times_real @ R3 @ ( cos_real @ A5 ) ) )
% 5.46/5.71 & ( Y2
% 5.46/5.71 = ( times_times_real @ R3 @ ( sin_real @ A5 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % polar_Ex
% 5.46/5.71 thf(fact_7807_sin__diff,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( sin_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.46/5.71 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_diff
% 5.46/5.71 thf(fact_7808_cos__one__sin__zero,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( ( cos_complex @ X2 )
% 5.46/5.71 = one_one_complex )
% 5.46/5.71 => ( ( sin_complex @ X2 )
% 5.46/5.71 = zero_zero_complex ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_one_sin_zero
% 5.46/5.71 thf(fact_7809_cos__one__sin__zero,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( cos_real @ X2 )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 => ( ( sin_real @ X2 )
% 5.46/5.71 = zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_one_sin_zero
% 5.46/5.71 thf(fact_7810_sin__add,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( sin_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_add
% 5.46/5.71 thf(fact_7811_insert__Diff__if,axiom,
% 5.46/5.71 ! [X2: vEBT_VEBT,B3: set_VEBT_VEBT,A2: set_VEBT_VEBT] :
% 5.46/5.71 ( ( ( member_VEBT_VEBT @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_5127226145743854075T_VEBT @ A2 @ B3 ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( insert_VEBT_VEBT @ X2 @ ( minus_5127226145743854075T_VEBT @ A2 @ B3 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_if
% 5.46/5.71 thf(fact_7812_insert__Diff__if,axiom,
% 5.46/5.71 ! [X2: complex,B3: set_complex,A2: set_complex] :
% 5.46/5.71 ( ( ( member_complex @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_811609699411566653omplex @ A2 @ B3 ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( insert_complex @ X2 @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_if
% 5.46/5.71 thf(fact_7813_insert__Diff__if,axiom,
% 5.46/5.71 ! [X2: real,B3: set_real,A2: set_real] :
% 5.46/5.71 ( ( ( member_real @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_minus_set_real @ A2 @ B3 ) ) )
% 5.46/5.71 & ( ~ ( member_real @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( insert_real @ X2 @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_if
% 5.46/5.71 thf(fact_7814_insert__Diff__if,axiom,
% 5.46/5.71 ! [X2: int,B3: set_int,A2: set_int] :
% 5.46/5.71 ( ( ( member_int @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_minus_set_int @ A2 @ B3 ) ) )
% 5.46/5.71 & ( ~ ( member_int @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( insert_int @ X2 @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_if
% 5.46/5.71 thf(fact_7815_insert__Diff__if,axiom,
% 5.46/5.71 ! [X2: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( ( member8440522571783428010at_nat @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_1356011639430497352at_nat @ A2 @ B3 ) ) )
% 5.46/5.71 & ( ~ ( member8440522571783428010at_nat @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( insert8211810215607154385at_nat @ X2 @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_if
% 5.46/5.71 thf(fact_7816_insert__Diff__if,axiom,
% 5.46/5.71 ! [X2: nat,B3: set_nat,A2: set_nat] :
% 5.46/5.71 ( ( ( member_nat @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( minus_minus_set_nat @ A2 @ B3 ) ) )
% 5.46/5.71 & ( ~ ( member_nat @ X2 @ B3 )
% 5.46/5.71 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A2 ) @ B3 )
% 5.46/5.71 = ( insert_nat @ X2 @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff_if
% 5.46/5.71 thf(fact_7817_cos__diff,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( cos_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_diff
% 5.46/5.71 thf(fact_7818_cos__add,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( cos_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.46/5.71 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_add
% 5.46/5.71 thf(fact_7819_sin__zero__norm__cos__one,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( sin_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X2 ) )
% 5.46/5.71 = one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_zero_norm_cos_one
% 5.46/5.71 thf(fact_7820_sin__zero__norm__cos__one,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( ( sin_complex @ X2 )
% 5.46/5.71 = zero_zero_complex )
% 5.46/5.71 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X2 ) )
% 5.46/5.71 = one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_zero_norm_cos_one
% 5.46/5.71 thf(fact_7821_sin__zero__abs__cos__one,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( sin_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 => ( ( abs_abs_real @ ( cos_real @ X2 ) )
% 5.46/5.71 = one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_zero_abs_cos_one
% 5.46/5.71 thf(fact_7822_sin__double,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.46/5.71 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X2 ) ) @ ( cos_complex @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_double
% 5.46/5.71 thf(fact_7823_sin__double,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.46/5.71 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X2 ) ) @ ( cos_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_double
% 5.46/5.71 thf(fact_7824_sincos__principal__value,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ? [Y3: real] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.46/5.71 & ( ord_less_eq_real @ Y3 @ pi )
% 5.46/5.71 & ( ( sin_real @ Y3 )
% 5.46/5.71 = ( sin_real @ X2 ) )
% 5.46/5.71 & ( ( cos_real @ Y3 )
% 5.46/5.71 = ( cos_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sincos_principal_value
% 5.46/5.71 thf(fact_7825_sin__x__le__x,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_x_le_x
% 5.46/5.71 thf(fact_7826_sin__le__one,axiom,
% 5.46/5.71 ! [X2: real] : ( ord_less_eq_real @ ( sin_real @ X2 ) @ one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_le_one
% 5.46/5.71 thf(fact_7827_cos__le__one,axiom,
% 5.46/5.71 ! [X2: real] : ( ord_less_eq_real @ ( cos_real @ X2 ) @ one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_le_one
% 5.46/5.71 thf(fact_7828_fact__ge__zero,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_zero
% 5.46/5.71 thf(fact_7829_fact__ge__zero,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_zero
% 5.46/5.71 thf(fact_7830_fact__ge__zero,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_zero
% 5.46/5.71 thf(fact_7831_fact__ge__zero,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_zero
% 5.46/5.71 thf(fact_7832_fact__gt__zero,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_gt_zero
% 5.46/5.71 thf(fact_7833_fact__gt__zero,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_gt_zero
% 5.46/5.71 thf(fact_7834_fact__gt__zero,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_gt_zero
% 5.46/5.71 thf(fact_7835_fact__gt__zero,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_gt_zero
% 5.46/5.71 thf(fact_7836_fact__not__neg,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.46/5.71
% 5.46/5.71 % fact_not_neg
% 5.46/5.71 thf(fact_7837_fact__not__neg,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.46/5.71
% 5.46/5.71 % fact_not_neg
% 5.46/5.71 thf(fact_7838_fact__not__neg,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % fact_not_neg
% 5.46/5.71 thf(fact_7839_fact__not__neg,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.46/5.71
% 5.46/5.71 % fact_not_neg
% 5.46/5.71 thf(fact_7840_fact__ge__1,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_1
% 5.46/5.71 thf(fact_7841_fact__ge__1,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_1
% 5.46/5.71 thf(fact_7842_fact__ge__1,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_1
% 5.46/5.71 thf(fact_7843_fact__ge__1,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_1
% 5.46/5.71 thf(fact_7844_abs__sin__x__le__abs__x,axiom,
% 5.46/5.71 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X2 ) ) @ ( abs_abs_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % abs_sin_x_le_abs_x
% 5.46/5.71 thf(fact_7845_fact__mono,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_mono
% 5.46/5.71 thf(fact_7846_fact__mono,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_mono
% 5.46/5.71 thf(fact_7847_fact__mono,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_mono
% 5.46/5.71 thf(fact_7848_fact__mono,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_mono
% 5.46/5.71 thf(fact_7849_fact__dvd,axiom,
% 5.46/5.71 ! [N: nat,M: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.71 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_dvd
% 5.46/5.71 thf(fact_7850_fact__dvd,axiom,
% 5.46/5.71 ! [N: nat,M: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.71 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_dvd
% 5.46/5.71 thf(fact_7851_fact__dvd,axiom,
% 5.46/5.71 ! [N: nat,M: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.71 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_dvd
% 5.46/5.71 thf(fact_7852_fact__dvd,axiom,
% 5.46/5.71 ! [N: nat,M: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.71 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_dvd
% 5.46/5.71 thf(fact_7853_Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.46/5.71 ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ B3 ) )
% 5.46/5.71 = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ B3 ) @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert
% 5.46/5.71 thf(fact_7854_Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_int,A: int,B3: set_int] :
% 5.46/5.71 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) )
% 5.46/5.71 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert
% 5.46/5.71 thf(fact_7855_Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_real,A: real,B3: set_real] :
% 5.46/5.71 ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) )
% 5.46/5.71 = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B3 ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert
% 5.46/5.71 thf(fact_7856_Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B3 ) )
% 5.46/5.71 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B3 ) @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert
% 5.46/5.71 thf(fact_7857_Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_nat,A: nat,B3: set_nat] :
% 5.46/5.71 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) )
% 5.46/5.71 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert
% 5.46/5.71 thf(fact_7858_insert__Diff,axiom,
% 5.46/5.71 ! [A: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ A @ A2 )
% 5.46/5.71 => ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff
% 5.46/5.71 thf(fact_7859_insert__Diff,axiom,
% 5.46/5.71 ! [A: complex,A2: set_complex] :
% 5.46/5.71 ( ( member_complex @ A @ A2 )
% 5.46/5.71 => ( ( insert_complex @ A @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff
% 5.46/5.71 thf(fact_7860_insert__Diff,axiom,
% 5.46/5.71 ! [A: int,A2: set_int] :
% 5.46/5.71 ( ( member_int @ A @ A2 )
% 5.46/5.71 => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff
% 5.46/5.71 thf(fact_7861_insert__Diff,axiom,
% 5.46/5.71 ! [A: real,A2: set_real] :
% 5.46/5.71 ( ( member_real @ A @ A2 )
% 5.46/5.71 => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff
% 5.46/5.71 thf(fact_7862_insert__Diff,axiom,
% 5.46/5.71 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( member8440522571783428010at_nat @ A @ A2 )
% 5.46/5.71 => ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff
% 5.46/5.71 thf(fact_7863_insert__Diff,axiom,
% 5.46/5.71 ! [A: nat,A2: set_nat] :
% 5.46/5.71 ( ( member_nat @ A @ A2 )
% 5.46/5.71 => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % insert_Diff
% 5.46/5.71 thf(fact_7864_Diff__insert2,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.46/5.71 ( ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ B3 ) )
% 5.46/5.71 = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) @ B3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert2
% 5.46/5.71 thf(fact_7865_Diff__insert2,axiom,
% 5.46/5.71 ! [A2: set_int,A: int,B3: set_int] :
% 5.46/5.71 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) )
% 5.46/5.71 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert2
% 5.46/5.71 thf(fact_7866_Diff__insert2,axiom,
% 5.46/5.71 ! [A2: set_real,A: real,B3: set_real] :
% 5.46/5.71 ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) )
% 5.46/5.71 = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert2
% 5.46/5.71 thf(fact_7867_Diff__insert2,axiom,
% 5.46/5.71 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B3 ) )
% 5.46/5.71 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ B3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert2
% 5.46/5.71 thf(fact_7868_Diff__insert2,axiom,
% 5.46/5.71 ! [A2: set_nat,A: nat,B3: set_nat] :
% 5.46/5.71 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) )
% 5.46/5.71 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert2
% 5.46/5.71 thf(fact_7869_Diff__insert__absorb,axiom,
% 5.46/5.71 ! [X2: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 5.46/5.71 ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A2 ) @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert_absorb
% 5.46/5.71 thf(fact_7870_Diff__insert__absorb,axiom,
% 5.46/5.71 ! [X2: complex,A2: set_complex] :
% 5.46/5.71 ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X2 @ A2 ) @ ( insert_complex @ X2 @ bot_bot_set_complex ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert_absorb
% 5.46/5.71 thf(fact_7871_Diff__insert__absorb,axiom,
% 5.46/5.71 ! [X2: int,A2: set_int] :
% 5.46/5.71 ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A2 ) @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert_absorb
% 5.46/5.71 thf(fact_7872_Diff__insert__absorb,axiom,
% 5.46/5.71 ! [X2: real,A2: set_real] :
% 5.46/5.71 ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A2 ) @ ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert_absorb
% 5.46/5.71 thf(fact_7873_Diff__insert__absorb,axiom,
% 5.46/5.71 ! [X2: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ~ ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X2 @ A2 ) @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert_absorb
% 5.46/5.71 thf(fact_7874_Diff__insert__absorb,axiom,
% 5.46/5.71 ! [X2: nat,A2: set_nat] :
% 5.46/5.71 ( ~ ( member_nat @ X2 @ A2 )
% 5.46/5.71 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A2 ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.46/5.71 = A2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_insert_absorb
% 5.46/5.71 thf(fact_7875_Compl__insert,axiom,
% 5.46/5.71 ! [X2: vEBT_VEBT,A2: set_VEBT_VEBT] :
% 5.46/5.71 ( ( uminus8041839845116263051T_VEBT @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( minus_5127226145743854075T_VEBT @ ( uminus8041839845116263051T_VEBT @ A2 ) @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Compl_insert
% 5.46/5.71 thf(fact_7876_Compl__insert,axiom,
% 5.46/5.71 ! [X2: int,A2: set_int] :
% 5.46/5.71 ( ( uminus1532241313380277803et_int @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.71 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Compl_insert
% 5.46/5.71 thf(fact_7877_Compl__insert,axiom,
% 5.46/5.71 ! [X2: real,A2: set_real] :
% 5.46/5.71 ( ( uminus612125837232591019t_real @ ( insert_real @ X2 @ A2 ) )
% 5.46/5.71 = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Compl_insert
% 5.46/5.71 thf(fact_7878_Compl__insert,axiom,
% 5.46/5.71 ! [X2: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ X2 @ A2 ) )
% 5.46/5.71 = ( minus_1356011639430497352at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Compl_insert
% 5.46/5.71 thf(fact_7879_Compl__insert,axiom,
% 5.46/5.71 ! [X2: nat,A2: set_nat] :
% 5.46/5.71 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X2 @ A2 ) )
% 5.46/5.71 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Compl_insert
% 5.46/5.71 thf(fact_7880_subset__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,B3: set_VEBT_VEBT,X2: vEBT_VEBT,C4: set_VEBT_VEBT] :
% 5.46/5.71 ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B3 @ ( insert_VEBT_VEBT @ X2 @ C4 ) ) )
% 5.46/5.71 = ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( minus_5127226145743854075T_VEBT @ B3 @ C4 ) )
% 5.46/5.71 & ~ ( member_VEBT_VEBT @ X2 @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_Diff_insert
% 5.46/5.71 thf(fact_7881_subset__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_complex,B3: set_complex,X2: complex,C4: set_complex] :
% 5.46/5.71 ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ ( insert_complex @ X2 @ C4 ) ) )
% 5.46/5.71 = ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ C4 ) )
% 5.46/5.71 & ~ ( member_complex @ X2 @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_Diff_insert
% 5.46/5.71 thf(fact_7882_subset__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_real,B3: set_real,X2: real,C4: set_real] :
% 5.46/5.71 ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ ( insert_real @ X2 @ C4 ) ) )
% 5.46/5.71 = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ C4 ) )
% 5.46/5.71 & ~ ( member_real @ X2 @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_Diff_insert
% 5.46/5.71 thf(fact_7883_subset__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_int,B3: set_int,X2: int,C4: set_int] :
% 5.46/5.71 ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ ( insert_int @ X2 @ C4 ) ) )
% 5.46/5.71 = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ C4 ) )
% 5.46/5.71 & ~ ( member_int @ X2 @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_Diff_insert
% 5.46/5.71 thf(fact_7884_subset__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B3 @ ( insert8211810215607154385at_nat @ X2 @ C4 ) ) )
% 5.46/5.71 = ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B3 @ C4 ) )
% 5.46/5.71 & ~ ( member8440522571783428010at_nat @ X2 @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_Diff_insert
% 5.46/5.71 thf(fact_7885_subset__Diff__insert,axiom,
% 5.46/5.71 ! [A2: set_nat,B3: set_nat,X2: nat,C4: set_nat] :
% 5.46/5.71 ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ ( insert_nat @ X2 @ C4 ) ) )
% 5.46/5.71 = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ C4 ) )
% 5.46/5.71 & ~ ( member_nat @ X2 @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_Diff_insert
% 5.46/5.71 thf(fact_7886_sin__cos__le1,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) ) ) @ one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % sin_cos_le1
% 5.46/5.71 thf(fact_7887_sin__squared__eq,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_squared_eq
% 5.46/5.71 thf(fact_7888_sin__squared__eq,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_squared_eq
% 5.46/5.71 thf(fact_7889_cos__squared__eq,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_squared_eq
% 5.46/5.71 thf(fact_7890_cos__squared__eq,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_squared_eq
% 5.46/5.71 thf(fact_7891_sin__gt__zero,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ pi )
% 5.46/5.71 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_gt_zero
% 5.46/5.71 thf(fact_7892_sin__x__ge__neg__x,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ ( sin_real @ X2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_x_ge_neg_x
% 5.46/5.71 thf(fact_7893_sin__ge__zero,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_ge_zero
% 5.46/5.71 thf(fact_7894_sin__ge__minus__one,axiom,
% 5.46/5.71 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_ge_minus_one
% 5.46/5.71 thf(fact_7895_cos__monotone__0__pi__le,axiom,
% 5.46/5.71 ! [Y2: real,X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.46/5.71 => ( ord_less_eq_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_monotone_0_pi_le
% 5.46/5.71 thf(fact_7896_cos__mono__le__eq,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.46/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ pi )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) )
% 5.46/5.71 = ( ord_less_eq_real @ Y2 @ X2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_mono_le_eq
% 5.46/5.71 thf(fact_7897_cos__inj__pi,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.46/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ pi )
% 5.46/5.71 => ( ( ( cos_real @ X2 )
% 5.46/5.71 = ( cos_real @ Y2 ) )
% 5.46/5.71 => ( X2 = Y2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_inj_pi
% 5.46/5.71 thf(fact_7898_cos__ge__minus__one,axiom,
% 5.46/5.71 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_ge_minus_one
% 5.46/5.71 thf(fact_7899_abs__sin__le__one,axiom,
% 5.46/5.71 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X2 ) ) @ one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % abs_sin_le_one
% 5.46/5.71 thf(fact_7900_abs__cos__le__one,axiom,
% 5.46/5.71 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X2 ) ) @ one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % abs_cos_le_one
% 5.46/5.71 thf(fact_7901_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > rat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.46/5.71 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.46/5.71 => ( ! [X3: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ S5 )
% 5.46/5.71 => ( ! [Y4: vEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_VEBT_VEBT @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7902_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_complex,P: set_complex > $o,F: complex > rat] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_complex )
% 5.46/5.71 => ( ! [X3: complex,S5: set_complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ S5 )
% 5.46/5.71 => ( ! [Y4: complex] :
% 5.46/5.71 ( ( member_complex @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_complex @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7903_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_nat,P: set_nat > $o,F: nat > rat] :
% 5.46/5.71 ( ( finite_finite_nat @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_nat )
% 5.46/5.71 => ( ! [X3: nat,S5: set_nat] :
% 5.46/5.71 ( ( finite_finite_nat @ S5 )
% 5.46/5.71 => ( ! [Y4: nat] :
% 5.46/5.71 ( ( member_nat @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_nat @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7904_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_int,P: set_int > $o,F: int > rat] :
% 5.46/5.71 ( ( finite_finite_int @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_int )
% 5.46/5.71 => ( ! [X3: int,S5: set_int] :
% 5.46/5.71 ( ( finite_finite_int @ S5 )
% 5.46/5.71 => ( ! [Y4: int] :
% 5.46/5.71 ( ( member_int @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_int @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7905_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_real,P: set_real > $o,F: real > rat] :
% 5.46/5.71 ( ( finite_finite_real @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_real )
% 5.46/5.71 => ( ! [X3: real,S5: set_real] :
% 5.46/5.71 ( ( finite_finite_real @ S5 )
% 5.46/5.71 => ( ! [Y4: real] :
% 5.46/5.71 ( ( member_real @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_real @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7906_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.46/5.71 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.46/5.71 => ( ! [X3: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ S5 )
% 5.46/5.71 => ( ! [Y4: vEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_VEBT_VEBT @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7907_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_complex )
% 5.46/5.71 => ( ! [X3: complex,S5: set_complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ S5 )
% 5.46/5.71 => ( ! [Y4: complex] :
% 5.46/5.71 ( ( member_complex @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_complex @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7908_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 5.46/5.71 ( ( finite_finite_nat @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_nat )
% 5.46/5.71 => ( ! [X3: nat,S5: set_nat] :
% 5.46/5.71 ( ( finite_finite_nat @ S5 )
% 5.46/5.71 => ( ! [Y4: nat] :
% 5.46/5.71 ( ( member_nat @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_nat @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7909_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_int,P: set_int > $o,F: int > num] :
% 5.46/5.71 ( ( finite_finite_int @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_int )
% 5.46/5.71 => ( ! [X3: int,S5: set_int] :
% 5.46/5.71 ( ( finite_finite_int @ S5 )
% 5.46/5.71 => ( ! [Y4: int] :
% 5.46/5.71 ( ( member_int @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_int @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7910_finite__ranking__induct,axiom,
% 5.46/5.71 ! [S2: set_real,P: set_real > $o,F: real > num] :
% 5.46/5.71 ( ( finite_finite_real @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_real )
% 5.46/5.71 => ( ! [X3: real,S5: set_real] :
% 5.46/5.71 ( ( finite_finite_real @ S5 )
% 5.46/5.71 => ( ! [Y4: real] :
% 5.46/5.71 ( ( member_real @ Y4 @ S5 )
% 5.46/5.71 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( P @ S5 )
% 5.46/5.71 => ( P @ ( insert_real @ X3 @ S5 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_ranking_induct
% 5.46/5.71 thf(fact_7911_finite__linorder__min__induct,axiom,
% 5.46/5.71 ! [A2: set_real,P: set_real > $o] :
% 5.46/5.71 ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_real )
% 5.46/5.71 => ( ! [B5: real,A7: set_real] :
% 5.46/5.71 ( ( finite_finite_real @ A7 )
% 5.46/5.71 => ( ! [X4: real] :
% 5.46/5.71 ( ( member_real @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_real @ B5 @ X4 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_min_induct
% 5.46/5.71 thf(fact_7912_finite__linorder__min__induct,axiom,
% 5.46/5.71 ! [A2: set_rat,P: set_rat > $o] :
% 5.46/5.71 ( ( finite_finite_rat @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_rat )
% 5.46/5.71 => ( ! [B5: rat,A7: set_rat] :
% 5.46/5.71 ( ( finite_finite_rat @ A7 )
% 5.46/5.71 => ( ! [X4: rat] :
% 5.46/5.71 ( ( member_rat @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_rat @ B5 @ X4 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_min_induct
% 5.46/5.71 thf(fact_7913_finite__linorder__min__induct,axiom,
% 5.46/5.71 ! [A2: set_num,P: set_num > $o] :
% 5.46/5.71 ( ( finite_finite_num @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_num )
% 5.46/5.71 => ( ! [B5: num,A7: set_num] :
% 5.46/5.71 ( ( finite_finite_num @ A7 )
% 5.46/5.71 => ( ! [X4: num] :
% 5.46/5.71 ( ( member_num @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_num @ B5 @ X4 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_min_induct
% 5.46/5.71 thf(fact_7914_finite__linorder__min__induct,axiom,
% 5.46/5.71 ! [A2: set_nat,P: set_nat > $o] :
% 5.46/5.71 ( ( finite_finite_nat @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_nat )
% 5.46/5.71 => ( ! [B5: nat,A7: set_nat] :
% 5.46/5.71 ( ( finite_finite_nat @ A7 )
% 5.46/5.71 => ( ! [X4: nat] :
% 5.46/5.71 ( ( member_nat @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_nat @ B5 @ X4 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_min_induct
% 5.46/5.71 thf(fact_7915_finite__linorder__min__induct,axiom,
% 5.46/5.71 ! [A2: set_int,P: set_int > $o] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_int )
% 5.46/5.71 => ( ! [B5: int,A7: set_int] :
% 5.46/5.71 ( ( finite_finite_int @ A7 )
% 5.46/5.71 => ( ! [X4: int] :
% 5.46/5.71 ( ( member_int @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_int @ B5 @ X4 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_min_induct
% 5.46/5.71 thf(fact_7916_finite__linorder__max__induct,axiom,
% 5.46/5.71 ! [A2: set_real,P: set_real > $o] :
% 5.46/5.71 ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_real )
% 5.46/5.71 => ( ! [B5: real,A7: set_real] :
% 5.46/5.71 ( ( finite_finite_real @ A7 )
% 5.46/5.71 => ( ! [X4: real] :
% 5.46/5.71 ( ( member_real @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_real @ X4 @ B5 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_max_induct
% 5.46/5.71 thf(fact_7917_finite__linorder__max__induct,axiom,
% 5.46/5.71 ! [A2: set_rat,P: set_rat > $o] :
% 5.46/5.71 ( ( finite_finite_rat @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_rat )
% 5.46/5.71 => ( ! [B5: rat,A7: set_rat] :
% 5.46/5.71 ( ( finite_finite_rat @ A7 )
% 5.46/5.71 => ( ! [X4: rat] :
% 5.46/5.71 ( ( member_rat @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_rat @ X4 @ B5 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_max_induct
% 5.46/5.71 thf(fact_7918_finite__linorder__max__induct,axiom,
% 5.46/5.71 ! [A2: set_num,P: set_num > $o] :
% 5.46/5.71 ( ( finite_finite_num @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_num )
% 5.46/5.71 => ( ! [B5: num,A7: set_num] :
% 5.46/5.71 ( ( finite_finite_num @ A7 )
% 5.46/5.71 => ( ! [X4: num] :
% 5.46/5.71 ( ( member_num @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_num @ X4 @ B5 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_max_induct
% 5.46/5.71 thf(fact_7919_finite__linorder__max__induct,axiom,
% 5.46/5.71 ! [A2: set_nat,P: set_nat > $o] :
% 5.46/5.71 ( ( finite_finite_nat @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_nat )
% 5.46/5.71 => ( ! [B5: nat,A7: set_nat] :
% 5.46/5.71 ( ( finite_finite_nat @ A7 )
% 5.46/5.71 => ( ! [X4: nat] :
% 5.46/5.71 ( ( member_nat @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_nat @ X4 @ B5 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_max_induct
% 5.46/5.71 thf(fact_7920_finite__linorder__max__induct,axiom,
% 5.46/5.71 ! [A2: set_int,P: set_int > $o] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_int )
% 5.46/5.71 => ( ! [B5: int,A7: set_int] :
% 5.46/5.71 ( ( finite_finite_int @ A7 )
% 5.46/5.71 => ( ! [X4: int] :
% 5.46/5.71 ( ( member_int @ X4 @ A7 )
% 5.46/5.71 => ( ord_less_int @ X4 @ B5 ) )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_linorder_max_induct
% 5.46/5.71 thf(fact_7921_fact__less__mono,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.71 => ( ( ord_less_nat @ M @ N )
% 5.46/5.71 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_less_mono
% 5.46/5.71 thf(fact_7922_fact__less__mono,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.71 => ( ( ord_less_nat @ M @ N )
% 5.46/5.71 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_less_mono
% 5.46/5.71 thf(fact_7923_fact__less__mono,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.71 => ( ( ord_less_nat @ M @ N )
% 5.46/5.71 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_less_mono
% 5.46/5.71 thf(fact_7924_fact__less__mono,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.71 => ( ( ord_less_nat @ M @ N )
% 5.46/5.71 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_less_mono
% 5.46/5.71 thf(fact_7925_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( groups2240296850493347238T_real @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7926_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_real,X2: real,G: real > real] :
% 5.46/5.71 ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ( ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.46/5.71 = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7927_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_int,X2: int,G: int > real] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.71 = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7928_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7929_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( groups136491112297645522BT_rat @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7930_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_real,X2: real,G: real > rat] :
% 5.46/5.71 ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ( ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.46/5.71 = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7931_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_nat,X2: nat,G: nat > rat] :
% 5.46/5.71 ( ( finite_finite_nat @ A2 )
% 5.46/5.71 => ( ( ( member_nat @ X2 @ A2 )
% 5.46/5.71 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.46/5.71 = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_nat @ X2 @ A2 )
% 5.46/5.71 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7932_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_int,X2: int,G: int > rat] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.71 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7933_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,G: complex > rat] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7934_sum_Oinsert__if,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( groups771621172384141258BT_nat @ G @ A2 ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_if
% 5.46/5.71 thf(fact_7935_sin__times__sin,axiom,
% 5.46/5.71 ! [W: complex,Z: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.46/5.71 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_times_sin
% 5.46/5.71 thf(fact_7936_sin__times__sin,axiom,
% 5.46/5.71 ! [W: real,Z: real] :
% 5.46/5.71 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.46/5.71 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_times_sin
% 5.46/5.71 thf(fact_7937_sin__times__cos,axiom,
% 5.46/5.71 ! [W: complex,Z: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.46/5.71 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_times_cos
% 5.46/5.71 thf(fact_7938_sin__times__cos,axiom,
% 5.46/5.71 ! [W: real,Z: real] :
% 5.46/5.71 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.46/5.71 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_times_cos
% 5.46/5.71 thf(fact_7939_cos__times__sin,axiom,
% 5.46/5.71 ! [W: complex,Z: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.46/5.71 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_times_sin
% 5.46/5.71 thf(fact_7940_cos__times__sin,axiom,
% 5.46/5.71 ! [W: real,Z: real] :
% 5.46/5.71 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.46/5.71 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_times_sin
% 5.46/5.71 thf(fact_7941_sin__plus__sin,axiom,
% 5.46/5.71 ! [W: complex,Z: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.46/5.71 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_plus_sin
% 5.46/5.71 thf(fact_7942_sin__plus__sin,axiom,
% 5.46/5.71 ! [W: real,Z: real] :
% 5.46/5.71 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.46/5.71 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_plus_sin
% 5.46/5.71 thf(fact_7943_sin__diff__sin,axiom,
% 5.46/5.71 ! [W: complex,Z: complex] :
% 5.46/5.71 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.46/5.71 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_diff_sin
% 5.46/5.71 thf(fact_7944_sin__diff__sin,axiom,
% 5.46/5.71 ! [W: real,Z: real] :
% 5.46/5.71 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.46/5.71 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_diff_sin
% 5.46/5.71 thf(fact_7945_cos__diff__cos,axiom,
% 5.46/5.71 ! [W: complex,Z: complex] :
% 5.46/5.71 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.46/5.71 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_diff_cos
% 5.46/5.71 thf(fact_7946_cos__diff__cos,axiom,
% 5.46/5.71 ! [W: real,Z: real] :
% 5.46/5.71 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.46/5.71 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_diff_cos
% 5.46/5.71 thf(fact_7947_fact__fact__dvd__fact,axiom,
% 5.46/5.71 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_fact_dvd_fact
% 5.46/5.71 thf(fact_7948_fact__fact__dvd__fact,axiom,
% 5.46/5.71 ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_fact_dvd_fact
% 5.46/5.71 thf(fact_7949_fact__fact__dvd__fact,axiom,
% 5.46/5.71 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_fact_dvd_fact
% 5.46/5.71 thf(fact_7950_fact__fact__dvd__fact,axiom,
% 5.46/5.71 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_fact_dvd_fact
% 5.46/5.71 thf(fact_7951_fact__fact__dvd__fact,axiom,
% 5.46/5.71 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_fact_dvd_fact
% 5.46/5.71 thf(fact_7952_fact__mod,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.46/5.71 = zero_zero_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_mod
% 5.46/5.71 thf(fact_7953_fact__mod,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.46/5.71 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_mod
% 5.46/5.71 thf(fact_7954_fact__mod,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.46/5.71 = zero_zero_nat ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_mod
% 5.46/5.71 thf(fact_7955_cos__double,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.46/5.71 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_double
% 5.46/5.71 thf(fact_7956_cos__double,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.46/5.71 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_double
% 5.46/5.71 thf(fact_7957_finite__empty__induct,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( P @ A2 )
% 5.46/5.71 => ( ! [A5: vEBT_VEBT,A7: set_VEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A7 )
% 5.46/5.71 => ( ( member_VEBT_VEBT @ A5 @ A7 )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ A5 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.46/5.71 => ( P @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_empty_induct
% 5.46/5.71 thf(fact_7958_finite__empty__induct,axiom,
% 5.46/5.71 ! [A2: set_complex,P: set_complex > $o] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( P @ A2 )
% 5.46/5.71 => ( ! [A5: complex,A7: set_complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A7 )
% 5.46/5.71 => ( ( member_complex @ A5 @ A7 )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ A5 @ bot_bot_set_complex ) ) ) ) ) )
% 5.46/5.71 => ( P @ bot_bot_set_complex ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_empty_induct
% 5.46/5.71 thf(fact_7959_finite__empty__induct,axiom,
% 5.46/5.71 ! [A2: set_int,P: set_int > $o] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( P @ A2 )
% 5.46/5.71 => ( ! [A5: int,A7: set_int] :
% 5.46/5.71 ( ( finite_finite_int @ A7 )
% 5.46/5.71 => ( ( member_int @ A5 @ A7 )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ A5 @ bot_bot_set_int ) ) ) ) ) )
% 5.46/5.71 => ( P @ bot_bot_set_int ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_empty_induct
% 5.46/5.71 thf(fact_7960_finite__empty__induct,axiom,
% 5.46/5.71 ! [A2: set_real,P: set_real > $o] :
% 5.46/5.71 ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ( P @ A2 )
% 5.46/5.71 => ( ! [A5: real,A7: set_real] :
% 5.46/5.71 ( ( finite_finite_real @ A7 )
% 5.46/5.71 => ( ( member_real @ A5 @ A7 )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ A5 @ bot_bot_set_real ) ) ) ) ) )
% 5.46/5.71 => ( P @ bot_bot_set_real ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_empty_induct
% 5.46/5.71 thf(fact_7961_finite__empty__induct,axiom,
% 5.46/5.71 ! [A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.46/5.71 ( ( finite6177210948735845034at_nat @ A2 )
% 5.46/5.71 => ( ( P @ A2 )
% 5.46/5.71 => ( ! [A5: product_prod_nat_nat,A7: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( finite6177210948735845034at_nat @ A7 )
% 5.46/5.71 => ( ( member8440522571783428010at_nat @ A5 @ A7 )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ A5 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 5.46/5.71 => ( P @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_empty_induct
% 5.46/5.71 thf(fact_7962_finite__empty__induct,axiom,
% 5.46/5.71 ! [A2: set_nat,P: set_nat > $o] :
% 5.46/5.71 ( ( finite_finite_nat @ A2 )
% 5.46/5.71 => ( ( P @ A2 )
% 5.46/5.71 => ( ! [A5: nat,A7: set_nat] :
% 5.46/5.71 ( ( finite_finite_nat @ A7 )
% 5.46/5.71 => ( ( member_nat @ A5 @ A7 )
% 5.46/5.71 => ( ( P @ A7 )
% 5.46/5.71 => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ A5 @ bot_bot_set_nat ) ) ) ) ) )
% 5.46/5.71 => ( P @ bot_bot_set_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_empty_induct
% 5.46/5.71 thf(fact_7963_infinite__coinduct,axiom,
% 5.46/5.71 ! [X7: set_VEBT_VEBT > $o,A2: set_VEBT_VEBT] :
% 5.46/5.71 ( ( X7 @ A2 )
% 5.46/5.71 => ( ! [A7: set_VEBT_VEBT] :
% 5.46/5.71 ( ( X7 @ A7 )
% 5.46/5.71 => ? [X4: vEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ X4 @ A7 )
% 5.46/5.71 & ( ( X7 @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 | ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.46/5.71 => ~ ( finite5795047828879050333T_VEBT @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_coinduct
% 5.46/5.71 thf(fact_7964_infinite__coinduct,axiom,
% 5.46/5.71 ! [X7: set_complex > $o,A2: set_complex] :
% 5.46/5.71 ( ( X7 @ A2 )
% 5.46/5.71 => ( ! [A7: set_complex] :
% 5.46/5.71 ( ( X7 @ A7 )
% 5.46/5.71 => ? [X4: complex] :
% 5.46/5.71 ( ( member_complex @ X4 @ A7 )
% 5.46/5.71 & ( ( X7 @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) )
% 5.46/5.71 | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ) )
% 5.46/5.71 => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_coinduct
% 5.46/5.71 thf(fact_7965_infinite__coinduct,axiom,
% 5.46/5.71 ! [X7: set_int > $o,A2: set_int] :
% 5.46/5.71 ( ( X7 @ A2 )
% 5.46/5.71 => ( ! [A7: set_int] :
% 5.46/5.71 ( ( X7 @ A7 )
% 5.46/5.71 => ? [X4: int] :
% 5.46/5.71 ( ( member_int @ X4 @ A7 )
% 5.46/5.71 & ( ( X7 @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) )
% 5.46/5.71 | ~ ( finite_finite_int @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ) )
% 5.46/5.71 => ~ ( finite_finite_int @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_coinduct
% 5.46/5.71 thf(fact_7966_infinite__coinduct,axiom,
% 5.46/5.71 ! [X7: set_real > $o,A2: set_real] :
% 5.46/5.71 ( ( X7 @ A2 )
% 5.46/5.71 => ( ! [A7: set_real] :
% 5.46/5.71 ( ( X7 @ A7 )
% 5.46/5.71 => ? [X4: real] :
% 5.46/5.71 ( ( member_real @ X4 @ A7 )
% 5.46/5.71 & ( ( X7 @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) )
% 5.46/5.71 | ~ ( finite_finite_real @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) ) ) )
% 5.46/5.71 => ~ ( finite_finite_real @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_coinduct
% 5.46/5.71 thf(fact_7967_infinite__coinduct,axiom,
% 5.46/5.71 ! [X7: set_Pr1261947904930325089at_nat > $o,A2: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( X7 @ A2 )
% 5.46/5.71 => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( X7 @ A7 )
% 5.46/5.71 => ? [X4: product_prod_nat_nat] :
% 5.46/5.71 ( ( member8440522571783428010at_nat @ X4 @ A7 )
% 5.46/5.71 & ( ( X7 @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) )
% 5.46/5.71 | ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 5.46/5.71 => ~ ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_coinduct
% 5.46/5.71 thf(fact_7968_infinite__coinduct,axiom,
% 5.46/5.71 ! [X7: set_nat > $o,A2: set_nat] :
% 5.46/5.71 ( ( X7 @ A2 )
% 5.46/5.71 => ( ! [A7: set_nat] :
% 5.46/5.71 ( ( X7 @ A7 )
% 5.46/5.71 => ? [X4: nat] :
% 5.46/5.71 ( ( member_nat @ X4 @ A7 )
% 5.46/5.71 & ( ( X7 @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) )
% 5.46/5.71 | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ) )
% 5.46/5.71 => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_coinduct
% 5.46/5.71 thf(fact_7969_infinite__remove,axiom,
% 5.46/5.71 ! [S2: set_VEBT_VEBT,A: vEBT_VEBT] :
% 5.46/5.71 ( ~ ( finite5795047828879050333T_VEBT @ S2 )
% 5.46/5.71 => ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_remove
% 5.46/5.71 thf(fact_7970_infinite__remove,axiom,
% 5.46/5.71 ! [S2: set_complex,A: complex] :
% 5.46/5.71 ( ~ ( finite3207457112153483333omplex @ S2 )
% 5.46/5.71 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_remove
% 5.46/5.71 thf(fact_7971_infinite__remove,axiom,
% 5.46/5.71 ! [S2: set_int,A: int] :
% 5.46/5.71 ( ~ ( finite_finite_int @ S2 )
% 5.46/5.71 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_remove
% 5.46/5.71 thf(fact_7972_infinite__remove,axiom,
% 5.46/5.71 ! [S2: set_real,A: real] :
% 5.46/5.71 ( ~ ( finite_finite_real @ S2 )
% 5.46/5.71 => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_remove
% 5.46/5.71 thf(fact_7973_infinite__remove,axiom,
% 5.46/5.71 ! [S2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 5.46/5.71 ( ~ ( finite6177210948735845034at_nat @ S2 )
% 5.46/5.71 => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_remove
% 5.46/5.71 thf(fact_7974_infinite__remove,axiom,
% 5.46/5.71 ! [S2: set_nat,A: nat] :
% 5.46/5.71 ( ~ ( finite_finite_nat @ S2 )
% 5.46/5.71 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % infinite_remove
% 5.46/5.71 thf(fact_7975_subset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.46/5.71 ( ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ord_le4337996190870823476T_VEBT @ A2 @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_insert_iff
% 5.46/5.71 thf(fact_7976_subset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,B3: set_complex] :
% 5.46/5.71 ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_insert_iff
% 5.46/5.71 thf(fact_7977_subset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_int,X2: int,B3: set_int] :
% 5.46/5.71 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_insert_iff
% 5.46/5.71 thf(fact_7978_subset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_real,X2: real,B3: set_real] :
% 5.46/5.71 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_insert_iff
% 5.46/5.71 thf(fact_7979_subset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.46/5.71 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.46/5.71 => ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_insert_iff
% 5.46/5.71 thf(fact_7980_subset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_nat,X2: nat,B3: set_nat] :
% 5.46/5.71 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_nat @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_nat @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % subset_insert_iff
% 5.46/5.71 thf(fact_7981_Diff__single__insert,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.46/5.71 ( ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) @ B3 )
% 5.46/5.71 => ( ord_le4337996190870823476T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_single_insert
% 5.46/5.71 thf(fact_7982_Diff__single__insert,axiom,
% 5.46/5.71 ! [A2: set_int,X2: int,B3: set_int] :
% 5.46/5.71 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B3 )
% 5.46/5.71 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_single_insert
% 5.46/5.71 thf(fact_7983_Diff__single__insert,axiom,
% 5.46/5.71 ! [A2: set_real,X2: real,B3: set_real] :
% 5.46/5.71 ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B3 )
% 5.46/5.71 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_single_insert
% 5.46/5.71 thf(fact_7984_Diff__single__insert,axiom,
% 5.46/5.71 ! [A2: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ B3 )
% 5.46/5.71 => ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_single_insert
% 5.46/5.71 thf(fact_7985_Diff__single__insert,axiom,
% 5.46/5.71 ! [A2: set_nat,X2: nat,B3: set_nat] :
% 5.46/5.71 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B3 )
% 5.46/5.71 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X2 @ B3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Diff_single_insert
% 5.46/5.71 thf(fact_7986_fact__le__power,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_le_power
% 5.46/5.71 thf(fact_7987_fact__le__power,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_le_power
% 5.46/5.71 thf(fact_7988_fact__le__power,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_le_power
% 5.46/5.71 thf(fact_7989_fact__le__power,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_le_power
% 5.46/5.71 thf(fact_7990_set__update__subset__insert,axiom,
% 5.46/5.71 ! [Xs2: list_real,I: nat,X2: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I @ X2 ) ) @ ( insert_real @ X2 @ ( set_real2 @ Xs2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_update_subset_insert
% 5.46/5.71 thf(fact_7991_set__update__subset__insert,axiom,
% 5.46/5.71 ! [Xs2: list_int,I: nat,X2: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I @ X2 ) ) @ ( insert_int @ X2 @ ( set_int2 @ Xs2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_update_subset_insert
% 5.46/5.71 thf(fact_7992_set__update__subset__insert,axiom,
% 5.46/5.71 ! [Xs2: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) ) @ ( insert_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_update_subset_insert
% 5.46/5.71 thf(fact_7993_set__update__subset__insert,axiom,
% 5.46/5.71 ! [Xs2: list_nat,I: nat,X2: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I @ X2 ) ) @ ( insert_nat @ X2 @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_update_subset_insert
% 5.46/5.71 thf(fact_7994_cos__double__sin,axiom,
% 5.46/5.71 ! [W: complex] :
% 5.46/5.71 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.46/5.71 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_double_sin
% 5.46/5.71 thf(fact_7995_cos__double__sin,axiom,
% 5.46/5.71 ! [W: real] :
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.46/5.71 = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_double_sin
% 5.46/5.71 thf(fact_7996_cos__two__neq__zero,axiom,
% 5.46/5.71 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.71 != zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % cos_two_neq_zero
% 5.46/5.71 thf(fact_7997_cos__mono__less__eq,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.46/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ pi )
% 5.46/5.71 => ( ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) )
% 5.46/5.71 = ( ord_less_real @ Y2 @ X2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_mono_less_eq
% 5.46/5.71 thf(fact_7998_cos__monotone__0__pi,axiom,
% 5.46/5.71 ! [Y2: real,X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.71 => ( ( ord_less_real @ Y2 @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.46/5.71 => ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_monotone_0_pi
% 5.46/5.71 thf(fact_7999_sin__eq__0__pi,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ pi )
% 5.46/5.71 => ( ( ( sin_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_eq_0_pi
% 5.46/5.71 thf(fact_8000_sin__zero__pi__iff,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ pi )
% 5.46/5.71 => ( ( ( sin_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 = ( X2 = zero_zero_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_zero_pi_iff
% 5.46/5.71 thf(fact_8001_cos__monotone__minus__pi__0_H,axiom,
% 5.46/5.71 ! [Y2: real,X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.71 => ( ord_less_eq_real @ ( cos_real @ Y2 ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_monotone_minus_pi_0'
% 5.46/5.71 thf(fact_8002_sin__zero__iff__int2,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( sin_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 = ( ? [I4: int] :
% 5.46/5.71 ( X2
% 5.46/5.71 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ pi ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_zero_iff_int2
% 5.46/5.71 thf(fact_8003_choose__dvd,axiom,
% 5.46/5.71 ! [K: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.71 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % choose_dvd
% 5.46/5.71 thf(fact_8004_choose__dvd,axiom,
% 5.46/5.71 ! [K: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.71 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % choose_dvd
% 5.46/5.71 thf(fact_8005_choose__dvd,axiom,
% 5.46/5.71 ! [K: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.71 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % choose_dvd
% 5.46/5.71 thf(fact_8006_choose__dvd,axiom,
% 5.46/5.71 ! [K: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.71 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % choose_dvd
% 5.46/5.71 thf(fact_8007_choose__dvd,axiom,
% 5.46/5.71 ! [K: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.71 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % choose_dvd
% 5.46/5.71 thf(fact_8008_remove__induct,axiom,
% 5.46/5.71 ! [P: set_VEBT_VEBT > $o,B3: set_VEBT_VEBT] :
% 5.46/5.71 ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.46/5.71 => ( ( ~ ( finite5795047828879050333T_VEBT @ B3 )
% 5.46/5.71 => ( P @ B3 ) )
% 5.46/5.71 => ( ! [A7: set_VEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 5.46/5.71 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: vEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % remove_induct
% 5.46/5.71 thf(fact_8009_remove__induct,axiom,
% 5.46/5.71 ! [P: set_complex > $o,B3: set_complex] :
% 5.46/5.71 ( ( P @ bot_bot_set_complex )
% 5.46/5.71 => ( ( ~ ( finite3207457112153483333omplex @ B3 )
% 5.46/5.71 => ( P @ B3 ) )
% 5.46/5.71 => ( ! [A7: set_complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bot_set_complex )
% 5.46/5.71 => ( ( ord_le211207098394363844omplex @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: complex] :
% 5.46/5.71 ( ( member_complex @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % remove_induct
% 5.46/5.71 thf(fact_8010_remove__induct,axiom,
% 5.46/5.71 ! [P: set_int > $o,B3: set_int] :
% 5.46/5.71 ( ( P @ bot_bot_set_int )
% 5.46/5.71 => ( ( ~ ( finite_finite_int @ B3 )
% 5.46/5.71 => ( P @ B3 ) )
% 5.46/5.71 => ( ! [A7: set_int] :
% 5.46/5.71 ( ( finite_finite_int @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bot_set_int )
% 5.46/5.71 => ( ( ord_less_eq_set_int @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: int] :
% 5.46/5.71 ( ( member_int @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % remove_induct
% 5.46/5.71 thf(fact_8011_remove__induct,axiom,
% 5.46/5.71 ! [P: set_real > $o,B3: set_real] :
% 5.46/5.71 ( ( P @ bot_bot_set_real )
% 5.46/5.71 => ( ( ~ ( finite_finite_real @ B3 )
% 5.46/5.71 => ( P @ B3 ) )
% 5.46/5.71 => ( ! [A7: set_real] :
% 5.46/5.71 ( ( finite_finite_real @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bot_set_real )
% 5.46/5.71 => ( ( ord_less_eq_set_real @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: real] :
% 5.46/5.71 ( ( member_real @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % remove_induct
% 5.46/5.71 thf(fact_8012_remove__induct,axiom,
% 5.46/5.71 ! [P: set_Pr1261947904930325089at_nat > $o,B3: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( P @ bot_bo2099793752762293965at_nat )
% 5.46/5.71 => ( ( ~ ( finite6177210948735845034at_nat @ B3 )
% 5.46/5.71 => ( P @ B3 ) )
% 5.46/5.71 => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( finite6177210948735845034at_nat @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bo2099793752762293965at_nat )
% 5.46/5.71 => ( ( ord_le3146513528884898305at_nat @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: product_prod_nat_nat] :
% 5.46/5.71 ( ( member8440522571783428010at_nat @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % remove_induct
% 5.46/5.71 thf(fact_8013_remove__induct,axiom,
% 5.46/5.71 ! [P: set_nat > $o,B3: set_nat] :
% 5.46/5.71 ( ( P @ bot_bot_set_nat )
% 5.46/5.71 => ( ( ~ ( finite_finite_nat @ B3 )
% 5.46/5.71 => ( P @ B3 ) )
% 5.46/5.71 => ( ! [A7: set_nat] :
% 5.46/5.71 ( ( finite_finite_nat @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bot_set_nat )
% 5.46/5.71 => ( ( ord_less_eq_set_nat @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: nat] :
% 5.46/5.71 ( ( member_nat @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % remove_induct
% 5.46/5.71 thf(fact_8014_finite__remove__induct,axiom,
% 5.46/5.71 ! [B3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ B3 )
% 5.46/5.71 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.46/5.71 => ( ! [A7: set_VEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bo8194388402131092736T_VEBT )
% 5.46/5.71 => ( ( ord_le4337996190870823476T_VEBT @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: vEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_5127226145743854075T_VEBT @ A7 @ ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_remove_induct
% 5.46/5.71 thf(fact_8015_finite__remove__induct,axiom,
% 5.46/5.71 ! [B3: set_complex,P: set_complex > $o] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ B3 )
% 5.46/5.71 => ( ( P @ bot_bot_set_complex )
% 5.46/5.71 => ( ! [A7: set_complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bot_set_complex )
% 5.46/5.71 => ( ( ord_le211207098394363844omplex @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: complex] :
% 5.46/5.71 ( ( member_complex @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_remove_induct
% 5.46/5.71 thf(fact_8016_finite__remove__induct,axiom,
% 5.46/5.71 ! [B3: set_int,P: set_int > $o] :
% 5.46/5.71 ( ( finite_finite_int @ B3 )
% 5.46/5.71 => ( ( P @ bot_bot_set_int )
% 5.46/5.71 => ( ! [A7: set_int] :
% 5.46/5.71 ( ( finite_finite_int @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bot_set_int )
% 5.46/5.71 => ( ( ord_less_eq_set_int @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: int] :
% 5.46/5.71 ( ( member_int @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_remove_induct
% 5.46/5.71 thf(fact_8017_finite__remove__induct,axiom,
% 5.46/5.71 ! [B3: set_real,P: set_real > $o] :
% 5.46/5.71 ( ( finite_finite_real @ B3 )
% 5.46/5.71 => ( ( P @ bot_bot_set_real )
% 5.46/5.71 => ( ! [A7: set_real] :
% 5.46/5.71 ( ( finite_finite_real @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bot_set_real )
% 5.46/5.71 => ( ( ord_less_eq_set_real @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: real] :
% 5.46/5.71 ( ( member_real @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_remove_induct
% 5.46/5.71 thf(fact_8018_finite__remove__induct,axiom,
% 5.46/5.71 ! [B3: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.46/5.71 ( ( finite6177210948735845034at_nat @ B3 )
% 5.46/5.71 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.46/5.71 => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( finite6177210948735845034at_nat @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bo2099793752762293965at_nat )
% 5.46/5.71 => ( ( ord_le3146513528884898305at_nat @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: product_prod_nat_nat] :
% 5.46/5.71 ( ( member8440522571783428010at_nat @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_remove_induct
% 5.46/5.71 thf(fact_8019_finite__remove__induct,axiom,
% 5.46/5.71 ! [B3: set_nat,P: set_nat > $o] :
% 5.46/5.71 ( ( finite_finite_nat @ B3 )
% 5.46/5.71 => ( ( P @ bot_bot_set_nat )
% 5.46/5.71 => ( ! [A7: set_nat] :
% 5.46/5.71 ( ( finite_finite_nat @ A7 )
% 5.46/5.71 => ( ( A7 != bot_bot_set_nat )
% 5.46/5.71 => ( ( ord_less_eq_set_nat @ A7 @ B3 )
% 5.46/5.71 => ( ! [X4: nat] :
% 5.46/5.71 ( ( member_nat @ X4 @ A7 )
% 5.46/5.71 => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 5.46/5.71 => ( P @ A7 ) ) ) ) )
% 5.46/5.71 => ( P @ B3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_remove_induct
% 5.46/5.71 thf(fact_8020_finite__induct__select,axiom,
% 5.46/5.71 ! [S2: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.46/5.71 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.46/5.71 => ( ! [T6: set_VEBT_VEBT] :
% 5.46/5.71 ( ( ord_le3480810397992357184T_VEBT @ T6 @ S2 )
% 5.46/5.71 => ( ( P @ T6 )
% 5.46/5.71 => ? [X4: vEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ S2 @ T6 ) )
% 5.46/5.71 & ( P @ ( insert_VEBT_VEBT @ X4 @ T6 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_induct_select
% 5.46/5.71 thf(fact_8021_finite__induct__select,axiom,
% 5.46/5.71 ! [S2: set_complex,P: set_complex > $o] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_complex )
% 5.46/5.71 => ( ! [T6: set_complex] :
% 5.46/5.71 ( ( ord_less_set_complex @ T6 @ S2 )
% 5.46/5.71 => ( ( P @ T6 )
% 5.46/5.71 => ? [X4: complex] :
% 5.46/5.71 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ S2 @ T6 ) )
% 5.46/5.71 & ( P @ ( insert_complex @ X4 @ T6 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_induct_select
% 5.46/5.71 thf(fact_8022_finite__induct__select,axiom,
% 5.46/5.71 ! [S2: set_int,P: set_int > $o] :
% 5.46/5.71 ( ( finite_finite_int @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_int )
% 5.46/5.71 => ( ! [T6: set_int] :
% 5.46/5.71 ( ( ord_less_set_int @ T6 @ S2 )
% 5.46/5.71 => ( ( P @ T6 )
% 5.46/5.71 => ? [X4: int] :
% 5.46/5.71 ( ( member_int @ X4 @ ( minus_minus_set_int @ S2 @ T6 ) )
% 5.46/5.71 & ( P @ ( insert_int @ X4 @ T6 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_induct_select
% 5.46/5.71 thf(fact_8023_finite__induct__select,axiom,
% 5.46/5.71 ! [S2: set_real,P: set_real > $o] :
% 5.46/5.71 ( ( finite_finite_real @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_real )
% 5.46/5.71 => ( ! [T6: set_real] :
% 5.46/5.71 ( ( ord_less_set_real @ T6 @ S2 )
% 5.46/5.71 => ( ( P @ T6 )
% 5.46/5.71 => ? [X4: real] :
% 5.46/5.71 ( ( member_real @ X4 @ ( minus_minus_set_real @ S2 @ T6 ) )
% 5.46/5.71 & ( P @ ( insert_real @ X4 @ T6 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_induct_select
% 5.46/5.71 thf(fact_8024_finite__induct__select,axiom,
% 5.46/5.71 ! [S2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.46/5.71 ( ( finite6177210948735845034at_nat @ S2 )
% 5.46/5.71 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.46/5.71 => ( ! [T6: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( ord_le7866589430770878221at_nat @ T6 @ S2 )
% 5.46/5.71 => ( ( P @ T6 )
% 5.46/5.71 => ? [X4: product_prod_nat_nat] :
% 5.46/5.71 ( ( member8440522571783428010at_nat @ X4 @ ( minus_1356011639430497352at_nat @ S2 @ T6 ) )
% 5.46/5.71 & ( P @ ( insert8211810215607154385at_nat @ X4 @ T6 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_induct_select
% 5.46/5.71 thf(fact_8025_finite__induct__select,axiom,
% 5.46/5.71 ! [S2: set_nat,P: set_nat > $o] :
% 5.46/5.71 ( ( finite_finite_nat @ S2 )
% 5.46/5.71 => ( ( P @ bot_bot_set_nat )
% 5.46/5.71 => ( ! [T6: set_nat] :
% 5.46/5.71 ( ( ord_less_set_nat @ T6 @ S2 )
% 5.46/5.71 => ( ( P @ T6 )
% 5.46/5.71 => ? [X4: nat] :
% 5.46/5.71 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ S2 @ T6 ) )
% 5.46/5.71 & ( P @ ( insert_nat @ X4 @ T6 ) ) ) ) )
% 5.46/5.71 => ( P @ S2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % finite_induct_select
% 5.46/5.71 thf(fact_8026_psubset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.46/5.71 ( ( ord_le3480810397992357184T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_VEBT_VEBT @ X2 @ B3 )
% 5.46/5.71 => ( ord_le3480810397992357184T_VEBT @ A2 @ B3 ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ X2 @ B3 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ord_le4337996190870823476T_VEBT @ A2 @ B3 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % psubset_insert_iff
% 5.46/5.71 thf(fact_8027_psubset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,B3: set_complex] :
% 5.46/5.71 ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_complex @ X2 @ B3 )
% 5.46/5.71 => ( ord_less_set_complex @ A2 @ B3 ) )
% 5.46/5.71 & ( ~ ( member_complex @ X2 @ B3 )
% 5.46/5.71 => ( ( ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % psubset_insert_iff
% 5.46/5.71 thf(fact_8028_psubset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_int,X2: int,B3: set_int] :
% 5.46/5.71 ( ( ord_less_set_int @ A2 @ ( insert_int @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_int @ X2 @ B3 )
% 5.46/5.71 => ( ord_less_set_int @ A2 @ B3 ) )
% 5.46/5.71 & ( ~ ( member_int @ X2 @ B3 )
% 5.46/5.71 => ( ( ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % psubset_insert_iff
% 5.46/5.71 thf(fact_8029_psubset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_real,X2: real,B3: set_real] :
% 5.46/5.71 ( ( ord_less_set_real @ A2 @ ( insert_real @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_real @ X2 @ B3 )
% 5.46/5.71 => ( ord_less_set_real @ A2 @ B3 ) )
% 5.46/5.71 & ( ~ ( member_real @ X2 @ B3 )
% 5.46/5.71 => ( ( ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % psubset_insert_iff
% 5.46/5.71 thf(fact_8030_psubset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.46/5.71 ( ( ord_le7866589430770878221at_nat @ A2 @ ( insert8211810215607154385at_nat @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member8440522571783428010at_nat @ X2 @ B3 )
% 5.46/5.71 => ( ord_le7866589430770878221at_nat @ A2 @ B3 ) )
% 5.46/5.71 & ( ~ ( member8440522571783428010at_nat @ X2 @ B3 )
% 5.46/5.71 => ( ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.46/5.71 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.46/5.71 => ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % psubset_insert_iff
% 5.46/5.71 thf(fact_8031_psubset__insert__iff,axiom,
% 5.46/5.71 ! [A2: set_nat,X2: nat,B3: set_nat] :
% 5.46/5.71 ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X2 @ B3 ) )
% 5.46/5.71 = ( ( ( member_nat @ X2 @ B3 )
% 5.46/5.71 => ( ord_less_set_nat @ A2 @ B3 ) )
% 5.46/5.71 & ( ~ ( member_nat @ X2 @ B3 )
% 5.46/5.71 => ( ( ( member_nat @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B3 ) )
% 5.46/5.71 & ( ~ ( member_nat @ X2 @ A2 )
% 5.46/5.71 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % psubset_insert_iff
% 5.46/5.71 thf(fact_8032_fact__numeral,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.46/5.71 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_numeral
% 5.46/5.71 thf(fact_8033_fact__numeral,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.46/5.71 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_numeral
% 5.46/5.71 thf(fact_8034_fact__numeral,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.46/5.71 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_numeral
% 5.46/5.71 thf(fact_8035_fact__numeral,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.46/5.71 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_numeral
% 5.46/5.71 thf(fact_8036_fact__numeral,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.46/5.71 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_numeral
% 5.46/5.71 thf(fact_8037_set__replicate__Suc,axiom,
% 5.46/5.71 ! [N: nat,X2: vEBT_VEBT] :
% 5.46/5.71 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X2 ) )
% 5.46/5.71 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate_Suc
% 5.46/5.71 thf(fact_8038_set__replicate__Suc,axiom,
% 5.46/5.71 ! [N: nat,X2: nat] :
% 5.46/5.71 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X2 ) )
% 5.46/5.71 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate_Suc
% 5.46/5.71 thf(fact_8039_set__replicate__Suc,axiom,
% 5.46/5.71 ! [N: nat,X2: int] :
% 5.46/5.71 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X2 ) )
% 5.46/5.71 = ( insert_int @ X2 @ bot_bot_set_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate_Suc
% 5.46/5.71 thf(fact_8040_set__replicate__Suc,axiom,
% 5.46/5.71 ! [N: nat,X2: real] :
% 5.46/5.71 ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X2 ) )
% 5.46/5.71 = ( insert_real @ X2 @ bot_bot_set_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate_Suc
% 5.46/5.71 thf(fact_8041_sincos__total__pi,axiom,
% 5.46/5.71 ! [Y2: real,X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.71 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 => ? [T5: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.46/5.71 & ( ord_less_eq_real @ T5 @ pi )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( cos_real @ T5 ) )
% 5.46/5.71 & ( Y2
% 5.46/5.71 = ( sin_real @ T5 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sincos_total_pi
% 5.46/5.71 thf(fact_8042_set__replicate__conv__if,axiom,
% 5.46/5.71 ! [N: nat,X2: vEBT_VEBT] :
% 5.46/5.71 ( ( ( N = zero_zero_nat )
% 5.46/5.71 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.46/5.71 = bot_bo8194388402131092736T_VEBT ) )
% 5.46/5.71 & ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.46/5.71 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate_conv_if
% 5.46/5.71 thf(fact_8043_set__replicate__conv__if,axiom,
% 5.46/5.71 ! [N: nat,X2: nat] :
% 5.46/5.71 ( ( ( N = zero_zero_nat )
% 5.46/5.71 => ( ( set_nat2 @ ( replicate_nat @ N @ X2 ) )
% 5.46/5.71 = bot_bot_set_nat ) )
% 5.46/5.71 & ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( set_nat2 @ ( replicate_nat @ N @ X2 ) )
% 5.46/5.71 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate_conv_if
% 5.46/5.71 thf(fact_8044_set__replicate__conv__if,axiom,
% 5.46/5.71 ! [N: nat,X2: int] :
% 5.46/5.71 ( ( ( N = zero_zero_nat )
% 5.46/5.71 => ( ( set_int2 @ ( replicate_int @ N @ X2 ) )
% 5.46/5.71 = bot_bot_set_int ) )
% 5.46/5.71 & ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( set_int2 @ ( replicate_int @ N @ X2 ) )
% 5.46/5.71 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate_conv_if
% 5.46/5.71 thf(fact_8045_set__replicate__conv__if,axiom,
% 5.46/5.71 ! [N: nat,X2: real] :
% 5.46/5.71 ( ( ( N = zero_zero_nat )
% 5.46/5.71 => ( ( set_real2 @ ( replicate_real @ N @ X2 ) )
% 5.46/5.71 = bot_bot_set_real ) )
% 5.46/5.71 & ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( set_real2 @ ( replicate_real @ N @ X2 ) )
% 5.46/5.71 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_replicate_conv_if
% 5.46/5.71 thf(fact_8046_sin__expansion__lemma,axiom,
% 5.46/5.71 ! [X2: real,M: nat] :
% 5.46/5.71 ( ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.71 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_expansion_lemma
% 5.46/5.71 thf(fact_8047_sum__diff1__nat,axiom,
% 5.46/5.71 ! [A: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.46/5.71 ( ( ( member_VEBT_VEBT @ A @ A2 )
% 5.46/5.71 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 5.46/5.71 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 = ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1_nat
% 5.46/5.71 thf(fact_8048_sum__diff1__nat,axiom,
% 5.46/5.71 ! [A: complex,A2: set_complex,F: complex > nat] :
% 5.46/5.71 ( ( ( member_complex @ A @ A2 )
% 5.46/5.71 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.46/5.71 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ A @ A2 )
% 5.46/5.71 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.46/5.71 = ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1_nat
% 5.46/5.71 thf(fact_8049_sum__diff1__nat,axiom,
% 5.46/5.71 ! [A: int,A2: set_int,F: int > nat] :
% 5.46/5.71 ( ( ( member_int @ A @ A2 )
% 5.46/5.71 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.46/5.71 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_int @ A @ A2 )
% 5.46/5.71 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.46/5.71 = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1_nat
% 5.46/5.71 thf(fact_8050_sum__diff1__nat,axiom,
% 5.46/5.71 ! [A: real,A2: set_real,F: real > nat] :
% 5.46/5.71 ( ( ( member_real @ A @ A2 )
% 5.46/5.71 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.46/5.71 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_real @ A @ A2 )
% 5.46/5.71 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.46/5.71 = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1_nat
% 5.46/5.71 thf(fact_8051_sum__diff1__nat,axiom,
% 5.46/5.71 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.46/5.71 ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 5.46/5.71 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 5.46/5.71 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 5.46/5.71 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 5.46/5.71 = ( groups977919841031483927at_nat @ F @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1_nat
% 5.46/5.71 thf(fact_8052_sum__diff1__nat,axiom,
% 5.46/5.71 ! [A: nat,A2: set_nat,F: nat > nat] :
% 5.46/5.71 ( ( ( member_nat @ A @ A2 )
% 5.46/5.71 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.46/5.71 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_nat @ A @ A2 )
% 5.46/5.71 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.46/5.71 = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1_nat
% 5.46/5.71 thf(fact_8053_simp__from__to,axiom,
% 5.46/5.71 ( set_or1266510415728281911st_int
% 5.46/5.71 = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % simp_from_to
% 5.46/5.71 thf(fact_8054_cos__expansion__lemma,axiom,
% 5.46/5.71 ! [X2: real,M: nat] :
% 5.46/5.71 ( ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_expansion_lemma
% 5.46/5.71 thf(fact_8055_sin__gt__zero__02,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.71 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_gt_zero_02
% 5.46/5.71 thf(fact_8056_cos__two__less__zero,axiom,
% 5.46/5.71 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.46/5.71
% 5.46/5.71 % cos_two_less_zero
% 5.46/5.71 thf(fact_8057_cos__is__zero,axiom,
% 5.46/5.71 ? [X3: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.71 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.71 & ( ( cos_real @ X3 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 & ! [Y4: real] :
% 5.46/5.71 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.46/5.71 & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.71 & ( ( cos_real @ Y4 )
% 5.46/5.71 = zero_zero_real ) )
% 5.46/5.71 => ( Y4 = X3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_is_zero
% 5.46/5.71 thf(fact_8058_cos__two__le__zero,axiom,
% 5.46/5.71 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.46/5.71
% 5.46/5.71 % cos_two_le_zero
% 5.46/5.71 thf(fact_8059_cos__monotone__minus__pi__0,axiom,
% 5.46/5.71 ! [Y2: real,X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 5.46/5.71 => ( ( ord_less_real @ Y2 @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.71 => ( ord_less_real @ ( cos_real @ Y2 ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_monotone_minus_pi_0
% 5.46/5.71 thf(fact_8060_cos__total,axiom,
% 5.46/5.71 ! [Y2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.71 => ? [X3: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.71 & ( ord_less_eq_real @ X3 @ pi )
% 5.46/5.71 & ( ( cos_real @ X3 )
% 5.46/5.71 = Y2 )
% 5.46/5.71 & ! [Y4: real] :
% 5.46/5.71 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.46/5.71 & ( ord_less_eq_real @ Y4 @ pi )
% 5.46/5.71 & ( ( cos_real @ Y4 )
% 5.46/5.71 = Y2 ) )
% 5.46/5.71 => ( Y4 = X3 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_total
% 5.46/5.71 thf(fact_8061_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,X2: vEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8062_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_complex,G: complex > real,X2: complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8063_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > rat,X2: vEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8064_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_complex,G: complex > rat,X2: complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8065_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > nat,X2: vEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8066_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_complex,G: complex > nat,X2: complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8067_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > int,X2: vEBT_VEBT] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( groups769130701875090982BT_int @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_int @ ( G @ X2 ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8068_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_complex,G: complex > int,X2: complex] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_int @ ( G @ X2 ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8069_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_int,G: int > real,X2: int] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8070_sum_Oinsert__remove,axiom,
% 5.46/5.71 ! [A2: set_int,G: int > rat,X2: int] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.insert_remove
% 5.46/5.71 thf(fact_8071_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups2240296850493347238T_real @ G @ A2 )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8072_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8073_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups136491112297645522BT_rat @ G @ A2 )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8074_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,G: complex > rat] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8075_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups771621172384141258BT_nat @ G @ A2 )
% 5.46/5.71 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8076_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,G: complex > nat] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.46/5.71 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8077_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > int] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.71 => ( ( groups769130701875090982BT_int @ G @ A2 )
% 5.46/5.71 = ( plus_plus_int @ ( G @ X2 ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8078_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_complex,X2: complex,G: complex > int] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( member_complex @ X2 @ A2 )
% 5.46/5.71 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.46/5.71 = ( plus_plus_int @ ( G @ X2 ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8079_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_int,X2: int,G: int > real] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.46/5.71 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8080_sum_Oremove,axiom,
% 5.46/5.71 ! [A2: set_int,X2: int,G: int > rat] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( member_int @ X2 @ A2 )
% 5.46/5.71 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.46/5.71 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.remove
% 5.46/5.71 thf(fact_8081_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 5.46/5.71 => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 = ( minus_minus_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 5.46/5.71 => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 = ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8082_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_complex,A: complex,F: complex > rat] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( ( member_complex @ A @ A2 )
% 5.46/5.71 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.46/5.71 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ A @ A2 )
% 5.46/5.71 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.46/5.71 = ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8083_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_int,A: int,F: int > rat] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( ( member_int @ A @ A2 )
% 5.46/5.71 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.46/5.71 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_int @ A @ A2 )
% 5.46/5.71 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.46/5.71 = ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8084_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_real,A: real,F: real > rat] :
% 5.46/5.71 ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ( ( member_real @ A @ A2 )
% 5.46/5.71 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.46/5.71 = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_real @ A @ A2 )
% 5.46/5.71 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.46/5.71 = ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8085_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > int] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 5.46/5.71 => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 = ( minus_minus_int @ ( groups769130701875090982BT_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 5.46/5.71 => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 = ( groups769130701875090982BT_int @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8086_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_complex,A: complex,F: complex > int] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ( ( member_complex @ A @ A2 )
% 5.46/5.71 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.46/5.71 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ A @ A2 )
% 5.46/5.71 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.46/5.71 = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8087_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_real,A: real,F: real > int] :
% 5.46/5.71 ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ( ( member_real @ A @ A2 )
% 5.46/5.71 => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.46/5.71 = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_real @ A @ A2 )
% 5.46/5.71 => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.46/5.71 = ( groups1932886352136224148al_int @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8088_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_nat,A: nat,F: nat > rat] :
% 5.46/5.71 ( ( finite_finite_nat @ A2 )
% 5.46/5.71 => ( ( ( member_nat @ A @ A2 )
% 5.46/5.71 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.46/5.71 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_nat @ A @ A2 )
% 5.46/5.71 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.46/5.71 = ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8089_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_nat,A: nat,F: nat > int] :
% 5.46/5.71 ( ( finite_finite_nat @ A2 )
% 5.46/5.71 => ( ( ( member_nat @ A @ A2 )
% 5.46/5.71 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.46/5.71 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_nat @ A @ A2 )
% 5.46/5.71 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.46/5.71 = ( groups3539618377306564664at_int @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8090_sum__diff1,axiom,
% 5.46/5.71 ! [A2: set_int,A: int,F: int > int] :
% 5.46/5.71 ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ( ( member_int @ A @ A2 )
% 5.46/5.71 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.46/5.71 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.46/5.71 & ( ~ ( member_int @ A @ A2 )
% 5.46/5.71 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.46/5.71 = ( groups4538972089207619220nt_int @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum_diff1
% 5.46/5.71 thf(fact_8091_sincos__total__pi__half,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.71 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 => ? [T5: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.46/5.71 & ( ord_less_eq_real @ T5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( cos_real @ T5 ) )
% 5.46/5.71 & ( Y2
% 5.46/5.71 = ( sin_real @ T5 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sincos_total_pi_half
% 5.46/5.71 thf(fact_8092_sincos__total__2pi__le,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 => ? [T5: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.46/5.71 & ( ord_less_eq_real @ T5 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( cos_real @ T5 ) )
% 5.46/5.71 & ( Y2
% 5.46/5.71 = ( sin_real @ T5 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sincos_total_2pi_le
% 5.46/5.71 thf(fact_8093_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 5.46/5.71 => ( ( groups2240296850493347238T_real
% 5.46/5.71 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 5.46/5.71 => ( ( groups2240296850493347238T_real
% 5.46/5.71 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8094_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.71 => ( ( ( member_complex @ A @ S2 )
% 5.46/5.71 => ( ( groups5808333547571424918x_real
% 5.46/5.71 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ A @ S2 )
% 5.46/5.71 => ( ( groups5808333547571424918x_real
% 5.46/5.71 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8095_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 5.46/5.71 => ( ( groups136491112297645522BT_rat
% 5.46/5.71 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 5.46/5.71 => ( ( groups136491112297645522BT_rat
% 5.46/5.71 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8096_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.71 => ( ( ( member_complex @ A @ S2 )
% 5.46/5.71 => ( ( groups5058264527183730370ex_rat
% 5.46/5.71 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ A @ S2 )
% 5.46/5.71 => ( ( groups5058264527183730370ex_rat
% 5.46/5.71 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8097_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C: vEBT_VEBT > nat] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 5.46/5.71 => ( ( groups771621172384141258BT_nat
% 5.46/5.71 @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 5.46/5.71 => ( ( groups771621172384141258BT_nat
% 5.46/5.71 @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8098_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.71 => ( ( ( member_complex @ A @ S2 )
% 5.46/5.71 => ( ( groups5693394587270226106ex_nat
% 5.46/5.71 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ A @ S2 )
% 5.46/5.71 => ( ( groups5693394587270226106ex_nat
% 5.46/5.71 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8099_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > int,C: vEBT_VEBT > int] :
% 5.46/5.71 ( ( finite5795047828879050333T_VEBT @ S2 )
% 5.46/5.71 => ( ( ( member_VEBT_VEBT @ A @ S2 )
% 5.46/5.71 => ( ( groups769130701875090982BT_int
% 5.46/5.71 @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_int @ ( B @ A ) @ ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_VEBT_VEBT @ A @ S2 )
% 5.46/5.71 => ( ( groups769130701875090982BT_int
% 5.46/5.71 @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8100_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_complex,A: complex,B: complex > int,C: complex > int] :
% 5.46/5.71 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.71 => ( ( ( member_complex @ A @ S2 )
% 5.46/5.71 => ( ( groups5690904116761175830ex_int
% 5.46/5.71 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_complex @ A @ S2 )
% 5.46/5.71 => ( ( groups5690904116761175830ex_int
% 5.46/5.71 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8101_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 5.46/5.71 ( ( finite_finite_int @ S2 )
% 5.46/5.71 => ( ( ( member_int @ A @ S2 )
% 5.46/5.71 => ( ( groups8778361861064173332t_real
% 5.46/5.71 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_real @ ( B @ A ) @ ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_int @ A @ S2 )
% 5.46/5.71 => ( ( groups8778361861064173332t_real
% 5.46/5.71 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8102_sum_Odelta__remove,axiom,
% 5.46/5.71 ! [S2: set_int,A: int,B: int > rat,C: int > rat] :
% 5.46/5.71 ( ( finite_finite_int @ S2 )
% 5.46/5.71 => ( ( ( member_int @ A @ S2 )
% 5.46/5.71 => ( ( groups3906332499630173760nt_rat
% 5.46/5.71 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( member_int @ A @ S2 )
% 5.46/5.71 => ( ( groups3906332499630173760nt_rat
% 5.46/5.71 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.46/5.71 @ S2 )
% 5.46/5.71 = ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sum.delta_remove
% 5.46/5.71 thf(fact_8103_square__fact__le__2__fact,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % square_fact_le_2_fact
% 5.46/5.71 thf(fact_8104_sincos__total__2pi,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 => ~ ! [T5: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.46/5.71 => ( ( ord_less_real @ T5 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.71 => ( ( X2
% 5.46/5.71 = ( cos_real @ T5 ) )
% 5.46/5.71 => ( Y2
% 5.46/5.71 != ( sin_real @ T5 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sincos_total_2pi
% 5.46/5.71 thf(fact_8105_sin__pi__divide__n__ge__0,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_pi_divide_n_ge_0
% 5.46/5.71 thf(fact_8106_member__le__sum,axiom,
% 5.46/5.71 ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ I @ A2 )
% 5.46/5.71 => ( ! [X3: vEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( F @ I ) @ ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8107_member__le__sum,axiom,
% 5.46/5.71 ! [I: complex,A2: set_complex,F: complex > real] :
% 5.46/5.71 ( ( member_complex @ I @ A2 )
% 5.46/5.71 => ( ! [X3: complex] :
% 5.46/5.71 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8108_member__le__sum,axiom,
% 5.46/5.71 ! [I: int,A2: set_int,F: int > real] :
% 5.46/5.71 ( ( member_int @ I @ A2 )
% 5.46/5.71 => ( ! [X3: int] :
% 5.46/5.71 ( ( member_int @ X3 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8109_member__le__sum,axiom,
% 5.46/5.71 ! [I: real,A2: set_real,F: real > real] :
% 5.46/5.71 ( ( member_real @ I @ A2 )
% 5.46/5.71 => ( ! [X3: real] :
% 5.46/5.71 ( ( member_real @ X3 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8110_member__le__sum,axiom,
% 5.46/5.71 ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ I @ A2 )
% 5.46/5.71 => ( ! [X3: vEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8111_member__le__sum,axiom,
% 5.46/5.71 ! [I: complex,A2: set_complex,F: complex > rat] :
% 5.46/5.71 ( ( member_complex @ I @ A2 )
% 5.46/5.71 => ( ! [X3: complex] :
% 5.46/5.71 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.46/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8112_member__le__sum,axiom,
% 5.46/5.71 ! [I: int,A2: set_int,F: int > rat] :
% 5.46/5.71 ( ( member_int @ I @ A2 )
% 5.46/5.71 => ( ! [X3: int] :
% 5.46/5.71 ( ( member_int @ X3 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.46/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite_finite_int @ A2 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8113_member__le__sum,axiom,
% 5.46/5.71 ! [I: real,A2: set_real,F: real > rat] :
% 5.46/5.71 ( ( member_real @ I @ A2 )
% 5.46/5.71 => ( ! [X3: real] :
% 5.46/5.71 ( ( member_real @ X3 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.46/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite_finite_real @ A2 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8114_member__le__sum,axiom,
% 5.46/5.71 ! [I: nat,A2: set_nat,F: nat > rat] :
% 5.46/5.71 ( ( member_nat @ I @ A2 )
% 5.46/5.71 => ( ! [X3: nat] :
% 5.46/5.71 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 5.46/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite_finite_nat @ A2 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8115_member__le__sum,axiom,
% 5.46/5.71 ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ I @ A2 )
% 5.46/5.71 => ( ! [X3: vEBT_VEBT] :
% 5.46/5.71 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.46/5.71 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.71 => ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.71 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % member_le_sum
% 5.46/5.71 thf(fact_8116_fact__num__eq__if,axiom,
% 5.46/5.71 ( semiri1406184849735516958ct_int
% 5.46/5.71 = ( ^ [M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_num_eq_if
% 5.46/5.71 thf(fact_8117_fact__num__eq__if,axiom,
% 5.46/5.71 ( semiri5044797733671781792omplex
% 5.46/5.71 = ( ^ [M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M3 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_num_eq_if
% 5.46/5.71 thf(fact_8118_fact__num__eq__if,axiom,
% 5.46/5.71 ( semiri773545260158071498ct_rat
% 5.46/5.71 = ( ^ [M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M3 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_num_eq_if
% 5.46/5.71 thf(fact_8119_fact__num__eq__if,axiom,
% 5.46/5.71 ( semiri2265585572941072030t_real
% 5.46/5.71 = ( ^ [M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_num_eq_if
% 5.46/5.71 thf(fact_8120_fact__num__eq__if,axiom,
% 5.46/5.71 ( semiri1408675320244567234ct_nat
% 5.46/5.71 = ( ^ [M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M3 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_num_eq_if
% 5.46/5.71 thf(fact_8121_fact__reduce,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ( ( semiri1406184849735516958ct_int @ N )
% 5.46/5.71 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_reduce
% 5.46/5.71 thf(fact_8122_fact__reduce,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ( ( semiri5044797733671781792omplex @ N )
% 5.46/5.71 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_reduce
% 5.46/5.71 thf(fact_8123_fact__reduce,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ( ( semiri773545260158071498ct_rat @ N )
% 5.46/5.71 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_reduce
% 5.46/5.71 thf(fact_8124_fact__reduce,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ( ( semiri2265585572941072030t_real @ N )
% 5.46/5.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_reduce
% 5.46/5.71 thf(fact_8125_fact__reduce,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.46/5.71 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_reduce
% 5.46/5.71 thf(fact_8126_cos__times__cos,axiom,
% 5.46/5.71 ! [W: complex,Z: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.46/5.71 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_times_cos
% 5.46/5.71 thf(fact_8127_cos__times__cos,axiom,
% 5.46/5.71 ! [W: real,Z: real] :
% 5.46/5.71 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.46/5.71 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_times_cos
% 5.46/5.71 thf(fact_8128_cos__plus__cos,axiom,
% 5.46/5.71 ! [W: complex,Z: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.46/5.71 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_plus_cos
% 5.46/5.71 thf(fact_8129_cos__plus__cos,axiom,
% 5.46/5.71 ! [W: real,Z: real] :
% 5.46/5.71 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.46/5.71 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_plus_cos
% 5.46/5.71 thf(fact_8130_sin__gt__zero2,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_gt_zero2
% 5.46/5.71 thf(fact_8131_sin__lt__zero,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ pi @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.71 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_lt_zero
% 5.46/5.71 thf(fact_8132_cos__double__less__one,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.71 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_double_less_one
% 5.46/5.71 thf(fact_8133_sin__30,axiom,
% 5.46/5.71 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.46/5.71 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_30
% 5.46/5.71 thf(fact_8134_cos__gt__zero,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_gt_zero
% 5.46/5.71 thf(fact_8135_sin__monotone__2pi__le,axiom,
% 5.46/5.71 ! [Y2: real,X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( sin_real @ Y2 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_monotone_2pi_le
% 5.46/5.71 thf(fact_8136_sin__mono__le__eq,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( sin_real @ X2 ) @ ( sin_real @ Y2 ) )
% 5.46/5.71 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_mono_le_eq
% 5.46/5.71 thf(fact_8137_sin__inj__pi,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ( ( sin_real @ X2 )
% 5.46/5.71 = ( sin_real @ Y2 ) )
% 5.46/5.71 => ( X2 = Y2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_inj_pi
% 5.46/5.71 thf(fact_8138_cos__60,axiom,
% 5.46/5.71 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.46/5.71 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_60
% 5.46/5.71 thf(fact_8139_cos__one__2pi__int,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( cos_real @ X2 )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 = ( ? [X: int] :
% 5.46/5.71 ( X2
% 5.46/5.71 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_one_2pi_int
% 5.46/5.71 thf(fact_8140_cos__double__cos,axiom,
% 5.46/5.71 ! [W: complex] :
% 5.46/5.71 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.46/5.71 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_double_cos
% 5.46/5.71 thf(fact_8141_cos__double__cos,axiom,
% 5.46/5.71 ! [W: real] :
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.46/5.71 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_double_cos
% 5.46/5.71 thf(fact_8142_cos__treble__cos,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X2 ) )
% 5.46/5.71 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_treble_cos
% 5.46/5.71 thf(fact_8143_cos__treble__cos,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X2 ) )
% 5.46/5.71 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_treble_cos
% 5.46/5.71 thf(fact_8144_Maclaurin__cos__expansion,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ? [T5: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X2 ) )
% 5.46/5.71 & ( ( cos_real @ X2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T5 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_cos_expansion
% 5.46/5.71 thf(fact_8145_sin__le__zero,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ pi @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.71 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_le_zero
% 5.46/5.71 thf(fact_8146_sin__less__zero,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.71 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_less_zero
% 5.46/5.71 thf(fact_8147_sin__monotone__2pi,axiom,
% 5.46/5.71 ! [Y2: real,X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.46/5.71 => ( ( ord_less_real @ Y2 @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_real @ ( sin_real @ Y2 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_monotone_2pi
% 5.46/5.71 thf(fact_8148_sin__mono__less__eq,axiom,
% 5.46/5.71 ! [X2: real,Y2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ( ord_less_real @ ( sin_real @ X2 ) @ ( sin_real @ Y2 ) )
% 5.46/5.71 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_mono_less_eq
% 5.46/5.71 thf(fact_8149_sin__total,axiom,
% 5.46/5.71 ! [Y2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.71 => ? [X3: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.46/5.71 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 & ( ( sin_real @ X3 )
% 5.46/5.71 = Y2 )
% 5.46/5.71 & ! [Y4: real] :
% 5.46/5.71 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.46/5.71 & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 & ( ( sin_real @ Y4 )
% 5.46/5.71 = Y2 ) )
% 5.46/5.71 => ( Y4 = X3 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_total
% 5.46/5.71 thf(fact_8150_cos__gt__zero__pi,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_gt_zero_pi
% 5.46/5.71 thf(fact_8151_cos__ge__zero,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_ge_zero
% 5.46/5.71 thf(fact_8152_cos__one__2pi,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( cos_real @ X2 )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 = ( ? [X: nat] :
% 5.46/5.71 ( X2
% 5.46/5.71 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.46/5.71 | ? [X: nat] :
% 5.46/5.71 ( X2
% 5.46/5.71 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_one_2pi
% 5.46/5.71 thf(fact_8153_Maclaurin__zero,axiom,
% 5.46/5.71 ! [X2: real,N: nat,Diff: nat > complex > real] :
% 5.46/5.71 ( ( X2 = zero_zero_real )
% 5.46/5.71 => ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_zero
% 5.46/5.71 thf(fact_8154_Maclaurin__zero,axiom,
% 5.46/5.71 ! [X2: real,N: nat,Diff: nat > real > real] :
% 5.46/5.71 ( ( X2 = zero_zero_real )
% 5.46/5.71 => ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_zero
% 5.46/5.71 thf(fact_8155_Maclaurin__zero,axiom,
% 5.46/5.71 ! [X2: real,N: nat,Diff: nat > rat > real] :
% 5.46/5.71 ( ( X2 = zero_zero_real )
% 5.46/5.71 => ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_zero
% 5.46/5.71 thf(fact_8156_Maclaurin__zero,axiom,
% 5.46/5.71 ! [X2: real,N: nat,Diff: nat > nat > real] :
% 5.46/5.71 ( ( X2 = zero_zero_real )
% 5.46/5.71 => ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_zero
% 5.46/5.71 thf(fact_8157_Maclaurin__zero,axiom,
% 5.46/5.71 ! [X2: real,N: nat,Diff: nat > int > real] :
% 5.46/5.71 ( ( X2 = zero_zero_real )
% 5.46/5.71 => ( ( N != zero_zero_nat )
% 5.46/5.71 => ( ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_zero
% 5.46/5.71 thf(fact_8158_Maclaurin__lemma,axiom,
% 5.46/5.71 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.46/5.71 => ? [B9: real] :
% 5.46/5.71 ( ( F @ H2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ B9 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_lemma
% 5.46/5.71 thf(fact_8159_Maclaurin__minus__cos__expansion,axiom,
% 5.46/5.71 ! [N: nat,X2: real] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.71 => ? [T5: real] :
% 5.46/5.71 ( ( ord_less_real @ X2 @ T5 )
% 5.46/5.71 & ( ord_less_real @ T5 @ zero_zero_real )
% 5.46/5.71 & ( ( cos_real @ X2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T5 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_minus_cos_expansion
% 5.46/5.71 thf(fact_8160_Maclaurin__cos__expansion2,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ? [T5: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.46/5.71 & ( ord_less_real @ T5 @ X2 )
% 5.46/5.71 & ( ( cos_real @ X2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T5 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_cos_expansion2
% 5.46/5.71 thf(fact_8161_sin__pi__divide__n__gt__0,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_pi_divide_n_gt_0
% 5.46/5.71 thf(fact_8162_Maclaurin__exp__le,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ? [T5: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X2 ) )
% 5.46/5.71 & ( ( exp_real @ X2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_exp_le
% 5.46/5.71 thf(fact_8163_sin__zero__iff__int,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( sin_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 = ( ? [I4: int] :
% 5.46/5.71 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_zero_iff_int
% 5.46/5.71 thf(fact_8164_cos__zero__iff__int,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( cos_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 = ( ? [I4: int] :
% 5.46/5.71 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_zero_iff_int
% 5.46/5.71 thf(fact_8165_sin__zero__lemma,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ( sin_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 => ? [N3: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_zero_lemma
% 5.46/5.71 thf(fact_8166_sin__zero__iff,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( sin_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 = ( ? [N2: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.71 | ? [N2: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_zero_iff
% 5.46/5.71 thf(fact_8167_cos__coeff__def,axiom,
% 5.46/5.71 ( cos_coeff
% 5.46/5.71 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ zero_zero_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_coeff_def
% 5.46/5.71 thf(fact_8168_cos__zero__lemma,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ( ( ( cos_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 => ? [N3: nat] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_zero_lemma
% 5.46/5.71 thf(fact_8169_cos__zero__iff,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( cos_real @ X2 )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 = ( ? [N2: nat] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.71 | ? [N2: nat] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.46/5.71 & ( X2
% 5.46/5.71 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_zero_iff
% 5.46/5.71 thf(fact_8170_Maclaurin__sin__expansion3,axiom,
% 5.46/5.71 ! [N: nat,X2: real] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.71 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ? [T5: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.46/5.71 & ( ord_less_real @ T5 @ X2 )
% 5.46/5.71 & ( ( sin_real @ X2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T5 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_sin_expansion3
% 5.46/5.71 thf(fact_8171_Maclaurin__sin__expansion4,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.71 => ? [T5: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.46/5.71 & ( ord_less_eq_real @ T5 @ X2 )
% 5.46/5.71 & ( ( sin_real @ X2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T5 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_sin_expansion4
% 5.46/5.71 thf(fact_8172_Maclaurin__sin__expansion2,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ? [T5: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X2 ) )
% 5.46/5.71 & ( ( sin_real @ X2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T5 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_sin_expansion2
% 5.46/5.71 thf(fact_8173_Maclaurin__sin__expansion,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ? [T5: real] :
% 5.46/5.71 ( ( sin_real @ X2 )
% 5.46/5.71 = ( plus_plus_real
% 5.46/5.71 @ ( groups6591440286371151544t_real
% 5.46/5.71 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.71 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.71 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T5 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Maclaurin_sin_expansion
% 5.46/5.71 thf(fact_8174_sin__coeff__def,axiom,
% 5.46/5.71 ( sin_coeff
% 5.46/5.71 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_coeff_def
% 5.46/5.71 thf(fact_8175_set__encode__insert,axiom,
% 5.46/5.71 ! [A2: set_nat,N: nat] :
% 5.46/5.71 ( ( finite_finite_nat @ A2 )
% 5.46/5.71 => ( ~ ( member_nat @ N @ A2 )
% 5.46/5.71 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 5.46/5.71 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_encode_insert
% 5.46/5.71 thf(fact_8176_fact__ge__self,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_self
% 5.46/5.71 thf(fact_8177_fact__mono__nat,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_mono_nat
% 5.46/5.71 thf(fact_8178_fact__less__mono__nat,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.71 => ( ( ord_less_nat @ M @ N )
% 5.46/5.71 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_less_mono_nat
% 5.46/5.71 thf(fact_8179_lessThan__Suc,axiom,
% 5.46/5.71 ! [K: nat] :
% 5.46/5.71 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.46/5.71 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % lessThan_Suc
% 5.46/5.71 thf(fact_8180_fact__ge__Suc__0__nat,axiom,
% 5.46/5.71 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_ge_Suc_0_nat
% 5.46/5.71 thf(fact_8181_dvd__fact,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.46/5.71 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dvd_fact
% 5.46/5.71 thf(fact_8182_atLeast0__atMost__Suc,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.46/5.71 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % atLeast0_atMost_Suc
% 5.46/5.71 thf(fact_8183_Icc__eq__insert__lb__nat,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.46/5.71 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Icc_eq_insert_lb_nat
% 5.46/5.71 thf(fact_8184_atLeastAtMostSuc__conv,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.71 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.46/5.71 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % atLeastAtMostSuc_conv
% 5.46/5.71 thf(fact_8185_atLeastAtMost__insertL,axiom,
% 5.46/5.71 ! [M: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.71 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.46/5.71 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % atLeastAtMost_insertL
% 5.46/5.71 thf(fact_8186_lessThan__nat__numeral,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.46/5.71 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % lessThan_nat_numeral
% 5.46/5.71 thf(fact_8187_fact__diff__Suc,axiom,
% 5.46/5.71 ! [N: nat,M: nat] :
% 5.46/5.71 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.46/5.71 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.46/5.71 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_diff_Suc
% 5.46/5.71 thf(fact_8188_fact__div__fact__le__pow,axiom,
% 5.46/5.71 ! [R: nat,N: nat] :
% 5.46/5.71 ( ( ord_less_eq_nat @ R @ N )
% 5.46/5.71 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % fact_div_fact_le_pow
% 5.46/5.71 thf(fact_8189_set__decode__plus__power__2,axiom,
% 5.46/5.71 ! [N: nat,Z: nat] :
% 5.46/5.71 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.46/5.71 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.46/5.71 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % set_decode_plus_power_2
% 5.46/5.71 thf(fact_8190_sin__coeff__Suc,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( sin_coeff @ ( suc @ N ) )
% 5.46/5.71 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_coeff_Suc
% 5.46/5.71 thf(fact_8191_cos__coeff__Suc,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( cos_coeff @ ( suc @ N ) )
% 5.46/5.71 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % cos_coeff_Suc
% 5.46/5.71 thf(fact_8192_tan__double,axiom,
% 5.46/5.71 ! [X2: complex] :
% 5.46/5.71 ( ( ( cos_complex @ X2 )
% 5.46/5.71 != zero_zero_complex )
% 5.46/5.71 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.46/5.71 != zero_zero_complex )
% 5.46/5.71 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.46/5.71 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % tan_double
% 5.46/5.71 thf(fact_8193_tan__double,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( ( cos_real @ X2 )
% 5.46/5.71 != zero_zero_real )
% 5.46/5.71 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.46/5.71 != zero_zero_real )
% 5.46/5.71 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.46/5.71 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X2 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % tan_double
% 5.46/5.71 thf(fact_8194_complex__unimodular__polar,axiom,
% 5.46/5.71 ! [Z: complex] :
% 5.46/5.71 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.46/5.71 = one_one_real )
% 5.46/5.71 => ~ ! [T5: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.46/5.71 => ( ( ord_less_real @ T5 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.71 => ( Z
% 5.46/5.71 != ( complex2 @ ( cos_real @ T5 ) @ ( sin_real @ T5 ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % complex_unimodular_polar
% 5.46/5.71 thf(fact_8195_and__int_Opsimps,axiom,
% 5.46/5.71 ! [K: int,L2: int] :
% 5.46/5.71 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 5.46/5.71 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.71 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.71 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.46/5.71 = ( uminus_uminus_int
% 5.46/5.71 @ ( zero_n2684676970156552555ol_int
% 5.46/5.71 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.46/5.71 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.71 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.71 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.46/5.71 = ( plus_plus_int
% 5.46/5.71 @ ( zero_n2684676970156552555ol_int
% 5.46/5.71 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.46/5.71 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.46/5.71 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % and_int.psimps
% 5.46/5.71 thf(fact_8196_and__int_Opelims,axiom,
% 5.46/5.71 ! [X2: int,Xa2: int,Y2: int] :
% 5.46/5.71 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.46/5.71 = Y2 )
% 5.46/5.71 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) )
% 5.46/5.71 => ~ ( ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.71 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.71 => ( Y2
% 5.46/5.71 = ( uminus_uminus_int
% 5.46/5.71 @ ( zero_n2684676970156552555ol_int
% 5.46/5.71 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.46/5.71 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.46/5.71 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.71 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.71 => ( Y2
% 5.46/5.71 = ( plus_plus_int
% 5.46/5.71 @ ( zero_n2684676970156552555ol_int
% 5.46/5.71 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.46/5.71 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.46/5.71 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.46/5.71 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % and_int.pelims
% 5.46/5.71 thf(fact_8197_sin__paired,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.46/5.71 @ ( sin_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % sin_paired
% 5.46/5.71 thf(fact_8198_tan__periodic__pi,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( tan_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.46/5.71 = ( tan_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % tan_periodic_pi
% 5.46/5.71 thf(fact_8199_tan__npi,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % tan_npi
% 5.46/5.71 thf(fact_8200_tan__periodic__n,axiom,
% 5.46/5.71 ! [X2: real,N: num] :
% 5.46/5.71 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.46/5.71 = ( tan_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % tan_periodic_n
% 5.46/5.71 thf(fact_8201_tan__periodic__nat,axiom,
% 5.46/5.71 ! [X2: real,N: nat] :
% 5.46/5.71 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.46/5.71 = ( tan_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % tan_periodic_nat
% 5.46/5.71 thf(fact_8202_tan__periodic__int,axiom,
% 5.46/5.71 ! [X2: real,I: int] :
% 5.46/5.71 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 5.46/5.71 = ( tan_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % tan_periodic_int
% 5.46/5.71 thf(fact_8203_powser__sums__zero__iff,axiom,
% 5.46/5.71 ! [A: nat > complex,X2: complex] :
% 5.46/5.71 ( ( sums_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.46/5.71 @ X2 )
% 5.46/5.71 = ( ( A @ zero_zero_nat )
% 5.46/5.71 = X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_sums_zero_iff
% 5.46/5.71 thf(fact_8204_powser__sums__zero__iff,axiom,
% 5.46/5.71 ! [A: nat > real,X2: real] :
% 5.46/5.71 ( ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.46/5.71 @ X2 )
% 5.46/5.71 = ( ( A @ zero_zero_nat )
% 5.46/5.71 = X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % powser_sums_zero_iff
% 5.46/5.71 thf(fact_8205_norm__cos__sin,axiom,
% 5.46/5.71 ! [T: real] :
% 5.46/5.71 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % norm_cos_sin
% 5.46/5.71 thf(fact_8206_tan__periodic,axiom,
% 5.46/5.71 ! [X2: real] :
% 5.46/5.71 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.71 = ( tan_real @ X2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % tan_periodic
% 5.46/5.71 thf(fact_8207_complex__diff,axiom,
% 5.46/5.71 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.71 ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 5.46/5.71 = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % complex_diff
% 5.46/5.71 thf(fact_8208_sums__le,axiom,
% 5.46/5.71 ! [F: nat > real,G: nat > real,S: real,T: real] :
% 5.46/5.71 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.46/5.71 => ( ( sums_real @ F @ S )
% 5.46/5.71 => ( ( sums_real @ G @ T )
% 5.46/5.71 => ( ord_less_eq_real @ S @ T ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_le
% 5.46/5.71 thf(fact_8209_sums__le,axiom,
% 5.46/5.71 ! [F: nat > nat,G: nat > nat,S: nat,T: nat] :
% 5.46/5.71 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.46/5.71 => ( ( sums_nat @ F @ S )
% 5.46/5.71 => ( ( sums_nat @ G @ T )
% 5.46/5.71 => ( ord_less_eq_nat @ S @ T ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_le
% 5.46/5.71 thf(fact_8210_sums__le,axiom,
% 5.46/5.71 ! [F: nat > int,G: nat > int,S: int,T: int] :
% 5.46/5.71 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.46/5.71 => ( ( sums_int @ F @ S )
% 5.46/5.71 => ( ( sums_int @ G @ T )
% 5.46/5.71 => ( ord_less_eq_int @ S @ T ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_le
% 5.46/5.71 thf(fact_8211_sums__mult2,axiom,
% 5.46/5.71 ! [F: nat > real,A: real,C: real] :
% 5.46/5.71 ( ( sums_real @ F @ A )
% 5.46/5.71 => ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.46/5.71 @ ( times_times_real @ A @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_mult2
% 5.46/5.71 thf(fact_8212_sums__mult,axiom,
% 5.46/5.71 ! [F: nat > real,A: real,C: real] :
% 5.46/5.71 ( ( sums_real @ F @ A )
% 5.46/5.71 => ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.46/5.71 @ ( times_times_real @ C @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_mult
% 5.46/5.71 thf(fact_8213_sums__add,axiom,
% 5.46/5.71 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.46/5.71 ( ( sums_real @ F @ A )
% 5.46/5.71 => ( ( sums_real @ G @ B )
% 5.46/5.71 => ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.46/5.71 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_add
% 5.46/5.71 thf(fact_8214_sums__add,axiom,
% 5.46/5.71 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.46/5.71 ( ( sums_nat @ F @ A )
% 5.46/5.71 => ( ( sums_nat @ G @ B )
% 5.46/5.71 => ( sums_nat
% 5.46/5.71 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.46/5.71 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_add
% 5.46/5.71 thf(fact_8215_sums__add,axiom,
% 5.46/5.71 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.46/5.71 ( ( sums_int @ F @ A )
% 5.46/5.71 => ( ( sums_int @ G @ B )
% 5.46/5.71 => ( sums_int
% 5.46/5.71 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.46/5.71 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_add
% 5.46/5.71 thf(fact_8216_sums__diff,axiom,
% 5.46/5.71 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.46/5.71 ( ( sums_real @ F @ A )
% 5.46/5.71 => ( ( sums_real @ G @ B )
% 5.46/5.71 => ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.46/5.71 @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_diff
% 5.46/5.71 thf(fact_8217_sums__divide,axiom,
% 5.46/5.71 ! [F: nat > complex,A: complex,C: complex] :
% 5.46/5.71 ( ( sums_complex @ F @ A )
% 5.46/5.71 => ( sums_complex
% 5.46/5.71 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C )
% 5.46/5.71 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_divide
% 5.46/5.71 thf(fact_8218_sums__divide,axiom,
% 5.46/5.71 ! [F: nat > real,A: real,C: real] :
% 5.46/5.71 ( ( sums_real @ F @ A )
% 5.46/5.71 => ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C )
% 5.46/5.71 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_divide
% 5.46/5.71 thf(fact_8219_sums__mult2__iff,axiom,
% 5.46/5.71 ! [C: complex,F: nat > complex,D2: complex] :
% 5.46/5.71 ( ( C != zero_zero_complex )
% 5.46/5.71 => ( ( sums_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 5.46/5.71 @ ( times_times_complex @ D2 @ C ) )
% 5.46/5.71 = ( sums_complex @ F @ D2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_mult2_iff
% 5.46/5.71 thf(fact_8220_sums__mult2__iff,axiom,
% 5.46/5.71 ! [C: real,F: nat > real,D2: real] :
% 5.46/5.71 ( ( C != zero_zero_real )
% 5.46/5.71 => ( ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.46/5.71 @ ( times_times_real @ D2 @ C ) )
% 5.46/5.71 = ( sums_real @ F @ D2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_mult2_iff
% 5.46/5.71 thf(fact_8221_sums__mult__iff,axiom,
% 5.46/5.71 ! [C: complex,F: nat > complex,D2: complex] :
% 5.46/5.71 ( ( C != zero_zero_complex )
% 5.46/5.71 => ( ( sums_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.46/5.71 @ ( times_times_complex @ C @ D2 ) )
% 5.46/5.71 = ( sums_complex @ F @ D2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_mult_iff
% 5.46/5.71 thf(fact_8222_sums__mult__iff,axiom,
% 5.46/5.71 ! [C: real,F: nat > real,D2: real] :
% 5.46/5.71 ( ( C != zero_zero_real )
% 5.46/5.71 => ( ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.46/5.71 @ ( times_times_real @ C @ D2 ) )
% 5.46/5.71 = ( sums_real @ F @ D2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_mult_iff
% 5.46/5.71 thf(fact_8223_Complex__eq__numeral,axiom,
% 5.46/5.71 ! [A: real,B: real,W: num] :
% 5.46/5.71 ( ( ( complex2 @ A @ B )
% 5.46/5.71 = ( numera6690914467698888265omplex @ W ) )
% 5.46/5.71 = ( ( A
% 5.46/5.71 = ( numeral_numeral_real @ W ) )
% 5.46/5.71 & ( B = zero_zero_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Complex_eq_numeral
% 5.46/5.71 thf(fact_8224_complex__add,axiom,
% 5.46/5.71 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.71 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 5.46/5.71 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % complex_add
% 5.46/5.71 thf(fact_8225_sums__mult__D,axiom,
% 5.46/5.71 ! [C: complex,F: nat > complex,A: complex] :
% 5.46/5.71 ( ( sums_complex
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.46/5.71 @ A )
% 5.46/5.71 => ( ( C != zero_zero_complex )
% 5.46/5.71 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_mult_D
% 5.46/5.71 thf(fact_8226_sums__mult__D,axiom,
% 5.46/5.71 ! [C: real,F: nat > real,A: real] :
% 5.46/5.71 ( ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.46/5.71 @ A )
% 5.46/5.71 => ( ( C != zero_zero_real )
% 5.46/5.71 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_mult_D
% 5.46/5.71 thf(fact_8227_sums__Suc__imp,axiom,
% 5.46/5.71 ! [F: nat > complex,S: complex] :
% 5.46/5.71 ( ( ( F @ zero_zero_nat )
% 5.46/5.71 = zero_zero_complex )
% 5.46/5.71 => ( ( sums_complex
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.46/5.71 @ S )
% 5.46/5.71 => ( sums_complex @ F @ S ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_Suc_imp
% 5.46/5.71 thf(fact_8228_sums__Suc__imp,axiom,
% 5.46/5.71 ! [F: nat > real,S: real] :
% 5.46/5.71 ( ( ( F @ zero_zero_nat )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 => ( ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.46/5.71 @ S )
% 5.46/5.71 => ( sums_real @ F @ S ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_Suc_imp
% 5.46/5.71 thf(fact_8229_sums__Suc,axiom,
% 5.46/5.71 ! [F: nat > real,L2: real] :
% 5.46/5.71 ( ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.46/5.71 @ L2 )
% 5.46/5.71 => ( sums_real @ F @ ( plus_plus_real @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_Suc
% 5.46/5.71 thf(fact_8230_sums__Suc,axiom,
% 5.46/5.71 ! [F: nat > nat,L2: nat] :
% 5.46/5.71 ( ( sums_nat
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.46/5.71 @ L2 )
% 5.46/5.71 => ( sums_nat @ F @ ( plus_plus_nat @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_Suc
% 5.46/5.71 thf(fact_8231_sums__Suc,axiom,
% 5.46/5.71 ! [F: nat > int,L2: int] :
% 5.46/5.71 ( ( sums_int
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.46/5.71 @ L2 )
% 5.46/5.71 => ( sums_int @ F @ ( plus_plus_int @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_Suc
% 5.46/5.71 thf(fact_8232_sums__Suc__iff,axiom,
% 5.46/5.71 ! [F: nat > real,S: real] :
% 5.46/5.71 ( ( sums_real
% 5.46/5.71 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.46/5.71 @ S )
% 5.46/5.71 = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_Suc_iff
% 5.46/5.71 thf(fact_8233_sums__zero__iff__shift,axiom,
% 5.46/5.71 ! [N: nat,F: nat > complex,S: complex] :
% 5.46/5.71 ( ! [I2: nat] :
% 5.46/5.71 ( ( ord_less_nat @ I2 @ N )
% 5.46/5.71 => ( ( F @ I2 )
% 5.46/5.71 = zero_zero_complex ) )
% 5.46/5.71 => ( ( sums_complex
% 5.46/5.71 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.46/5.71 @ S )
% 5.46/5.71 = ( sums_complex @ F @ S ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_zero_iff_shift
% 5.46/5.71 thf(fact_8234_sums__zero__iff__shift,axiom,
% 5.46/5.71 ! [N: nat,F: nat > real,S: real] :
% 5.46/5.71 ( ! [I2: nat] :
% 5.46/5.71 ( ( ord_less_nat @ I2 @ N )
% 5.46/5.71 => ( ( F @ I2 )
% 5.46/5.71 = zero_zero_real ) )
% 5.46/5.71 => ( ( sums_real
% 5.46/5.71 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.46/5.71 @ S )
% 5.46/5.71 = ( sums_real @ F @ S ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % sums_zero_iff_shift
% 5.46/5.71 thf(fact_8235_Complex__eq__neg__numeral,axiom,
% 5.46/5.71 ! [A: real,B: real,W: num] :
% 5.46/5.71 ( ( ( complex2 @ A @ B )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.71 = ( ( A
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.71 & ( B = zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Complex_eq_neg_numeral
% 5.46/5.72 thf(fact_8236_complex__mult,axiom,
% 5.46/5.72 ! [A: real,B: real,C: real,D2: real] :
% 5.46/5.72 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 5.46/5.72 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D2 ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % complex_mult
% 5.46/5.72 thf(fact_8237_one__complex_Ocode,axiom,
% 5.46/5.72 ( one_one_complex
% 5.46/5.72 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_complex.code
% 5.46/5.72 thf(fact_8238_Complex__eq__1,axiom,
% 5.46/5.72 ! [A: real,B: real] :
% 5.46/5.72 ( ( ( complex2 @ A @ B )
% 5.46/5.72 = one_one_complex )
% 5.46/5.72 = ( ( A = one_one_real )
% 5.46/5.72 & ( B = zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Complex_eq_1
% 5.46/5.72 thf(fact_8239_powser__sums__if,axiom,
% 5.46/5.72 ! [M: nat,Z: complex] :
% 5.46/5.72 ( sums_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( if_complex @ ( N2 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N2 ) )
% 5.46/5.72 @ ( power_power_complex @ Z @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % powser_sums_if
% 5.46/5.72 thf(fact_8240_powser__sums__if,axiom,
% 5.46/5.72 ! [M: nat,Z: real] :
% 5.46/5.72 ( sums_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( if_real @ ( N2 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N2 ) )
% 5.46/5.72 @ ( power_power_real @ Z @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % powser_sums_if
% 5.46/5.72 thf(fact_8241_powser__sums__if,axiom,
% 5.46/5.72 ! [M: nat,Z: int] :
% 5.46/5.72 ( sums_int
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_int @ ( if_int @ ( N2 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N2 ) )
% 5.46/5.72 @ ( power_power_int @ Z @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % powser_sums_if
% 5.46/5.72 thf(fact_8242_powser__sums__zero,axiom,
% 5.46/5.72 ! [A: nat > complex] :
% 5.46/5.72 ( sums_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.46/5.72 @ ( A @ zero_zero_nat ) ) ).
% 5.46/5.72
% 5.46/5.72 % powser_sums_zero
% 5.46/5.72 thf(fact_8243_powser__sums__zero,axiom,
% 5.46/5.72 ! [A: nat > real] :
% 5.46/5.72 ( sums_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.46/5.72 @ ( A @ zero_zero_nat ) ) ).
% 5.46/5.72
% 5.46/5.72 % powser_sums_zero
% 5.46/5.72 thf(fact_8244_tan__def,axiom,
% 5.46/5.72 ( tan_complex
% 5.46/5.72 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X ) @ ( cos_complex @ X ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_def
% 5.46/5.72 thf(fact_8245_tan__def,axiom,
% 5.46/5.72 ( tan_real
% 5.46/5.72 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ X ) @ ( cos_real @ X ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_def
% 5.46/5.72 thf(fact_8246_sums__iff__shift,axiom,
% 5.46/5.72 ! [F: nat > real,N: nat,S: real] :
% 5.46/5.72 ( ( sums_real
% 5.46/5.72 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.46/5.72 @ S )
% 5.46/5.72 = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sums_iff_shift
% 5.46/5.72 thf(fact_8247_sums__split__initial__segment,axiom,
% 5.46/5.72 ! [F: nat > real,S: real,N: nat] :
% 5.46/5.72 ( ( sums_real @ F @ S )
% 5.46/5.72 => ( sums_real
% 5.46/5.72 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.46/5.72 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sums_split_initial_segment
% 5.46/5.72 thf(fact_8248_sums__iff__shift_H,axiom,
% 5.46/5.72 ! [F: nat > real,N: nat,S: real] :
% 5.46/5.72 ( ( sums_real
% 5.46/5.72 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.46/5.72 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.46/5.72 = ( sums_real @ F @ S ) ) ).
% 5.46/5.72
% 5.46/5.72 % sums_iff_shift'
% 5.46/5.72 thf(fact_8249_sums__If__finite__set_H,axiom,
% 5.46/5.72 ! [G: nat > real,S2: real,A2: set_nat,S4: real,F: nat > real] :
% 5.46/5.72 ( ( sums_real @ G @ S2 )
% 5.46/5.72 => ( ( finite_finite_nat @ A2 )
% 5.46/5.72 => ( ( S4
% 5.46/5.72 = ( plus_plus_real @ S2
% 5.46/5.72 @ ( groups6591440286371151544t_real
% 5.46/5.72 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.46/5.72 @ A2 ) ) )
% 5.46/5.72 => ( sums_real
% 5.46/5.72 @ ^ [N2: nat] : ( if_real @ ( member_nat @ N2 @ A2 ) @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.46/5.72 @ S4 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sums_If_finite_set'
% 5.46/5.72 thf(fact_8250_Complex__eq__neg__1,axiom,
% 5.46/5.72 ! [A: real,B: real] :
% 5.46/5.72 ( ( ( complex2 @ A @ B )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.72 = ( ( A
% 5.46/5.72 = ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.72 & ( B = zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Complex_eq_neg_1
% 5.46/5.72 thf(fact_8251_tan__45,axiom,
% 5.46/5.72 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % tan_45
% 5.46/5.72 thf(fact_8252_geometric__sums,axiom,
% 5.46/5.72 ! [C: real] :
% 5.46/5.72 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.46/5.72 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % geometric_sums
% 5.46/5.72 thf(fact_8253_geometric__sums,axiom,
% 5.46/5.72 ! [C: complex] :
% 5.46/5.72 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.46/5.72 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % geometric_sums
% 5.46/5.72 thf(fact_8254_power__half__series,axiom,
% 5.46/5.72 ( sums_real
% 5.46/5.72 @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 5.46/5.72 @ one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % power_half_series
% 5.46/5.72 thf(fact_8255_lemma__tan__total,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ? [X3: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.46/5.72 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 & ( ord_less_real @ Y2 @ ( tan_real @ X3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % lemma_tan_total
% 5.46/5.72 thf(fact_8256_tan__gt__zero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_gt_zero
% 5.46/5.72 thf(fact_8257_lemma__tan__total1,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ? [X3: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.46/5.72 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 & ( ( tan_real @ X3 )
% 5.46/5.72 = Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % lemma_tan_total1
% 5.46/5.72 thf(fact_8258_tan__mono__lt__eq,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_mono_lt_eq
% 5.46/5.72 thf(fact_8259_tan__monotone_H,axiom,
% 5.46/5.72 ! [Y2: real,X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ X2 )
% 5.46/5.72 = ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X2 ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_monotone'
% 5.46/5.72 thf(fact_8260_tan__monotone,axiom,
% 5.46/5.72 ! [Y2: real,X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_monotone
% 5.46/5.72 thf(fact_8261_tan__total,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ? [X3: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.46/5.72 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 & ( ( tan_real @ X3 )
% 5.46/5.72 = Y2 )
% 5.46/5.72 & ! [Y4: real] :
% 5.46/5.72 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.46/5.72 & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 & ( ( tan_real @ Y4 )
% 5.46/5.72 = Y2 ) )
% 5.46/5.72 => ( Y4 = X3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_total
% 5.46/5.72 thf(fact_8262_tan__minus__45,axiom,
% 5.46/5.72 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.72 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_minus_45
% 5.46/5.72 thf(fact_8263_tan__inverse,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y2 ) )
% 5.46/5.72 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_inverse
% 5.46/5.72 thf(fact_8264_add__tan__eq,axiom,
% 5.46/5.72 ! [X2: complex,Y2: complex] :
% 5.46/5.72 ( ( ( cos_complex @ X2 )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( ( cos_complex @ Y2 )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_tan_eq
% 5.46/5.72 thf(fact_8265_add__tan__eq,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ( cos_real @ X2 )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( ( cos_real @ Y2 )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_tan_eq
% 5.46/5.72 thf(fact_8266_sums__if_H,axiom,
% 5.46/5.72 ! [G: nat > real,X2: real] :
% 5.46/5.72 ( ( sums_real @ G @ X2 )
% 5.46/5.72 => ( sums_real
% 5.46/5.72 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % sums_if'
% 5.46/5.72 thf(fact_8267_sums__if,axiom,
% 5.46/5.72 ! [G: nat > real,X2: real,F: nat > real,Y2: real] :
% 5.46/5.72 ( ( sums_real @ G @ X2 )
% 5.46/5.72 => ( ( sums_real @ F @ Y2 )
% 5.46/5.72 => ( sums_real
% 5.46/5.72 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( F @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 @ ( plus_plus_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sums_if
% 5.46/5.72 thf(fact_8268_tan__pos__pi2__le,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_pos_pi2_le
% 5.46/5.72 thf(fact_8269_tan__total__pos,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ? [X3: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.72 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 & ( ( tan_real @ X3 )
% 5.46/5.72 = Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_total_pos
% 5.46/5.72 thf(fact_8270_tan__less__zero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ ( tan_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_less_zero
% 5.46/5.72 thf(fact_8271_tan__mono__le__eq,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_mono_le_eq
% 5.46/5.72 thf(fact_8272_tan__mono__le,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_mono_le
% 5.46/5.72 thf(fact_8273_tan__bound__pi2,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X2 ) ) @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_bound_pi2
% 5.46/5.72 thf(fact_8274_arctan__unique,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ( tan_real @ X2 )
% 5.46/5.72 = Y2 )
% 5.46/5.72 => ( ( arctan @ Y2 )
% 5.46/5.72 = X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arctan_unique
% 5.46/5.72 thf(fact_8275_arctan__tan,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( arctan @ ( tan_real @ X2 ) )
% 5.46/5.72 = X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arctan_tan
% 5.46/5.72 thf(fact_8276_arctan,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 5.46/5.72 & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 & ( ( tan_real @ ( arctan @ Y2 ) )
% 5.46/5.72 = Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % arctan
% 5.46/5.72 thf(fact_8277_and__int_Opinduct,axiom,
% 5.46/5.72 ! [A0: int,A12: int,P: int > int > $o] :
% 5.46/5.72 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.46/5.72 => ( ! [K3: int,L4: int] :
% 5.46/5.72 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 5.46/5.72 => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.72 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.72 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 => ( P @ K3 @ L4 ) ) )
% 5.46/5.72 => ( P @ A0 @ A12 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % and_int.pinduct
% 5.46/5.72 thf(fact_8278_lemma__tan__add1,axiom,
% 5.46/5.72 ! [X2: complex,Y2: complex] :
% 5.46/5.72 ( ( ( cos_complex @ X2 )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( ( cos_complex @ Y2 )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X2 @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % lemma_tan_add1
% 5.46/5.72 thf(fact_8279_lemma__tan__add1,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ( cos_real @ X2 )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( ( cos_real @ Y2 )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) )
% 5.46/5.72 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % lemma_tan_add1
% 5.46/5.72 thf(fact_8280_tan__diff,axiom,
% 5.46/5.72 ! [X2: complex,Y2: complex] :
% 5.46/5.72 ( ( ( cos_complex @ X2 )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( ( cos_complex @ Y2 )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( ( cos_complex @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( tan_complex @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_diff
% 5.46/5.72 thf(fact_8281_tan__diff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ( cos_real @ X2 )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( ( cos_real @ Y2 )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( ( cos_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( tan_real @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_diff
% 5.46/5.72 thf(fact_8282_tan__add,axiom,
% 5.46/5.72 ! [X2: complex,Y2: complex] :
% 5.46/5.72 ( ( ( cos_complex @ X2 )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( ( cos_complex @ Y2 )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( ( cos_complex @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( tan_complex @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_add
% 5.46/5.72 thf(fact_8283_tan__add,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ( cos_real @ X2 )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( ( cos_real @ Y2 )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( ( cos_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( tan_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_add
% 5.46/5.72 thf(fact_8284_tan__total__pi4,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.72 => ? [Z3: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 5.46/5.72 & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 & ( ( tan_real @ Z3 )
% 5.46/5.72 = X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_total_pi4
% 5.46/5.72 thf(fact_8285_cos__paired,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( sums_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_real @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.72 @ ( cos_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_paired
% 5.46/5.72 thf(fact_8286_tan__half,axiom,
% 5.46/5.72 ( tan_complex
% 5.46/5.72 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_half
% 5.46/5.72 thf(fact_8287_tan__half,axiom,
% 5.46/5.72 ( tan_real
% 5.46/5.72 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_half
% 5.46/5.72 thf(fact_8288_geometric__deriv__sums,axiom,
% 5.46/5.72 ! [Z: real] :
% 5.46/5.72 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.46/5.72 => ( sums_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) )
% 5.46/5.72 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % geometric_deriv_sums
% 5.46/5.72 thf(fact_8289_geometric__deriv__sums,axiom,
% 5.46/5.72 ! [Z: complex] :
% 5.46/5.72 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.46/5.72 => ( sums_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) )
% 5.46/5.72 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % geometric_deriv_sums
% 5.46/5.72 thf(fact_8290_diffs__equiv,axiom,
% 5.46/5.72 ! [C: nat > real,X2: real] :
% 5.46/5.72 ( ( summable_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) )
% 5.46/5.72 => ( sums_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( C @ N2 ) ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.46/5.72 @ ( suminf_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diffs_equiv
% 5.46/5.72 thf(fact_8291_diffs__equiv,axiom,
% 5.46/5.72 ! [C: nat > complex,X2: complex] :
% 5.46/5.72 ( ( summable_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) )
% 5.46/5.72 => ( sums_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( C @ N2 ) ) @ ( power_power_complex @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.46/5.72 @ ( suminf_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diffs_equiv
% 5.46/5.72 thf(fact_8292_ceiling__log__eq__powr__iff,axiom,
% 5.46/5.72 ! [X2: real,B: real,K: nat] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X2 ) )
% 5.46/5.72 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.46/5.72 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X2 )
% 5.46/5.72 & ( ord_less_eq_real @ X2 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ceiling_log_eq_powr_iff
% 5.46/5.72 thf(fact_8293_sin__tan,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( sin_real @ X2 )
% 5.46/5.72 = ( divide_divide_real @ ( tan_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_tan
% 5.46/5.72 thf(fact_8294_cos__tan,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( cos_real @ X2 )
% 5.46/5.72 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_tan
% 5.46/5.72 thf(fact_8295_monoseq__def,axiom,
% 5.46/5.72 ( topolo6980174941875973593q_real
% 5.46/5.72 = ( ^ [X5: nat > real] :
% 5.46/5.72 ( ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( X5 @ M3 ) @ ( X5 @ N2 ) ) )
% 5.46/5.72 | ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( X5 @ N2 ) @ ( X5 @ M3 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_def
% 5.46/5.72 thf(fact_8296_monoseq__def,axiom,
% 5.46/5.72 ( topolo7278393974255667507et_nat
% 5.46/5.72 = ( ^ [X5: nat > set_nat] :
% 5.46/5.72 ( ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_set_nat @ ( X5 @ M3 ) @ ( X5 @ N2 ) ) )
% 5.46/5.72 | ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_set_nat @ ( X5 @ N2 ) @ ( X5 @ M3 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_def
% 5.46/5.72 thf(fact_8297_monoseq__def,axiom,
% 5.46/5.72 ( topolo4267028734544971653eq_rat
% 5.46/5.72 = ( ^ [X5: nat > rat] :
% 5.46/5.72 ( ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_rat @ ( X5 @ M3 ) @ ( X5 @ N2 ) ) )
% 5.46/5.72 | ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_rat @ ( X5 @ N2 ) @ ( X5 @ M3 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_def
% 5.46/5.72 thf(fact_8298_monoseq__def,axiom,
% 5.46/5.72 ( topolo1459490580787246023eq_num
% 5.46/5.72 = ( ^ [X5: nat > num] :
% 5.46/5.72 ( ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_num @ ( X5 @ M3 ) @ ( X5 @ N2 ) ) )
% 5.46/5.72 | ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_num @ ( X5 @ N2 ) @ ( X5 @ M3 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_def
% 5.46/5.72 thf(fact_8299_monoseq__def,axiom,
% 5.46/5.72 ( topolo4902158794631467389eq_nat
% 5.46/5.72 = ( ^ [X5: nat > nat] :
% 5.46/5.72 ( ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_nat @ ( X5 @ M3 ) @ ( X5 @ N2 ) ) )
% 5.46/5.72 | ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_nat @ ( X5 @ N2 ) @ ( X5 @ M3 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_def
% 5.46/5.72 thf(fact_8300_monoseq__def,axiom,
% 5.46/5.72 ( topolo4899668324122417113eq_int
% 5.46/5.72 = ( ^ [X5: nat > int] :
% 5.46/5.72 ( ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_int @ ( X5 @ M3 ) @ ( X5 @ N2 ) ) )
% 5.46/5.72 | ! [M3: nat,N2: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.46/5.72 => ( ord_less_eq_int @ ( X5 @ N2 ) @ ( X5 @ M3 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_def
% 5.46/5.72 thf(fact_8301_real__sqrt__eq__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ( sqrt @ X2 )
% 5.46/5.72 = ( sqrt @ Y2 ) )
% 5.46/5.72 = ( X2 = Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_eq_iff
% 5.46/5.72 thf(fact_8302_powr__one__eq__one,axiom,
% 5.46/5.72 ! [A: real] :
% 5.46/5.72 ( ( powr_real @ one_one_real @ A )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % powr_one_eq_one
% 5.46/5.72 thf(fact_8303_real__sqrt__zero,axiom,
% 5.46/5.72 ( ( sqrt @ zero_zero_real )
% 5.46/5.72 = zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_zero
% 5.46/5.72 thf(fact_8304_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ( sqrt @ X2 )
% 5.46/5.72 = zero_zero_real )
% 5.46/5.72 = ( X2 = zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_eq_zero_cancel_iff
% 5.46/5.72 thf(fact_8305_real__sqrt__less__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_less_iff
% 5.46/5.72 thf(fact_8306_real__sqrt__le__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_le_iff
% 5.46/5.72 thf(fact_8307_real__sqrt__eq__1__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ( sqrt @ X2 )
% 5.46/5.72 = one_one_real )
% 5.46/5.72 = ( X2 = one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_eq_1_iff
% 5.46/5.72 thf(fact_8308_real__sqrt__one,axiom,
% 5.46/5.72 ( ( sqrt @ one_one_real )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_one
% 5.46/5.72 thf(fact_8309_powr__zero__eq__one,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ( X2 = zero_zero_real )
% 5.46/5.72 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.46/5.72 = zero_zero_real ) )
% 5.46/5.72 & ( ( X2 != zero_zero_real )
% 5.46/5.72 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.46/5.72 = one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_zero_eq_one
% 5.46/5.72 thf(fact_8310_real__sqrt__gt__0__iff,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ zero_zero_real @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_gt_0_iff
% 5.46/5.72 thf(fact_8311_real__sqrt__lt__0__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.46/5.72 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_lt_0_iff
% 5.46/5.72 thf(fact_8312_real__sqrt__le__0__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_le_0_iff
% 5.46/5.72 thf(fact_8313_real__sqrt__ge__0__iff,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_ge_0_iff
% 5.46/5.72 thf(fact_8314_powr__gt__zero,axiom,
% 5.46/5.72 ! [X2: real,A: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X2 @ A ) )
% 5.46/5.72 = ( X2 != zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_gt_zero
% 5.46/5.72 thf(fact_8315_powr__nonneg__iff,axiom,
% 5.46/5.72 ! [A: real,X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( powr_real @ A @ X2 ) @ zero_zero_real )
% 5.46/5.72 = ( A = zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_nonneg_iff
% 5.46/5.72 thf(fact_8316_real__sqrt__gt__1__iff,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ one_one_real @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_gt_1_iff
% 5.46/5.72 thf(fact_8317_real__sqrt__lt__1__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.46/5.72 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_lt_1_iff
% 5.46/5.72 thf(fact_8318_real__sqrt__le__1__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_le_1_iff
% 5.46/5.72 thf(fact_8319_real__sqrt__ge__1__iff,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_ge_1_iff
% 5.46/5.72 thf(fact_8320_powr__less__cancel__iff,axiom,
% 5.46/5.72 ! [X2: real,A: real,B: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.46/5.72 = ( ord_less_real @ A @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_less_cancel_iff
% 5.46/5.72 thf(fact_8321_real__sqrt__abs2,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( sqrt @ ( times_times_real @ X2 @ X2 ) )
% 5.46/5.72 = ( abs_abs_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_abs2
% 5.46/5.72 thf(fact_8322_real__sqrt__mult__self,axiom,
% 5.46/5.72 ! [A: real] :
% 5.46/5.72 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.46/5.72 = ( abs_abs_real @ A ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_mult_self
% 5.46/5.72 thf(fact_8323_real__sqrt__four,axiom,
% 5.46/5.72 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_four
% 5.46/5.72 thf(fact_8324_powr__eq__one__iff,axiom,
% 5.46/5.72 ! [A: real,X2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.72 => ( ( ( powr_real @ A @ X2 )
% 5.46/5.72 = one_one_real )
% 5.46/5.72 = ( X2 = zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_eq_one_iff
% 5.46/5.72 thf(fact_8325_powr__one__gt__zero__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ( powr_real @ X2 @ one_one_real )
% 5.46/5.72 = X2 )
% 5.46/5.72 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_one_gt_zero_iff
% 5.46/5.72 thf(fact_8326_powr__one,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( powr_real @ X2 @ one_one_real )
% 5.46/5.72 = X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_one
% 5.46/5.72 thf(fact_8327_powr__le__cancel__iff,axiom,
% 5.46/5.72 ! [X2: real,A: real,B: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.46/5.72 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_le_cancel_iff
% 5.46/5.72 thf(fact_8328_numeral__powr__numeral__real,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.72 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_powr_numeral_real
% 5.46/5.72 thf(fact_8329_log__powr__cancel,axiom,
% 5.46/5.72 ! [A: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ( A != one_one_real )
% 5.46/5.72 => ( ( log @ A @ ( powr_real @ A @ Y2 ) )
% 5.46/5.72 = Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % log_powr_cancel
% 5.46/5.72 thf(fact_8330_powr__log__cancel,axiom,
% 5.46/5.72 ! [A: real,X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ( A != one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( powr_real @ A @ ( log @ A @ X2 ) )
% 5.46/5.72 = X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_log_cancel
% 5.46/5.72 thf(fact_8331_real__sqrt__abs,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( sqrt @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( abs_abs_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_abs
% 5.46/5.72 thf(fact_8332_powr__numeral,axiom,
% 5.46/5.72 ! [X2: real,N: num] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( powr_real @ X2 @ ( numeral_numeral_real @ N ) )
% 5.46/5.72 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_numeral
% 5.46/5.72 thf(fact_8333_real__sqrt__pow2,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_pow2
% 5.46/5.72 thf(fact_8334_real__sqrt__pow2__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = X2 )
% 5.46/5.72 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_pow2_iff
% 5.46/5.72 thf(fact_8335_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.46/5.72 ! [X2: real,Y2: real,Xa2: real,Ya: real] :
% 5.46/5.72 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_sum_squares_mult_squared_eq
% 5.46/5.72 thf(fact_8336_square__powr__half,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( powr_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( abs_abs_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_powr_half
% 5.46/5.72 thf(fact_8337_real__sqrt__power,axiom,
% 5.46/5.72 ! [X2: real,K: nat] :
% 5.46/5.72 ( ( sqrt @ ( power_power_real @ X2 @ K ) )
% 5.46/5.72 = ( power_power_real @ ( sqrt @ X2 ) @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_power
% 5.46/5.72 thf(fact_8338_real__sqrt__mult,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( sqrt @ ( times_times_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( times_times_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_mult
% 5.46/5.72 thf(fact_8339_real__sqrt__divide,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( sqrt @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_divide
% 5.46/5.72 thf(fact_8340_powr__powr,axiom,
% 5.46/5.72 ! [X2: real,A: real,B: real] :
% 5.46/5.72 ( ( powr_real @ ( powr_real @ X2 @ A ) @ B )
% 5.46/5.72 = ( powr_real @ X2 @ ( times_times_real @ A @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_powr
% 5.46/5.72 thf(fact_8341_real__sqrt__le__mono,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_le_mono
% 5.46/5.72 thf(fact_8342_real__sqrt__less__mono,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_less_mono
% 5.46/5.72 thf(fact_8343_real__sqrt__minus,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( sqrt @ ( uminus_uminus_real @ X2 ) )
% 5.46/5.72 = ( uminus_uminus_real @ ( sqrt @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_minus
% 5.46/5.72 thf(fact_8344_powr__non__neg,axiom,
% 5.46/5.72 ! [A: real,X2: real] :
% 5.46/5.72 ~ ( ord_less_real @ ( powr_real @ A @ X2 ) @ zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % powr_non_neg
% 5.46/5.72 thf(fact_8345_powr__less__mono2__neg,axiom,
% 5.46/5.72 ! [A: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X2 @ A ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_less_mono2_neg
% 5.46/5.72 thf(fact_8346_powr__ge__pzero,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_ge_pzero
% 5.46/5.72 thf(fact_8347_powr__mono2,axiom,
% 5.46/5.72 ! [A: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_mono2
% 5.46/5.72 thf(fact_8348_real__sqrt__gt__zero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_gt_zero
% 5.46/5.72 thf(fact_8349_real__sqrt__ge__zero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_ge_zero
% 5.46/5.72 thf(fact_8350_real__sqrt__eq__zero__cancel,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ( sqrt @ X2 )
% 5.46/5.72 = zero_zero_real )
% 5.46/5.72 => ( X2 = zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_eq_zero_cancel
% 5.46/5.72 thf(fact_8351_powr__less__mono,axiom,
% 5.46/5.72 ! [A: real,B: real,X2: real] :
% 5.46/5.72 ( ( ord_less_real @ A @ B )
% 5.46/5.72 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_less_mono
% 5.46/5.72 thf(fact_8352_powr__less__cancel,axiom,
% 5.46/5.72 ! [X2: real,A: real,B: real] :
% 5.46/5.72 ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.46/5.72 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ord_less_real @ A @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_less_cancel
% 5.46/5.72 thf(fact_8353_powr__mono,axiom,
% 5.46/5.72 ! [A: real,B: real,X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.72 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_mono
% 5.46/5.72 thf(fact_8354_real__sqrt__ge__one,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_ge_one
% 5.46/5.72 thf(fact_8355_powr__less__mono2,axiom,
% 5.46/5.72 ! [A: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_less_mono2
% 5.46/5.72 thf(fact_8356_powr__mono2_H,axiom,
% 5.46/5.72 ! [A: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X2 @ A ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_mono2'
% 5.46/5.72 thf(fact_8357_gr__one__powr,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ord_less_real @ one_one_real @ ( powr_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gr_one_powr
% 5.46/5.72 thf(fact_8358_powr__inj,axiom,
% 5.46/5.72 ! [A: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ( A != one_one_real )
% 5.46/5.72 => ( ( ( powr_real @ A @ X2 )
% 5.46/5.72 = ( powr_real @ A @ Y2 ) )
% 5.46/5.72 = ( X2 = Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_inj
% 5.46/5.72 thf(fact_8359_ge__one__powr__ge__zero,axiom,
% 5.46/5.72 ! [X2: real,A: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X2 @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ge_one_powr_ge_zero
% 5.46/5.72 thf(fact_8360_powr__mono__both,axiom,
% 5.46/5.72 ! [A: real,B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ( ord_less_eq_real @ A @ B )
% 5.46/5.72 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y2 @ B ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_mono_both
% 5.46/5.72 thf(fact_8361_powr__le1,axiom,
% 5.46/5.72 ! [A: real,X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_le1
% 5.46/5.72 thf(fact_8362_powr__divide,axiom,
% 5.46/5.72 ! [X2: real,Y2: real,A: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ( powr_real @ ( divide_divide_real @ X2 @ Y2 ) @ A )
% 5.46/5.72 = ( divide_divide_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_divide
% 5.46/5.72 thf(fact_8363_powr__mult,axiom,
% 5.46/5.72 ! [X2: real,Y2: real,A: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ( powr_real @ ( times_times_real @ X2 @ Y2 ) @ A )
% 5.46/5.72 = ( times_times_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_mult
% 5.46/5.72 thf(fact_8364_real__div__sqrt,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( divide_divide_real @ X2 @ ( sqrt @ X2 ) )
% 5.46/5.72 = ( sqrt @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_div_sqrt
% 5.46/5.72 thf(fact_8365_sqrt__add__le__add__sqrt,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X2 @ Y2 ) ) @ ( plus_plus_real @ ( sqrt @ X2 ) @ ( sqrt @ Y2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sqrt_add_le_add_sqrt
% 5.46/5.72 thf(fact_8366_le__real__sqrt__sumsq,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_real_sqrt_sumsq
% 5.46/5.72 thf(fact_8367_divide__powr__uminus,axiom,
% 5.46/5.72 ! [A: real,B: real,C: real] :
% 5.46/5.72 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.46/5.72 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_powr_uminus
% 5.46/5.72 thf(fact_8368_log__base__powr,axiom,
% 5.46/5.72 ! [A: real,B: real,X2: real] :
% 5.46/5.72 ( ( A != zero_zero_real )
% 5.46/5.72 => ( ( log @ ( powr_real @ A @ B ) @ X2 )
% 5.46/5.72 = ( divide_divide_real @ ( log @ A @ X2 ) @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % log_base_powr
% 5.46/5.72 thf(fact_8369_log__powr,axiom,
% 5.46/5.72 ! [X2: real,B: real,Y2: real] :
% 5.46/5.72 ( ( X2 != zero_zero_real )
% 5.46/5.72 => ( ( log @ B @ ( powr_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( times_times_real @ Y2 @ ( log @ B @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % log_powr
% 5.46/5.72 thf(fact_8370_ln__powr,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( X2 != zero_zero_real )
% 5.46/5.72 => ( ( ln_ln_real @ ( powr_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( times_times_real @ Y2 @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ln_powr
% 5.46/5.72 thf(fact_8371_powr__add,axiom,
% 5.46/5.72 ! [X2: real,A: real,B: real] :
% 5.46/5.72 ( ( powr_real @ X2 @ ( plus_plus_real @ A @ B ) )
% 5.46/5.72 = ( times_times_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_add
% 5.46/5.72 thf(fact_8372_powr__diff,axiom,
% 5.46/5.72 ! [W: real,Z1: real,Z22: real] :
% 5.46/5.72 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.46/5.72 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_diff
% 5.46/5.72 thf(fact_8373_powr__half__sqrt,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( sqrt @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_half_sqrt
% 5.46/5.72 thf(fact_8374_sqrt2__less__2,axiom,
% 5.46/5.72 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.46/5.72
% 5.46/5.72 % sqrt2_less_2
% 5.46/5.72 thf(fact_8375_powr__realpow,axiom,
% 5.46/5.72 ! [X2: real,N: nat] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( powr_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.72 = ( power_power_real @ X2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_realpow
% 5.46/5.72 thf(fact_8376_less__log__iff,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ ( log @ B @ X2 ) )
% 5.46/5.72 = ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_log_iff
% 5.46/5.72 thf(fact_8377_log__less__iff,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ ( log @ B @ X2 ) @ Y2 )
% 5.46/5.72 = ( ord_less_real @ X2 @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % log_less_iff
% 5.46/5.72 thf(fact_8378_less__powr__iff,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( powr_real @ B @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ ( log @ B @ X2 ) @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_powr_iff
% 5.46/5.72 thf(fact_8379_powr__less__iff,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X2 )
% 5.46/5.72 = ( ord_less_real @ Y2 @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_less_iff
% 5.46/5.72 thf(fact_8380_diffs__def,axiom,
% 5.46/5.72 ( diffs_int
% 5.46/5.72 = ( ^ [C3: nat > int,N2: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diffs_def
% 5.46/5.72 thf(fact_8381_diffs__def,axiom,
% 5.46/5.72 ( diffs_real
% 5.46/5.72 = ( ^ [C3: nat > real,N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diffs_def
% 5.46/5.72 thf(fact_8382_diffs__def,axiom,
% 5.46/5.72 ( diffs_complex
% 5.46/5.72 = ( ^ [C3: nat > complex,N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diffs_def
% 5.46/5.72 thf(fact_8383_diffs__def,axiom,
% 5.46/5.72 ( diffs_rat
% 5.46/5.72 = ( ^ [C3: nat > rat,N2: nat] : ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diffs_def
% 5.46/5.72 thf(fact_8384_powr__minus__divide,axiom,
% 5.46/5.72 ! [X2: real,A: real] :
% 5.46/5.72 ( ( powr_real @ X2 @ ( uminus_uminus_real @ A ) )
% 5.46/5.72 = ( divide_divide_real @ one_one_real @ ( powr_real @ X2 @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_minus_divide
% 5.46/5.72 thf(fact_8385_real__less__rsqrt,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 5.46/5.72 => ( ord_less_real @ X2 @ ( sqrt @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_less_rsqrt
% 5.46/5.72 thf(fact_8386_sqrt__le__D,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y2 )
% 5.46/5.72 => ( ord_less_eq_real @ X2 @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sqrt_le_D
% 5.46/5.72 thf(fact_8387_real__le__rsqrt,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 5.46/5.72 => ( ord_less_eq_real @ X2 @ ( sqrt @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_le_rsqrt
% 5.46/5.72 thf(fact_8388_powr__neg__one,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.72 = ( divide_divide_real @ one_one_real @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_neg_one
% 5.46/5.72 thf(fact_8389_termdiff__converges__all,axiom,
% 5.46/5.72 ! [C: nat > complex,X2: complex] :
% 5.46/5.72 ( ! [X3: complex] :
% 5.46/5.72 ( summable_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) )
% 5.46/5.72 => ( summable_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % termdiff_converges_all
% 5.46/5.72 thf(fact_8390_termdiff__converges__all,axiom,
% 5.46/5.72 ! [C: nat > real,X2: real] :
% 5.46/5.72 ( ! [X3: real] :
% 5.46/5.72 ( summable_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) )
% 5.46/5.72 => ( summable_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % termdiff_converges_all
% 5.46/5.72 thf(fact_8391_powr__mult__base,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( times_times_real @ X2 @ ( powr_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( powr_real @ X2 @ ( plus_plus_real @ one_one_real @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_mult_base
% 5.46/5.72 thf(fact_8392_tan__60,axiom,
% 5.46/5.72 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.46/5.72 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_60
% 5.46/5.72 thf(fact_8393_powr__le__iff,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X2 )
% 5.46/5.72 = ( ord_less_eq_real @ Y2 @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_le_iff
% 5.46/5.72 thf(fact_8394_le__powr__iff,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_powr_iff
% 5.46/5.72 thf(fact_8395_log__le__iff,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y2 )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % log_le_iff
% 5.46/5.72 thf(fact_8396_le__log__iff,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ ( log @ B @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_log_iff
% 5.46/5.72 thf(fact_8397_real__le__lsqrt,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_le_lsqrt
% 5.46/5.72 thf(fact_8398_real__sqrt__unique,axiom,
% 5.46/5.72 ! [Y2: real,X2: real] :
% 5.46/5.72 ( ( ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ( sqrt @ X2 )
% 5.46/5.72 = Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_unique
% 5.46/5.72 thf(fact_8399_lemma__real__divide__sqrt__less,axiom,
% 5.46/5.72 ! [U: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ U )
% 5.46/5.72 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.46/5.72
% 5.46/5.72 % lemma_real_divide_sqrt_less
% 5.46/5.72 thf(fact_8400_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 = X2 )
% 5.46/5.72 => ( Y2 = zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_sum_squares_eq_cancel
% 5.46/5.72 thf(fact_8401_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 = Y2 )
% 5.46/5.72 => ( X2 = zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_sum_squares_eq_cancel2
% 5.46/5.72 thf(fact_8402_real__sqrt__sum__squares__ge1,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_sum_squares_ge1
% 5.46/5.72 thf(fact_8403_real__sqrt__sum__squares__ge2,axiom,
% 5.46/5.72 ! [Y2: real,X2: real] : ( ord_less_eq_real @ Y2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_sum_squares_ge2
% 5.46/5.72 thf(fact_8404_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.46/5.72 ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_sum_squares_triangle_ineq
% 5.46/5.72 thf(fact_8405_sqrt__ge__absD,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ Y2 ) )
% 5.46/5.72 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % sqrt_ge_absD
% 5.46/5.72 thf(fact_8406_ln__powr__bound,axiom,
% 5.46/5.72 ! [X2: real,A: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( divide_divide_real @ ( powr_real @ X2 @ A ) @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ln_powr_bound
% 5.46/5.72 thf(fact_8407_ln__powr__bound2,axiom,
% 5.46/5.72 ! [X2: real,A: real] :
% 5.46/5.72 ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X2 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ln_powr_bound2
% 5.46/5.72 thf(fact_8408_cos__45,axiom,
% 5.46/5.72 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_45
% 5.46/5.72 thf(fact_8409_sin__45,axiom,
% 5.46/5.72 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_45
% 5.46/5.72 thf(fact_8410_add__log__eq__powr,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.72 => ( ( B != one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( plus_plus_real @ Y2 @ ( log @ B @ X2 ) )
% 5.46/5.72 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y2 ) @ X2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_log_eq_powr
% 5.46/5.72 thf(fact_8411_log__add__eq__powr,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.72 => ( ( B != one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( plus_plus_real @ ( log @ B @ X2 ) @ Y2 )
% 5.46/5.72 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ Y2 ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % log_add_eq_powr
% 5.46/5.72 thf(fact_8412_minus__log__eq__powr,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.72 => ( ( B != one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( minus_minus_real @ Y2 @ ( log @ B @ X2 ) )
% 5.46/5.72 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y2 ) @ X2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_log_eq_powr
% 5.46/5.72 thf(fact_8413_powr__def,axiom,
% 5.46/5.72 ( powr_real
% 5.46/5.72 = ( ^ [X: real,A3: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A3 @ ( ln_ln_real @ X ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_def
% 5.46/5.72 thf(fact_8414_real__less__lsqrt,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ord_less_real @ ( sqrt @ X2 ) @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_less_lsqrt
% 5.46/5.72 thf(fact_8415_sqrt__sum__squares__le__sum,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sqrt_sum_squares_le_sum
% 5.46/5.72 thf(fact_8416_tan__30,axiom,
% 5.46/5.72 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.46/5.72 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_30
% 5.46/5.72 thf(fact_8417_sqrt__even__pow2,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.72 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sqrt_even_pow2
% 5.46/5.72 thf(fact_8418_sqrt__sum__squares__le__sum__abs,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sqrt_sum_squares_le_sum_abs
% 5.46/5.72 thf(fact_8419_real__sqrt__ge__abs2,axiom,
% 5.46/5.72 ! [Y2: real,X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_ge_abs2
% 5.46/5.72 thf(fact_8420_real__sqrt__ge__abs1,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_ge_abs1
% 5.46/5.72 thf(fact_8421_ln__sqrt,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ln_ln_real @ ( sqrt @ X2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ln_sqrt
% 5.46/5.72 thf(fact_8422_cos__30,axiom,
% 5.46/5.72 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.46/5.72 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_30
% 5.46/5.72 thf(fact_8423_sin__60,axiom,
% 5.46/5.72 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.46/5.72 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_60
% 5.46/5.72 thf(fact_8424_log__minus__eq__powr,axiom,
% 5.46/5.72 ! [B: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.72 => ( ( B != one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( minus_minus_real @ ( log @ B @ X2 ) @ Y2 )
% 5.46/5.72 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ ( uminus_uminus_real @ Y2 ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % log_minus_eq_powr
% 5.46/5.72 thf(fact_8425_complex__norm,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( real_V1022390504157884413omplex @ ( complex2 @ X2 @ Y2 ) )
% 5.46/5.72 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % complex_norm
% 5.46/5.72 thf(fact_8426_termdiff__converges,axiom,
% 5.46/5.72 ! [X2: real,K5: real,C: nat > real] :
% 5.46/5.72 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ K5 )
% 5.46/5.72 => ( ! [X3: real] :
% 5.46/5.72 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 5.46/5.72 => ( summable_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 5.46/5.72 => ( summable_real
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % termdiff_converges
% 5.46/5.72 thf(fact_8427_termdiff__converges,axiom,
% 5.46/5.72 ! [X2: complex,K5: real,C: nat > complex] :
% 5.46/5.72 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ K5 )
% 5.46/5.72 => ( ! [X3: complex] :
% 5.46/5.72 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 5.46/5.72 => ( summable_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) )
% 5.46/5.72 => ( summable_complex
% 5.46/5.72 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % termdiff_converges
% 5.46/5.72 thf(fact_8428_arsinh__real__aux,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arsinh_real_aux
% 5.46/5.72 thf(fact_8429_real__sqrt__power__even,axiom,
% 5.46/5.72 ! [N: nat,X2: real] :
% 5.46/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( power_power_real @ ( sqrt @ X2 ) @ N )
% 5.46/5.72 = ( power_power_real @ X2 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_power_even
% 5.46/5.72 thf(fact_8430_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.46/5.72 ! [X2: real,Y2: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_sum_squares_mult_ge_zero
% 5.46/5.72 thf(fact_8431_arith__geo__mean__sqrt,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X2 @ Y2 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arith_geo_mean_sqrt
% 5.46/5.72 thf(fact_8432_powr__neg__numeral,axiom,
% 5.46/5.72 ! [X2: real,N: num] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.72 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_neg_numeral
% 5.46/5.72 thf(fact_8433_cos__x__y__le__one,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % cos_x_y_le_one
% 5.46/5.72 thf(fact_8434_real__sqrt__sum__squares__less,axiom,
% 5.46/5.72 ! [X2: real,U: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_sum_squares_less
% 5.46/5.72 thf(fact_8435_arcosh__real__def,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.46/5.72 => ( ( arcosh_real @ X2 )
% 5.46/5.72 = ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcosh_real_def
% 5.46/5.72 thf(fact_8436_cos__arctan,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( cos_real @ ( arctan @ X2 ) )
% 5.46/5.72 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_arctan
% 5.46/5.72 thf(fact_8437_sin__arctan,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( sin_real @ ( arctan @ X2 ) )
% 5.46/5.72 = ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_arctan
% 5.46/5.72 thf(fact_8438_sqrt__sum__squares__half__less,axiom,
% 5.46/5.72 ! [X2: real,U: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ X2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sqrt_sum_squares_half_less
% 5.46/5.72 thf(fact_8439_sin__cos__sqrt,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) )
% 5.46/5.72 => ( ( sin_real @ X2 )
% 5.46/5.72 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_cos_sqrt
% 5.46/5.72 thf(fact_8440_arctan__half,axiom,
% 5.46/5.72 ( arctan
% 5.46/5.72 = ( ^ [X: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arctan_half
% 5.46/5.72 thf(fact_8441_mono__SucI1,axiom,
% 5.46/5.72 ! [X7: nat > real] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_real @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.46/5.72 => ( topolo6980174941875973593q_real @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI1
% 5.46/5.72 thf(fact_8442_mono__SucI1,axiom,
% 5.46/5.72 ! [X7: nat > set_nat] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.46/5.72 => ( topolo7278393974255667507et_nat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI1
% 5.46/5.72 thf(fact_8443_mono__SucI1,axiom,
% 5.46/5.72 ! [X7: nat > rat] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.46/5.72 => ( topolo4267028734544971653eq_rat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI1
% 5.46/5.72 thf(fact_8444_mono__SucI1,axiom,
% 5.46/5.72 ! [X7: nat > num] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_num @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.46/5.72 => ( topolo1459490580787246023eq_num @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI1
% 5.46/5.72 thf(fact_8445_mono__SucI1,axiom,
% 5.46/5.72 ! [X7: nat > nat] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.46/5.72 => ( topolo4902158794631467389eq_nat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI1
% 5.46/5.72 thf(fact_8446_mono__SucI1,axiom,
% 5.46/5.72 ! [X7: nat > int] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_int @ ( X7 @ N3 ) @ ( X7 @ ( suc @ N3 ) ) )
% 5.46/5.72 => ( topolo4899668324122417113eq_int @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI1
% 5.46/5.72 thf(fact_8447_mono__SucI2,axiom,
% 5.46/5.72 ! [X7: nat > real] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_real @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.46/5.72 => ( topolo6980174941875973593q_real @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI2
% 5.46/5.72 thf(fact_8448_mono__SucI2,axiom,
% 5.46/5.72 ! [X7: nat > set_nat] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.46/5.72 => ( topolo7278393974255667507et_nat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI2
% 5.46/5.72 thf(fact_8449_mono__SucI2,axiom,
% 5.46/5.72 ! [X7: nat > rat] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.46/5.72 => ( topolo4267028734544971653eq_rat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI2
% 5.46/5.72 thf(fact_8450_mono__SucI2,axiom,
% 5.46/5.72 ! [X7: nat > num] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_num @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.46/5.72 => ( topolo1459490580787246023eq_num @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI2
% 5.46/5.72 thf(fact_8451_mono__SucI2,axiom,
% 5.46/5.72 ! [X7: nat > nat] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.46/5.72 => ( topolo4902158794631467389eq_nat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI2
% 5.46/5.72 thf(fact_8452_mono__SucI2,axiom,
% 5.46/5.72 ! [X7: nat > int] :
% 5.46/5.72 ( ! [N3: nat] : ( ord_less_eq_int @ ( X7 @ ( suc @ N3 ) ) @ ( X7 @ N3 ) )
% 5.46/5.72 => ( topolo4899668324122417113eq_int @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mono_SucI2
% 5.46/5.72 thf(fact_8453_monoseq__Suc,axiom,
% 5.46/5.72 ( topolo6980174941875973593q_real
% 5.46/5.72 = ( ^ [X5: nat > real] :
% 5.46/5.72 ( ! [N2: nat] : ( ord_less_eq_real @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.46/5.72 | ! [N2: nat] : ( ord_less_eq_real @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_Suc
% 5.46/5.72 thf(fact_8454_monoseq__Suc,axiom,
% 5.46/5.72 ( topolo7278393974255667507et_nat
% 5.46/5.72 = ( ^ [X5: nat > set_nat] :
% 5.46/5.72 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.46/5.72 | ! [N2: nat] : ( ord_less_eq_set_nat @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_Suc
% 5.46/5.72 thf(fact_8455_monoseq__Suc,axiom,
% 5.46/5.72 ( topolo4267028734544971653eq_rat
% 5.46/5.72 = ( ^ [X5: nat > rat] :
% 5.46/5.72 ( ! [N2: nat] : ( ord_less_eq_rat @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.46/5.72 | ! [N2: nat] : ( ord_less_eq_rat @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_Suc
% 5.46/5.72 thf(fact_8456_monoseq__Suc,axiom,
% 5.46/5.72 ( topolo1459490580787246023eq_num
% 5.46/5.72 = ( ^ [X5: nat > num] :
% 5.46/5.72 ( ! [N2: nat] : ( ord_less_eq_num @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.46/5.72 | ! [N2: nat] : ( ord_less_eq_num @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_Suc
% 5.46/5.72 thf(fact_8457_monoseq__Suc,axiom,
% 5.46/5.72 ( topolo4902158794631467389eq_nat
% 5.46/5.72 = ( ^ [X5: nat > nat] :
% 5.46/5.72 ( ! [N2: nat] : ( ord_less_eq_nat @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.46/5.72 | ! [N2: nat] : ( ord_less_eq_nat @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_Suc
% 5.46/5.72 thf(fact_8458_monoseq__Suc,axiom,
% 5.46/5.72 ( topolo4899668324122417113eq_int
% 5.46/5.72 = ( ^ [X5: nat > int] :
% 5.46/5.72 ( ! [N2: nat] : ( ord_less_eq_int @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.46/5.72 | ! [N2: nat] : ( ord_less_eq_int @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoseq_Suc
% 5.46/5.72 thf(fact_8459_monoI1,axiom,
% 5.46/5.72 ! [X7: nat > real] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_real @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.46/5.72 => ( topolo6980174941875973593q_real @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI1
% 5.46/5.72 thf(fact_8460_monoI1,axiom,
% 5.46/5.72 ! [X7: nat > set_nat] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_set_nat @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.46/5.72 => ( topolo7278393974255667507et_nat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI1
% 5.46/5.72 thf(fact_8461_monoI1,axiom,
% 5.46/5.72 ! [X7: nat > rat] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_rat @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.46/5.72 => ( topolo4267028734544971653eq_rat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI1
% 5.46/5.72 thf(fact_8462_monoI1,axiom,
% 5.46/5.72 ! [X7: nat > num] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_num @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.46/5.72 => ( topolo1459490580787246023eq_num @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI1
% 5.46/5.72 thf(fact_8463_monoI1,axiom,
% 5.46/5.72 ! [X7: nat > nat] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_nat @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.46/5.72 => ( topolo4902158794631467389eq_nat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI1
% 5.46/5.72 thf(fact_8464_monoI1,axiom,
% 5.46/5.72 ! [X7: nat > int] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_int @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) )
% 5.46/5.72 => ( topolo4899668324122417113eq_int @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI1
% 5.46/5.72 thf(fact_8465_monoI2,axiom,
% 5.46/5.72 ! [X7: nat > real] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_real @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.46/5.72 => ( topolo6980174941875973593q_real @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI2
% 5.46/5.72 thf(fact_8466_monoI2,axiom,
% 5.46/5.72 ! [X7: nat > set_nat] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_set_nat @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.46/5.72 => ( topolo7278393974255667507et_nat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI2
% 5.46/5.72 thf(fact_8467_monoI2,axiom,
% 5.46/5.72 ! [X7: nat > rat] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_rat @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.46/5.72 => ( topolo4267028734544971653eq_rat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI2
% 5.46/5.72 thf(fact_8468_monoI2,axiom,
% 5.46/5.72 ! [X7: nat > num] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_num @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.46/5.72 => ( topolo1459490580787246023eq_num @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI2
% 5.46/5.72 thf(fact_8469_monoI2,axiom,
% 5.46/5.72 ! [X7: nat > nat] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_nat @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.46/5.72 => ( topolo4902158794631467389eq_nat @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI2
% 5.46/5.72 thf(fact_8470_monoI2,axiom,
% 5.46/5.72 ! [X7: nat > int] :
% 5.46/5.72 ( ! [M4: nat,N3: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.46/5.72 => ( ord_less_eq_int @ ( X7 @ N3 ) @ ( X7 @ M4 ) ) )
% 5.46/5.72 => ( topolo4899668324122417113eq_int @ X7 ) ) ).
% 5.46/5.72
% 5.46/5.72 % monoI2
% 5.46/5.72 thf(fact_8471_arsinh__real__def,axiom,
% 5.46/5.72 ( arsinh_real
% 5.46/5.72 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arsinh_real_def
% 5.46/5.72 thf(fact_8472_arcosh__def,axiom,
% 5.46/5.72 ( arcosh_real
% 5.46/5.72 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcosh_def
% 5.46/5.72 thf(fact_8473_cos__arcsin,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.72 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.46/5.72 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_arcsin
% 5.46/5.72 thf(fact_8474_sin__arccos__abs,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.46/5.72 => ( ( sin_real @ ( arccos @ Y2 ) )
% 5.46/5.72 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_arccos_abs
% 5.46/5.72 thf(fact_8475_sin__arccos,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.72 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.46/5.72 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_arccos
% 5.46/5.72 thf(fact_8476_of__real__eq__1__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ( real_V1803761363581548252l_real @ X2 )
% 5.46/5.72 = one_one_real )
% 5.46/5.72 = ( X2 = one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_eq_1_iff
% 5.46/5.72 thf(fact_8477_of__real__eq__1__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ( real_V4546457046886955230omplex @ X2 )
% 5.46/5.72 = one_one_complex )
% 5.46/5.72 = ( X2 = one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_eq_1_iff
% 5.46/5.72 thf(fact_8478_of__real__1,axiom,
% 5.46/5.72 ( ( real_V1803761363581548252l_real @ one_one_real )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_1
% 5.46/5.72 thf(fact_8479_of__real__1,axiom,
% 5.46/5.72 ( ( real_V4546457046886955230omplex @ one_one_real )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_1
% 5.46/5.72 thf(fact_8480_of__real__numeral,axiom,
% 5.46/5.72 ! [W: num] :
% 5.46/5.72 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.72 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_numeral
% 5.46/5.72 thf(fact_8481_of__real__numeral,axiom,
% 5.46/5.72 ! [W: num] :
% 5.46/5.72 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 5.46/5.72 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_numeral
% 5.46/5.72 thf(fact_8482_of__real__mult,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( real_V1803761363581548252l_real @ ( times_times_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( times_times_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_mult
% 5.46/5.72 thf(fact_8483_of__real__mult,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( real_V4546457046886955230omplex @ ( times_times_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( times_times_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_mult
% 5.46/5.72 thf(fact_8484_of__real__divide,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_divide
% 5.46/5.72 thf(fact_8485_of__real__divide,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_divide
% 5.46/5.72 thf(fact_8486_of__real__add,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_add
% 5.46/5.72 thf(fact_8487_of__real__add,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_add
% 5.46/5.72 thf(fact_8488_of__real__power,axiom,
% 5.46/5.72 ! [X2: real,N: nat] :
% 5.46/5.72 ( ( real_V1803761363581548252l_real @ ( power_power_real @ X2 @ N ) )
% 5.46/5.72 = ( power_power_real @ ( real_V1803761363581548252l_real @ X2 ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_power
% 5.46/5.72 thf(fact_8489_of__real__power,axiom,
% 5.46/5.72 ! [X2: real,N: nat] :
% 5.46/5.72 ( ( real_V4546457046886955230omplex @ ( power_power_real @ X2 @ N ) )
% 5.46/5.72 = ( power_power_complex @ ( real_V4546457046886955230omplex @ X2 ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_power
% 5.46/5.72 thf(fact_8490_of__real__diff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( real_V4546457046886955230omplex @ ( minus_minus_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( minus_minus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_diff
% 5.46/5.72 thf(fact_8491_arccos__1,axiom,
% 5.46/5.72 ( ( arccos @ one_one_real )
% 5.46/5.72 = zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_1
% 5.46/5.72 thf(fact_8492_arccos__minus__1,axiom,
% 5.46/5.72 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.72 = pi ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_minus_1
% 5.46/5.72 thf(fact_8493_of__real__neg__numeral,axiom,
% 5.46/5.72 ! [W: num] :
% 5.46/5.72 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_neg_numeral
% 5.46/5.72 thf(fact_8494_of__real__neg__numeral,axiom,
% 5.46/5.72 ! [W: num] :
% 5.46/5.72 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_neg_numeral
% 5.46/5.72 thf(fact_8495_cos__of__real__pi,axiom,
% 5.46/5.72 ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.46/5.72 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_of_real_pi
% 5.46/5.72 thf(fact_8496_cos__of__real__pi,axiom,
% 5.46/5.72 ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_of_real_pi
% 5.46/5.72 thf(fact_8497_cos__arccos,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ( cos_real @ ( arccos @ Y2 ) )
% 5.46/5.72 = Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_arccos
% 5.46/5.72 thf(fact_8498_sin__arcsin,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ( sin_real @ ( arcsin @ Y2 ) )
% 5.46/5.72 = Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_arcsin
% 5.46/5.72 thf(fact_8499_norm__of__real__add1,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ one_one_real ) )
% 5.46/5.72 = ( abs_abs_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % norm_of_real_add1
% 5.46/5.72 thf(fact_8500_norm__of__real__add1,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ one_one_complex ) )
% 5.46/5.72 = ( abs_abs_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % norm_of_real_add1
% 5.46/5.72 thf(fact_8501_norm__of__real__addn,axiom,
% 5.46/5.72 ! [X2: real,B: num] :
% 5.46/5.72 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( numeral_numeral_real @ B ) ) )
% 5.46/5.72 = ( abs_abs_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % norm_of_real_addn
% 5.46/5.72 thf(fact_8502_norm__of__real__addn,axiom,
% 5.46/5.72 ! [X2: real,B: num] :
% 5.46/5.72 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( numera6690914467698888265omplex @ B ) ) )
% 5.46/5.72 = ( abs_abs_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % norm_of_real_addn
% 5.46/5.72 thf(fact_8503_arccos__0,axiom,
% 5.46/5.72 ( ( arccos @ zero_zero_real )
% 5.46/5.72 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_0
% 5.46/5.72 thf(fact_8504_arcsin__1,axiom,
% 5.46/5.72 ( ( arcsin @ one_one_real )
% 5.46/5.72 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_1
% 5.46/5.72 thf(fact_8505_cos__of__real__pi__half,axiom,
% 5.46/5.72 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % cos_of_real_pi_half
% 5.46/5.72 thf(fact_8506_cos__of__real__pi__half,axiom,
% 5.46/5.72 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = zero_zero_complex ) ).
% 5.46/5.72
% 5.46/5.72 % cos_of_real_pi_half
% 5.46/5.72 thf(fact_8507_sin__of__real__pi__half,axiom,
% 5.46/5.72 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % sin_of_real_pi_half
% 5.46/5.72 thf(fact_8508_sin__of__real__pi__half,axiom,
% 5.46/5.72 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % sin_of_real_pi_half
% 5.46/5.72 thf(fact_8509_arcsin__minus__1,axiom,
% 5.46/5.72 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.72 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_minus_1
% 5.46/5.72 thf(fact_8510_nonzero__of__real__divide,axiom,
% 5.46/5.72 ! [Y2: real,X2: real] :
% 5.46/5.72 ( ( Y2 != zero_zero_real )
% 5.46/5.72 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_of_real_divide
% 5.46/5.72 thf(fact_8511_nonzero__of__real__divide,axiom,
% 5.46/5.72 ! [Y2: real,X2: real] :
% 5.46/5.72 ( ( Y2 != zero_zero_real )
% 5.46/5.72 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_of_real_divide
% 5.46/5.72 thf(fact_8512_Complex__mult__complex__of__real,axiom,
% 5.46/5.72 ! [X2: real,Y2: real,R: real] :
% 5.46/5.72 ( ( times_times_complex @ ( complex2 @ X2 @ Y2 ) @ ( real_V4546457046886955230omplex @ R ) )
% 5.46/5.72 = ( complex2 @ ( times_times_real @ X2 @ R ) @ ( times_times_real @ Y2 @ R ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Complex_mult_complex_of_real
% 5.46/5.72 thf(fact_8513_complex__of__real__mult__Complex,axiom,
% 5.46/5.72 ! [R: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X2 @ Y2 ) )
% 5.46/5.72 = ( complex2 @ ( times_times_real @ R @ X2 ) @ ( times_times_real @ R @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % complex_of_real_mult_Complex
% 5.46/5.72 thf(fact_8514_complex__of__real__add__Complex,axiom,
% 5.46/5.72 ! [R: real,X2: real,Y2: real] :
% 5.46/5.72 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X2 @ Y2 ) )
% 5.46/5.72 = ( complex2 @ ( plus_plus_real @ R @ X2 ) @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % complex_of_real_add_Complex
% 5.46/5.72 thf(fact_8515_Complex__add__complex__of__real,axiom,
% 5.46/5.72 ! [X2: real,Y2: real,R: real] :
% 5.46/5.72 ( ( plus_plus_complex @ ( complex2 @ X2 @ Y2 ) @ ( real_V4546457046886955230omplex @ R ) )
% 5.46/5.72 = ( complex2 @ ( plus_plus_real @ X2 @ R ) @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % Complex_add_complex_of_real
% 5.46/5.72 thf(fact_8516_arccos__le__arccos,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_le_arccos
% 5.46/5.72 thf(fact_8517_arccos__eq__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.72 & ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real ) )
% 5.46/5.72 => ( ( ( arccos @ X2 )
% 5.46/5.72 = ( arccos @ Y2 ) )
% 5.46/5.72 = ( X2 = Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_eq_iff
% 5.46/5.72 thf(fact_8518_arccos__le__mono,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( arccos @ X2 ) @ ( arccos @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ Y2 @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_le_mono
% 5.46/5.72 thf(fact_8519_arcsin__minus,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.72 => ( ( arcsin @ ( uminus_uminus_real @ X2 ) )
% 5.46/5.72 = ( uminus_uminus_real @ ( arcsin @ X2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_minus
% 5.46/5.72 thf(fact_8520_arcsin__le__arcsin,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_le_arcsin
% 5.46/5.72 thf(fact_8521_arcsin__eq__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.46/5.72 => ( ( ( arcsin @ X2 )
% 5.46/5.72 = ( arcsin @ Y2 ) )
% 5.46/5.72 = ( X2 = Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_eq_iff
% 5.46/5.72 thf(fact_8522_arcsin__le__mono,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_le_mono
% 5.46/5.72 thf(fact_8523_norm__less__p1,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X2 ) ) @ one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % norm_less_p1
% 5.46/5.72 thf(fact_8524_norm__less__p1,axiom,
% 5.46/5.72 ! [X2: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X2 ) ) @ one_one_complex ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % norm_less_p1
% 5.46/5.72 thf(fact_8525_arccos__lbound,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_lbound
% 5.46/5.72 thf(fact_8526_arccos__less__arccos,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ord_less_real @ ( arccos @ Y2 ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_less_arccos
% 5.46/5.72 thf(fact_8527_arccos__less__mono,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ ( arccos @ X2 ) @ ( arccos @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ Y2 @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_less_mono
% 5.46/5.72 thf(fact_8528_arccos__ubound,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_ubound
% 5.46/5.72 thf(fact_8529_arccos__cos,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.46/5.72 => ( ( arccos @ ( cos_real @ X2 ) )
% 5.46/5.72 = X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_cos
% 5.46/5.72 thf(fact_8530_arcsin__less__arcsin,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_less_arcsin
% 5.46/5.72 thf(fact_8531_arcsin__less__mono,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_less_mono
% 5.46/5.72 thf(fact_8532_cos__arccos__abs,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.46/5.72 => ( ( cos_real @ ( arccos @ Y2 ) )
% 5.46/5.72 = Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_arccos_abs
% 5.46/5.72 thf(fact_8533_norm__of__real__diff,axiom,
% 5.46/5.72 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % norm_of_real_diff
% 5.46/5.72 thf(fact_8534_arccos__cos__eq__abs,axiom,
% 5.46/5.72 ! [Theta: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.46/5.72 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.46/5.72 = ( abs_abs_real @ Theta ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_cos_eq_abs
% 5.46/5.72 thf(fact_8535_arccos__lt__bounded,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 5.46/5.72 & ( ord_less_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_lt_bounded
% 5.46/5.72 thf(fact_8536_arccos__bounded,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 5.46/5.72 & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_bounded
% 5.46/5.72 thf(fact_8537_sin__arccos__nonzero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.72 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.46/5.72 != zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_arccos_nonzero
% 5.46/5.72 thf(fact_8538_cos__int__times__real,axiom,
% 5.46/5.72 ! [M: int,X2: real] :
% 5.46/5.72 ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X2 ) ) )
% 5.46/5.72 = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_int_times_real
% 5.46/5.72 thf(fact_8539_cos__int__times__real,axiom,
% 5.46/5.72 ! [M: int,X2: real] :
% 5.46/5.72 ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X2 ) ) )
% 5.46/5.72 = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_int_times_real
% 5.46/5.72 thf(fact_8540_sin__int__times__real,axiom,
% 5.46/5.72 ! [M: int,X2: real] :
% 5.46/5.72 ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X2 ) ) )
% 5.46/5.72 = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_int_times_real
% 5.46/5.72 thf(fact_8541_sin__int__times__real,axiom,
% 5.46/5.72 ! [M: int,X2: real] :
% 5.46/5.72 ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X2 ) ) )
% 5.46/5.72 = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_int_times_real
% 5.46/5.72 thf(fact_8542_arccos__cos2,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.46/5.72 => ( ( arccos @ ( cos_real @ X2 ) )
% 5.46/5.72 = ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_cos2
% 5.46/5.72 thf(fact_8543_arccos__minus,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.72 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.46/5.72 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_minus
% 5.46/5.72 thf(fact_8544_cos__arcsin__nonzero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.72 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.46/5.72 != zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_arcsin_nonzero
% 5.46/5.72 thf(fact_8545_arccos,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 5.46/5.72 & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi )
% 5.46/5.72 & ( ( cos_real @ ( arccos @ Y2 ) )
% 5.46/5.72 = Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos
% 5.46/5.72 thf(fact_8546_arccos__minus__abs,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.72 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.46/5.72 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_minus_abs
% 5.46/5.72 thf(fact_8547_sin__cos__eq,axiom,
% 5.46/5.72 ( sin_real
% 5.46/5.72 = ( ^ [X: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_cos_eq
% 5.46/5.72 thf(fact_8548_sin__cos__eq,axiom,
% 5.46/5.72 ( sin_complex
% 5.46/5.72 = ( ^ [X: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sin_cos_eq
% 5.46/5.72 thf(fact_8549_cos__sin__eq,axiom,
% 5.46/5.72 ( cos_real
% 5.46/5.72 = ( ^ [X: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_sin_eq
% 5.46/5.72 thf(fact_8550_cos__sin__eq,axiom,
% 5.46/5.72 ( cos_complex
% 5.46/5.72 = ( ^ [X: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cos_sin_eq
% 5.46/5.72 thf(fact_8551_arsinh__def,axiom,
% 5.46/5.72 ( arsinh_real
% 5.46/5.72 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arsinh_def
% 5.46/5.72 thf(fact_8552_minus__sin__cos__eq,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( uminus_uminus_real @ ( sin_real @ X2 ) )
% 5.46/5.72 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_sin_cos_eq
% 5.46/5.72 thf(fact_8553_minus__sin__cos__eq,axiom,
% 5.46/5.72 ! [X2: complex] :
% 5.46/5.72 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X2 ) )
% 5.46/5.72 = ( cos_complex @ ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_sin_cos_eq
% 5.46/5.72 thf(fact_8554_arccos__le__pi2,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_le_pi2
% 5.46/5.72 thf(fact_8555_arcsin__lt__bounded,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.46/5.72 & ( ord_less_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_lt_bounded
% 5.46/5.72 thf(fact_8556_arcsin__bounded,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.46/5.72 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_bounded
% 5.46/5.72 thf(fact_8557_arcsin__ubound,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_ubound
% 5.46/5.72 thf(fact_8558_arcsin__lbound,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_lbound
% 5.46/5.72 thf(fact_8559_arcsin__sin,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( arcsin @ ( sin_real @ X2 ) )
% 5.46/5.72 = X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_sin
% 5.46/5.72 thf(fact_8560_le__arcsin__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ ( arcsin @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( sin_real @ Y2 ) @ X2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_arcsin_iff
% 5.46/5.72 thf(fact_8561_arcsin__le__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ Y2 )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ ( sin_real @ Y2 ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_le_iff
% 5.46/5.72 thf(fact_8562_arcsin__pi,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.46/5.72 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ pi )
% 5.46/5.72 & ( ( sin_real @ ( arcsin @ Y2 ) )
% 5.46/5.72 = Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_pi
% 5.46/5.72 thf(fact_8563_arcsin,axiom,
% 5.46/5.72 ! [Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.46/5.72 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 & ( ( sin_real @ ( arcsin @ Y2 ) )
% 5.46/5.72 = Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin
% 5.46/5.72 thf(fact_8564_arccos__cos__eq__abs__2pi,axiom,
% 5.46/5.72 ! [Theta: real] :
% 5.46/5.72 ~ ! [K3: int] :
% 5.46/5.72 ( ( arccos @ ( cos_real @ Theta ) )
% 5.46/5.72 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_cos_eq_abs_2pi
% 5.46/5.72 thf(fact_8565_pochhammer__double,axiom,
% 5.46/5.72 ! [Z: real,N: nat] :
% 5.46/5.72 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.72 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_double
% 5.46/5.72 thf(fact_8566_pochhammer__double,axiom,
% 5.46/5.72 ! [Z: complex,N: nat] :
% 5.46/5.72 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.72 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_double
% 5.46/5.72 thf(fact_8567_pochhammer__double,axiom,
% 5.46/5.72 ! [Z: rat,N: nat] :
% 5.46/5.72 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.72 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_double
% 5.46/5.72 thf(fact_8568_floor__log__nat__eq__powr__iff,axiom,
% 5.46/5.72 ! [B: nat,K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.46/5.72 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.72 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.46/5.72 = ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.72 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.46/5.72 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_log_nat_eq_powr_iff
% 5.46/5.72 thf(fact_8569_of__nat__code,axiom,
% 5.46/5.72 ( semiri1314217659103216013at_int
% 5.46/5.72 = ( ^ [N2: nat] :
% 5.46/5.72 ( semiri8420488043553186161ux_int
% 5.46/5.72 @ ^ [I4: int] : ( plus_plus_int @ I4 @ one_one_int )
% 5.46/5.72 @ N2
% 5.46/5.72 @ zero_zero_int ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_nat_code
% 5.46/5.72 thf(fact_8570_of__nat__code,axiom,
% 5.46/5.72 ( semiri5074537144036343181t_real
% 5.46/5.72 = ( ^ [N2: nat] :
% 5.46/5.72 ( semiri7260567687927622513x_real
% 5.46/5.72 @ ^ [I4: real] : ( plus_plus_real @ I4 @ one_one_real )
% 5.46/5.72 @ N2
% 5.46/5.72 @ zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_nat_code
% 5.46/5.72 thf(fact_8571_of__nat__code,axiom,
% 5.46/5.72 ( semiri1316708129612266289at_nat
% 5.46/5.72 = ( ^ [N2: nat] :
% 5.46/5.72 ( semiri8422978514062236437ux_nat
% 5.46/5.72 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ one_one_nat )
% 5.46/5.72 @ N2
% 5.46/5.72 @ zero_zero_nat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_nat_code
% 5.46/5.72 thf(fact_8572_of__nat__code,axiom,
% 5.46/5.72 ( semiri8010041392384452111omplex
% 5.46/5.72 = ( ^ [N2: nat] :
% 5.46/5.72 ( semiri2816024913162550771omplex
% 5.46/5.72 @ ^ [I4: complex] : ( plus_plus_complex @ I4 @ one_one_complex )
% 5.46/5.72 @ N2
% 5.46/5.72 @ zero_zero_complex ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_nat_code
% 5.46/5.72 thf(fact_8573_of__nat__code,axiom,
% 5.46/5.72 ( semiri681578069525770553at_rat
% 5.46/5.72 = ( ^ [N2: nat] :
% 5.46/5.72 ( semiri7787848453975740701ux_rat
% 5.46/5.72 @ ^ [I4: rat] : ( plus_plus_rat @ I4 @ one_one_rat )
% 5.46/5.72 @ N2
% 5.46/5.72 @ zero_zero_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_nat_code
% 5.46/5.72 thf(fact_8574_gchoose__row__sum__weighted,axiom,
% 5.46/5.72 ! [R: complex,M: nat] :
% 5.46/5.72 ( ( groups2073611262835488442omplex
% 5.46/5.72 @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ R @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.46/5.72 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R @ ( suc @ M ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gchoose_row_sum_weighted
% 5.46/5.72 thf(fact_8575_gchoose__row__sum__weighted,axiom,
% 5.46/5.72 ! [R: rat,M: nat] :
% 5.46/5.72 ( ( groups2906978787729119204at_rat
% 5.46/5.72 @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ R @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.46/5.72 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R @ ( suc @ M ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gchoose_row_sum_weighted
% 5.46/5.72 thf(fact_8576_gchoose__row__sum__weighted,axiom,
% 5.46/5.72 ! [R: real,M: nat] :
% 5.46/5.72 ( ( groups6591440286371151544t_real
% 5.46/5.72 @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ R @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ R @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.46/5.72 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R @ ( suc @ M ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gchoose_row_sum_weighted
% 5.46/5.72 thf(fact_8577_of__int__floor__cancel,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = X2 )
% 5.46/5.72 = ( ? [N2: int] :
% 5.46/5.72 ( X2
% 5.46/5.72 = ( ring_1_of_int_real @ N2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_int_floor_cancel
% 5.46/5.72 thf(fact_8578_of__int__floor__cancel,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = X2 )
% 5.46/5.72 = ( ? [N2: int] :
% 5.46/5.72 ( X2
% 5.46/5.72 = ( ring_1_of_int_rat @ N2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_int_floor_cancel
% 5.46/5.72 thf(fact_8579_gbinomial__0_I2_J,axiom,
% 5.46/5.72 ! [K: nat] :
% 5.46/5.72 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.46/5.72 = zero_zero_complex ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(2)
% 5.46/5.72 thf(fact_8580_gbinomial__0_I2_J,axiom,
% 5.46/5.72 ! [K: nat] :
% 5.46/5.72 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.46/5.72 = zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(2)
% 5.46/5.72 thf(fact_8581_gbinomial__0_I2_J,axiom,
% 5.46/5.72 ! [K: nat] :
% 5.46/5.72 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.46/5.72 = zero_zero_rat ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(2)
% 5.46/5.72 thf(fact_8582_gbinomial__0_I2_J,axiom,
% 5.46/5.72 ! [K: nat] :
% 5.46/5.72 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.46/5.72 = zero_zero_nat ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(2)
% 5.46/5.72 thf(fact_8583_gbinomial__0_I2_J,axiom,
% 5.46/5.72 ! [K: nat] :
% 5.46/5.72 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.46/5.72 = zero_zero_int ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(2)
% 5.46/5.72 thf(fact_8584_floor__numeral,axiom,
% 5.46/5.72 ! [V: num] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.46/5.72 = ( numeral_numeral_int @ V ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_numeral
% 5.46/5.72 thf(fact_8585_floor__numeral,axiom,
% 5.46/5.72 ! [V: num] :
% 5.46/5.72 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.46/5.72 = ( numeral_numeral_int @ V ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_numeral
% 5.46/5.72 thf(fact_8586_gbinomial__0_I1_J,axiom,
% 5.46/5.72 ! [A: complex] :
% 5.46/5.72 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(1)
% 5.46/5.72 thf(fact_8587_gbinomial__0_I1_J,axiom,
% 5.46/5.72 ! [A: real] :
% 5.46/5.72 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(1)
% 5.46/5.72 thf(fact_8588_gbinomial__0_I1_J,axiom,
% 5.46/5.72 ! [A: rat] :
% 5.46/5.72 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_rat ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(1)
% 5.46/5.72 thf(fact_8589_gbinomial__0_I1_J,axiom,
% 5.46/5.72 ! [A: nat] :
% 5.46/5.72 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_nat ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(1)
% 5.46/5.72 thf(fact_8590_gbinomial__0_I1_J,axiom,
% 5.46/5.72 ! [A: int] :
% 5.46/5.72 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_0(1)
% 5.46/5.72 thf(fact_8591_floor__one,axiom,
% 5.46/5.72 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.46/5.72 = one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % floor_one
% 5.46/5.72 thf(fact_8592_floor__one,axiom,
% 5.46/5.72 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 5.46/5.72 = one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % floor_one
% 5.46/5.72 thf(fact_8593_pochhammer__0,axiom,
% 5.46/5.72 ! [A: complex] :
% 5.46/5.72 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0
% 5.46/5.72 thf(fact_8594_pochhammer__0,axiom,
% 5.46/5.72 ! [A: real] :
% 5.46/5.72 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0
% 5.46/5.72 thf(fact_8595_pochhammer__0,axiom,
% 5.46/5.72 ! [A: rat] :
% 5.46/5.72 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_rat ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0
% 5.46/5.72 thf(fact_8596_pochhammer__0,axiom,
% 5.46/5.72 ! [A: nat] :
% 5.46/5.72 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_nat ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0
% 5.46/5.72 thf(fact_8597_pochhammer__0,axiom,
% 5.46/5.72 ! [A: int] :
% 5.46/5.72 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.46/5.72 = one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0
% 5.46/5.72 thf(fact_8598_floor__diff__of__int,axiom,
% 5.46/5.72 ! [X2: real,Z: int] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.46/5.72 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ Z ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_diff_of_int
% 5.46/5.72 thf(fact_8599_floor__diff__of__int,axiom,
% 5.46/5.72 ! [X2: rat,Z: int] :
% 5.46/5.72 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.46/5.72 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_diff_of_int
% 5.46/5.72 thf(fact_8600_zero__le__floor,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_le_floor
% 5.46/5.72 thf(fact_8601_zero__le__floor,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ zero_zero_rat @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_le_floor
% 5.46/5.72 thf(fact_8602_floor__less__zero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.46/5.72 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_zero
% 5.46/5.72 thf(fact_8603_floor__less__zero,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.46/5.72 = ( ord_less_rat @ X2 @ zero_zero_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_zero
% 5.46/5.72 thf(fact_8604_numeral__le__floor,axiom,
% 5.46/5.72 ! [V: num,X2: real] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_le_floor
% 5.46/5.72 thf(fact_8605_numeral__le__floor,axiom,
% 5.46/5.72 ! [V: num,X2: rat] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_le_floor
% 5.46/5.72 thf(fact_8606_zero__less__floor,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_floor
% 5.46/5.72 thf(fact_8607_zero__less__floor,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_floor
% 5.46/5.72 thf(fact_8608_floor__le__zero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.46/5.72 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_zero
% 5.46/5.72 thf(fact_8609_floor__le__zero,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.46/5.72 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_zero
% 5.46/5.72 thf(fact_8610_floor__less__numeral,axiom,
% 5.46/5.72 ! [X2: real,V: num] :
% 5.46/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.72 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_numeral
% 5.46/5.72 thf(fact_8611_floor__less__numeral,axiom,
% 5.46/5.72 ! [X2: rat,V: num] :
% 5.46/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.72 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_numeral
% 5.46/5.72 thf(fact_8612_one__le__floor,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_le_floor
% 5.46/5.72 thf(fact_8613_one__le__floor,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_le_floor
% 5.46/5.72 thf(fact_8614_floor__less__one,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.46/5.72 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_one
% 5.46/5.72 thf(fact_8615_floor__less__one,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.46/5.72 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_one
% 5.46/5.72 thf(fact_8616_floor__neg__numeral,axiom,
% 5.46/5.72 ! [V: num] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_neg_numeral
% 5.46/5.72 thf(fact_8617_floor__neg__numeral,axiom,
% 5.46/5.72 ! [V: num] :
% 5.46/5.72 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_neg_numeral
% 5.46/5.72 thf(fact_8618_floor__diff__numeral,axiom,
% 5.46/5.72 ! [X2: real,V: num] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.72 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_diff_numeral
% 5.46/5.72 thf(fact_8619_floor__diff__numeral,axiom,
% 5.46/5.72 ! [X2: rat,V: num] :
% 5.46/5.72 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.72 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_diff_numeral
% 5.46/5.72 thf(fact_8620_floor__diff__one,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.46/5.72 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_diff_one
% 5.46/5.72 thf(fact_8621_floor__diff__one,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.46/5.72 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_diff_one
% 5.46/5.72 thf(fact_8622_floor__numeral__power,axiom,
% 5.46/5.72 ! [X2: num,N: nat] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.46/5.72 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_numeral_power
% 5.46/5.72 thf(fact_8623_floor__numeral__power,axiom,
% 5.46/5.72 ! [X2: num,N: nat] :
% 5.46/5.72 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.46/5.72 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_numeral_power
% 5.46/5.72 thf(fact_8624_floor__divide__eq__div__numeral,axiom,
% 5.46/5.72 ! [A: num,B: num] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.46/5.72 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_eq_div_numeral
% 5.46/5.72 thf(fact_8625_numeral__less__floor,axiom,
% 5.46/5.72 ! [V: num,X2: real] :
% 5.46/5.72 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_less_floor
% 5.46/5.72 thf(fact_8626_numeral__less__floor,axiom,
% 5.46/5.72 ! [V: num,X2: rat] :
% 5.46/5.72 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_less_floor
% 5.46/5.72 thf(fact_8627_floor__le__numeral,axiom,
% 5.46/5.72 ! [X2: real,V: num] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.72 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_numeral
% 5.46/5.72 thf(fact_8628_floor__le__numeral,axiom,
% 5.46/5.72 ! [X2: rat,V: num] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.72 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_numeral
% 5.46/5.72 thf(fact_8629_one__less__floor,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_less_floor
% 5.46/5.72 thf(fact_8630_one__less__floor,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_less_floor
% 5.46/5.72 thf(fact_8631_floor__le__one,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.46/5.72 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_one
% 5.46/5.72 thf(fact_8632_floor__le__one,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.46/5.72 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_one
% 5.46/5.72 thf(fact_8633_neg__numeral__le__floor,axiom,
% 5.46/5.72 ! [V: num,X2: real] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_floor
% 5.46/5.72 thf(fact_8634_neg__numeral__le__floor,axiom,
% 5.46/5.72 ! [V: num,X2: rat] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_floor
% 5.46/5.72 thf(fact_8635_floor__less__neg__numeral,axiom,
% 5.46/5.72 ! [X2: real,V: num] :
% 5.46/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.72 = ( ord_less_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_neg_numeral
% 5.46/5.72 thf(fact_8636_floor__less__neg__numeral,axiom,
% 5.46/5.72 ! [X2: rat,V: num] :
% 5.46/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.72 = ( ord_less_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_neg_numeral
% 5.46/5.72 thf(fact_8637_floor__one__divide__eq__div__numeral,axiom,
% 5.46/5.72 ! [B: num] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.46/5.72 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_one_divide_eq_div_numeral
% 5.46/5.72 thf(fact_8638_floor__minus__divide__eq__div__numeral,axiom,
% 5.46/5.72 ! [A: num,B: num] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.46/5.72 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_minus_divide_eq_div_numeral
% 5.46/5.72 thf(fact_8639_neg__numeral__less__floor,axiom,
% 5.46/5.72 ! [V: num,X2: real] :
% 5.46/5.72 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_floor
% 5.46/5.72 thf(fact_8640_neg__numeral__less__floor,axiom,
% 5.46/5.72 ! [V: num,X2: rat] :
% 5.46/5.72 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_floor
% 5.46/5.72 thf(fact_8641_floor__le__neg__numeral,axiom,
% 5.46/5.72 ! [X2: real,V: num] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.72 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_neg_numeral
% 5.46/5.72 thf(fact_8642_floor__le__neg__numeral,axiom,
% 5.46/5.72 ! [X2: rat,V: num] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.72 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_neg_numeral
% 5.46/5.72 thf(fact_8643_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.46/5.72 ! [B: num] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.46/5.72 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_minus_one_divide_eq_div_numeral
% 5.46/5.72 thf(fact_8644_floor__mono,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_mono
% 5.46/5.72 thf(fact_8645_floor__mono,axiom,
% 5.46/5.72 ! [X2: rat,Y2: rat] :
% 5.46/5.72 ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_mono
% 5.46/5.72 thf(fact_8646_of__int__floor__le,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 ) ).
% 5.46/5.72
% 5.46/5.72 % of_int_floor_le
% 5.46/5.72 thf(fact_8647_of__int__floor__le,axiom,
% 5.46/5.72 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 ) ).
% 5.46/5.72
% 5.46/5.72 % of_int_floor_le
% 5.46/5.72 thf(fact_8648_floor__less__cancel,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y2 ) )
% 5.46/5.72 => ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_cancel
% 5.46/5.72 thf(fact_8649_floor__less__cancel,axiom,
% 5.46/5.72 ! [X2: rat,Y2: rat] :
% 5.46/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y2 ) )
% 5.46/5.72 => ( ord_less_rat @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_cancel
% 5.46/5.72 thf(fact_8650_pochhammer__pos,axiom,
% 5.46/5.72 ! [X2: real,N: nat] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_pos
% 5.46/5.72 thf(fact_8651_pochhammer__pos,axiom,
% 5.46/5.72 ! [X2: rat,N: nat] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.46/5.72 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_pos
% 5.46/5.72 thf(fact_8652_pochhammer__pos,axiom,
% 5.46/5.72 ! [X2: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.46/5.72 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_pos
% 5.46/5.72 thf(fact_8653_pochhammer__pos,axiom,
% 5.46/5.72 ! [X2: int,N: nat] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.46/5.72 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_pos
% 5.46/5.72 thf(fact_8654_pochhammer__neq__0__mono,axiom,
% 5.46/5.72 ! [A: complex,M: nat,N: nat] :
% 5.46/5.72 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.46/5.72 != zero_zero_complex )
% 5.46/5.72 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.72 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.46/5.72 != zero_zero_complex ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_neq_0_mono
% 5.46/5.72 thf(fact_8655_pochhammer__neq__0__mono,axiom,
% 5.46/5.72 ! [A: real,M: nat,N: nat] :
% 5.46/5.72 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.46/5.72 != zero_zero_real )
% 5.46/5.72 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.72 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.46/5.72 != zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_neq_0_mono
% 5.46/5.72 thf(fact_8656_pochhammer__neq__0__mono,axiom,
% 5.46/5.72 ! [A: rat,M: nat,N: nat] :
% 5.46/5.72 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.46/5.72 != zero_zero_rat )
% 5.46/5.72 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.72 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.46/5.72 != zero_zero_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_neq_0_mono
% 5.46/5.72 thf(fact_8657_pochhammer__eq__0__mono,axiom,
% 5.46/5.72 ! [A: complex,N: nat,M: nat] :
% 5.46/5.72 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.46/5.72 = zero_zero_complex )
% 5.46/5.72 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.72 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.46/5.72 = zero_zero_complex ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_eq_0_mono
% 5.46/5.72 thf(fact_8658_pochhammer__eq__0__mono,axiom,
% 5.46/5.72 ! [A: real,N: nat,M: nat] :
% 5.46/5.72 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.46/5.72 = zero_zero_real )
% 5.46/5.72 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.72 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.46/5.72 = zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_eq_0_mono
% 5.46/5.72 thf(fact_8659_pochhammer__eq__0__mono,axiom,
% 5.46/5.72 ! [A: rat,N: nat,M: nat] :
% 5.46/5.72 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.46/5.72 = zero_zero_rat )
% 5.46/5.72 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.72 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.46/5.72 = zero_zero_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_eq_0_mono
% 5.46/5.72 thf(fact_8660_pochhammer__fact,axiom,
% 5.46/5.72 ( semiri5044797733671781792omplex
% 5.46/5.72 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_fact
% 5.46/5.72 thf(fact_8661_pochhammer__fact,axiom,
% 5.46/5.72 ( semiri773545260158071498ct_rat
% 5.46/5.72 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_fact
% 5.46/5.72 thf(fact_8662_pochhammer__fact,axiom,
% 5.46/5.72 ( semiri1406184849735516958ct_int
% 5.46/5.72 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_fact
% 5.46/5.72 thf(fact_8663_pochhammer__fact,axiom,
% 5.46/5.72 ( semiri2265585572941072030t_real
% 5.46/5.72 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_fact
% 5.46/5.72 thf(fact_8664_pochhammer__fact,axiom,
% 5.46/5.72 ( semiri1408675320244567234ct_nat
% 5.46/5.72 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_fact
% 5.46/5.72 thf(fact_8665_le__floor__iff,axiom,
% 5.46/5.72 ! [Z: int,X2: real] :
% 5.46/5.72 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_floor_iff
% 5.46/5.72 thf(fact_8666_le__floor__iff,axiom,
% 5.46/5.72 ! [Z: int,X2: rat] :
% 5.46/5.72 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_floor_iff
% 5.46/5.72 thf(fact_8667_floor__less__iff,axiom,
% 5.46/5.72 ! [X2: real,Z: int] :
% 5.46/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.46/5.72 = ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_iff
% 5.46/5.72 thf(fact_8668_floor__less__iff,axiom,
% 5.46/5.72 ! [X2: rat,Z: int] :
% 5.46/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.46/5.72 = ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_less_iff
% 5.46/5.72 thf(fact_8669_le__floor__add,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y2 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_floor_add
% 5.46/5.72 thf(fact_8670_le__floor__add,axiom,
% 5.46/5.72 ! [X2: rat,Y2: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y2 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_floor_add
% 5.46/5.72 thf(fact_8671_floor__add__int,axiom,
% 5.46/5.72 ! [X2: real,Z: int] :
% 5.46/5.72 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.46/5.72 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_add_int
% 5.46/5.72 thf(fact_8672_floor__add__int,axiom,
% 5.46/5.72 ! [X2: rat,Z: int] :
% 5.46/5.72 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.46/5.72 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_add_int
% 5.46/5.72 thf(fact_8673_int__add__floor,axiom,
% 5.46/5.72 ! [Z: int,X2: real] :
% 5.46/5.72 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % int_add_floor
% 5.46/5.72 thf(fact_8674_int__add__floor,axiom,
% 5.46/5.72 ! [Z: int,X2: rat] :
% 5.46/5.72 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % int_add_floor
% 5.46/5.72 thf(fact_8675_floor__divide__of__int__eq,axiom,
% 5.46/5.72 ! [K: int,L2: int] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L2 ) ) )
% 5.46/5.72 = ( divide_divide_int @ K @ L2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_of_int_eq
% 5.46/5.72 thf(fact_8676_floor__divide__of__int__eq,axiom,
% 5.46/5.72 ! [K: int,L2: int] :
% 5.46/5.72 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L2 ) ) )
% 5.46/5.72 = ( divide_divide_int @ K @ L2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_of_int_eq
% 5.46/5.72 thf(fact_8677_gbinomial__pochhammer,axiom,
% 5.46/5.72 ( gbinomial_complex
% 5.46/5.72 = ( ^ [A3: complex,K2: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A3 ) @ K2 ) ) @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_pochhammer
% 5.46/5.72 thf(fact_8678_gbinomial__pochhammer,axiom,
% 5.46/5.72 ( gbinomial_rat
% 5.46/5.72 = ( ^ [A3: rat,K2: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A3 ) @ K2 ) ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_pochhammer
% 5.46/5.72 thf(fact_8679_gbinomial__pochhammer,axiom,
% 5.46/5.72 ( gbinomial_real
% 5.46/5.72 = ( ^ [A3: real,K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A3 ) @ K2 ) ) @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_pochhammer
% 5.46/5.72 thf(fact_8680_gbinomial__pochhammer_H,axiom,
% 5.46/5.72 ( gbinomial_complex
% 5.46/5.72 = ( ^ [A3: complex,K2: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_pochhammer'
% 5.46/5.72 thf(fact_8681_gbinomial__pochhammer_H,axiom,
% 5.46/5.72 ( gbinomial_rat
% 5.46/5.72 = ( ^ [A3: rat,K2: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_pochhammer'
% 5.46/5.72 thf(fact_8682_gbinomial__pochhammer_H,axiom,
% 5.46/5.72 ( gbinomial_real
% 5.46/5.72 = ( ^ [A3: real,K2: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_pochhammer'
% 5.46/5.72 thf(fact_8683_floor__power,axiom,
% 5.46/5.72 ! [X2: real,N: nat] :
% 5.46/5.72 ( ( X2
% 5.46/5.72 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) )
% 5.46/5.72 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X2 @ N ) )
% 5.46/5.72 = ( power_power_int @ ( archim6058952711729229775r_real @ X2 ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_power
% 5.46/5.72 thf(fact_8684_floor__power,axiom,
% 5.46/5.72 ! [X2: rat,N: nat] :
% 5.46/5.72 ( ( X2
% 5.46/5.72 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) )
% 5.46/5.72 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X2 @ N ) )
% 5.46/5.72 = ( power_power_int @ ( archim3151403230148437115or_rat @ X2 ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_power
% 5.46/5.72 thf(fact_8685_gbinomial__Suc__Suc,axiom,
% 5.46/5.72 ! [A: complex,K: nat] :
% 5.46/5.72 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.46/5.72 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_Suc_Suc
% 5.46/5.72 thf(fact_8686_gbinomial__Suc__Suc,axiom,
% 5.46/5.72 ! [A: real,K: nat] :
% 5.46/5.72 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.46/5.72 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_Suc_Suc
% 5.46/5.72 thf(fact_8687_gbinomial__Suc__Suc,axiom,
% 5.46/5.72 ! [A: rat,K: nat] :
% 5.46/5.72 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.46/5.72 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_Suc_Suc
% 5.46/5.72 thf(fact_8688_gbinomial__of__nat__symmetric,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.46/5.72 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_of_nat_symmetric
% 5.46/5.72 thf(fact_8689_gbinomial__of__nat__symmetric,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K )
% 5.46/5.72 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_of_nat_symmetric
% 5.46/5.72 thf(fact_8690_gbinomial__of__nat__symmetric,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 5.46/5.72 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_of_nat_symmetric
% 5.46/5.72 thf(fact_8691_pochhammer__nonneg,axiom,
% 5.46/5.72 ! [X2: real,N: nat] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_nonneg
% 5.46/5.72 thf(fact_8692_pochhammer__nonneg,axiom,
% 5.46/5.72 ! [X2: rat,N: nat] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.46/5.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_nonneg
% 5.46/5.72 thf(fact_8693_pochhammer__nonneg,axiom,
% 5.46/5.72 ! [X2: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.46/5.72 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_nonneg
% 5.46/5.72 thf(fact_8694_pochhammer__nonneg,axiom,
% 5.46/5.72 ! [X2: int,N: nat] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.46/5.72 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_nonneg
% 5.46/5.72 thf(fact_8695_pochhammer__0__left,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( N = zero_zero_nat )
% 5.46/5.72 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.46/5.72 = one_one_complex ) )
% 5.46/5.72 & ( ( N != zero_zero_nat )
% 5.46/5.72 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.46/5.72 = zero_zero_complex ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0_left
% 5.46/5.72 thf(fact_8696_pochhammer__0__left,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( N = zero_zero_nat )
% 5.46/5.72 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.46/5.72 = one_one_real ) )
% 5.46/5.72 & ( ( N != zero_zero_nat )
% 5.46/5.72 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.46/5.72 = zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0_left
% 5.46/5.72 thf(fact_8697_pochhammer__0__left,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( N = zero_zero_nat )
% 5.46/5.72 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.46/5.72 = one_one_rat ) )
% 5.46/5.72 & ( ( N != zero_zero_nat )
% 5.46/5.72 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.46/5.72 = zero_zero_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0_left
% 5.46/5.72 thf(fact_8698_pochhammer__0__left,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( N = zero_zero_nat )
% 5.46/5.72 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.46/5.72 = one_one_nat ) )
% 5.46/5.72 & ( ( N != zero_zero_nat )
% 5.46/5.72 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.46/5.72 = zero_zero_nat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0_left
% 5.46/5.72 thf(fact_8699_pochhammer__0__left,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( N = zero_zero_nat )
% 5.46/5.72 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.46/5.72 = one_one_int ) )
% 5.46/5.72 & ( ( N != zero_zero_nat )
% 5.46/5.72 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.46/5.72 = zero_zero_int ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_0_left
% 5.46/5.72 thf(fact_8700_one__add__floor,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.46/5.72 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_add_floor
% 5.46/5.72 thf(fact_8701_one__add__floor,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.46/5.72 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_add_floor
% 5.46/5.72 thf(fact_8702_floor__divide__of__nat__eq,axiom,
% 5.46/5.72 ! [M: nat,N: nat] :
% 5.46/5.72 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.72 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_of_nat_eq
% 5.46/5.72 thf(fact_8703_floor__divide__of__nat__eq,axiom,
% 5.46/5.72 ! [M: nat,N: nat] :
% 5.46/5.72 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 5.46/5.72 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_of_nat_eq
% 5.46/5.72 thf(fact_8704_gbinomial__addition__formula,axiom,
% 5.46/5.72 ! [A: complex,K: nat] :
% 5.46/5.72 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.46/5.72 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_addition_formula
% 5.46/5.72 thf(fact_8705_gbinomial__addition__formula,axiom,
% 5.46/5.72 ! [A: real,K: nat] :
% 5.46/5.72 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.46/5.72 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_addition_formula
% 5.46/5.72 thf(fact_8706_gbinomial__addition__formula,axiom,
% 5.46/5.72 ! [A: rat,K: nat] :
% 5.46/5.72 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.46/5.72 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_addition_formula
% 5.46/5.72 thf(fact_8707_ceiling__diff__floor__le__1,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim6058952711729229775r_real @ X2 ) ) @ one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % ceiling_diff_floor_le_1
% 5.46/5.72 thf(fact_8708_ceiling__diff__floor__le__1,axiom,
% 5.46/5.72 ! [X2: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim3151403230148437115or_rat @ X2 ) ) @ one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % ceiling_diff_floor_le_1
% 5.46/5.72 thf(fact_8709_gbinomial__absorb__comp,axiom,
% 5.46/5.72 ! [A: real,K: nat] :
% 5.46/5.72 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.46/5.72 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_absorb_comp
% 5.46/5.72 thf(fact_8710_gbinomial__absorb__comp,axiom,
% 5.46/5.72 ! [A: complex,K: nat] :
% 5.46/5.72 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.46/5.72 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_absorb_comp
% 5.46/5.72 thf(fact_8711_gbinomial__absorb__comp,axiom,
% 5.46/5.72 ! [A: rat,K: nat] :
% 5.46/5.72 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.46/5.72 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_absorb_comp
% 5.46/5.72 thf(fact_8712_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.46/5.72 ! [K: nat,A: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.46/5.72 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_ge_n_over_k_pow_k
% 5.46/5.72 thf(fact_8713_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.46/5.72 ! [K: nat,A: rat] :
% 5.46/5.72 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.46/5.72 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_ge_n_over_k_pow_k
% 5.46/5.72 thf(fact_8714_gbinomial__mult__1,axiom,
% 5.46/5.72 ! [A: real,K: nat] :
% 5.46/5.72 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.46/5.72 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_mult_1
% 5.46/5.72 thf(fact_8715_gbinomial__mult__1,axiom,
% 5.46/5.72 ! [A: complex,K: nat] :
% 5.46/5.72 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 5.46/5.72 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_mult_1
% 5.46/5.72 thf(fact_8716_gbinomial__mult__1,axiom,
% 5.46/5.72 ! [A: rat,K: nat] :
% 5.46/5.72 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.46/5.72 = ( 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 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_mult_1
% 5.46/5.72 thf(fact_8717_gbinomial__mult__1_H,axiom,
% 5.46/5.72 ! [A: real,K: nat] :
% 5.46/5.72 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.46/5.72 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_mult_1'
% 5.46/5.72 thf(fact_8718_gbinomial__mult__1_H,axiom,
% 5.46/5.72 ! [A: complex,K: nat] :
% 5.46/5.72 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 5.46/5.72 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_mult_1'
% 5.46/5.72 thf(fact_8719_gbinomial__mult__1_H,axiom,
% 5.46/5.72 ! [A: rat,K: nat] :
% 5.46/5.72 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.46/5.72 = ( 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 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_mult_1'
% 5.46/5.72 thf(fact_8720_floor__eq,axiom,
% 5.46/5.72 ! [N: int,X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.46/5.72 => ( ( archim6058952711729229775r_real @ X2 )
% 5.46/5.72 = N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_eq
% 5.46/5.72 thf(fact_8721_real__of__int__floor__add__one__gt,axiom,
% 5.46/5.72 ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_of_int_floor_add_one_gt
% 5.46/5.72 thf(fact_8722_real__of__int__floor__add__one__ge,axiom,
% 5.46/5.72 ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_of_int_floor_add_one_ge
% 5.46/5.72 thf(fact_8723_real__of__int__floor__gt__diff__one,axiom,
% 5.46/5.72 ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_of_int_floor_gt_diff_one
% 5.46/5.72 thf(fact_8724_real__of__int__floor__ge__diff__one,axiom,
% 5.46/5.72 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_of_int_floor_ge_diff_one
% 5.46/5.72 thf(fact_8725_pochhammer__rec,axiom,
% 5.46/5.72 ! [A: complex,N: nat] :
% 5.46/5.72 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec
% 5.46/5.72 thf(fact_8726_pochhammer__rec,axiom,
% 5.46/5.72 ! [A: real,N: nat] :
% 5.46/5.72 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec
% 5.46/5.72 thf(fact_8727_pochhammer__rec,axiom,
% 5.46/5.72 ! [A: rat,N: nat] :
% 5.46/5.72 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec
% 5.46/5.72 thf(fact_8728_pochhammer__rec,axiom,
% 5.46/5.72 ! [A: nat,N: nat] :
% 5.46/5.72 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec
% 5.46/5.72 thf(fact_8729_pochhammer__rec,axiom,
% 5.46/5.72 ! [A: int,N: nat] :
% 5.46/5.72 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec
% 5.46/5.72 thf(fact_8730_pochhammer__Suc,axiom,
% 5.46/5.72 ! [A: int,N: nat] :
% 5.46/5.72 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_Suc
% 5.46/5.72 thf(fact_8731_pochhammer__Suc,axiom,
% 5.46/5.72 ! [A: real,N: nat] :
% 5.46/5.72 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_Suc
% 5.46/5.72 thf(fact_8732_pochhammer__Suc,axiom,
% 5.46/5.72 ! [A: nat,N: nat] :
% 5.46/5.72 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_Suc
% 5.46/5.72 thf(fact_8733_pochhammer__Suc,axiom,
% 5.46/5.72 ! [A: complex,N: nat] :
% 5.46/5.72 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_Suc
% 5.46/5.72 thf(fact_8734_pochhammer__Suc,axiom,
% 5.46/5.72 ! [A: rat,N: nat] :
% 5.46/5.72 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_Suc
% 5.46/5.72 thf(fact_8735_pochhammer__rec_H,axiom,
% 5.46/5.72 ! [Z: int,N: nat] :
% 5.46/5.72 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec'
% 5.46/5.72 thf(fact_8736_pochhammer__rec_H,axiom,
% 5.46/5.72 ! [Z: real,N: nat] :
% 5.46/5.72 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec'
% 5.46/5.72 thf(fact_8737_pochhammer__rec_H,axiom,
% 5.46/5.72 ! [Z: nat,N: nat] :
% 5.46/5.72 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec'
% 5.46/5.72 thf(fact_8738_pochhammer__rec_H,axiom,
% 5.46/5.72 ! [Z: complex,N: nat] :
% 5.46/5.72 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec'
% 5.46/5.72 thf(fact_8739_pochhammer__rec_H,axiom,
% 5.46/5.72 ! [Z: rat,N: nat] :
% 5.46/5.72 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 5.46/5.72 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_rec'
% 5.46/5.72 thf(fact_8740_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_nat @ N @ K )
% 5.46/5.72 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.46/5.72 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.72 thf(fact_8741_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_nat @ N @ K )
% 5.46/5.72 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.46/5.72 = zero_zero_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.72 thf(fact_8742_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_nat @ N @ K )
% 5.46/5.72 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.46/5.72 = zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.72 thf(fact_8743_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_nat @ N @ K )
% 5.46/5.72 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.46/5.72 = zero_zero_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.72 thf(fact_8744_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_nat @ N @ K )
% 5.46/5.72 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.46/5.72 = zero_zero_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.72 thf(fact_8745_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.46/5.72 = zero_z3403309356797280102nteger )
% 5.46/5.72 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_iff
% 5.46/5.72 thf(fact_8746_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_iff
% 5.46/5.72 thf(fact_8747_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.46/5.72 = zero_zero_real )
% 5.46/5.72 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_iff
% 5.46/5.72 thf(fact_8748_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.46/5.72 = zero_zero_complex )
% 5.46/5.72 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_iff
% 5.46/5.72 thf(fact_8749_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.46/5.72 = zero_zero_rat )
% 5.46/5.72 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_iff
% 5.46/5.72 thf(fact_8750_pochhammer__eq__0__iff,axiom,
% 5.46/5.72 ! [A: real,N: nat] :
% 5.46/5.72 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.46/5.72 = zero_zero_real )
% 5.46/5.72 = ( ? [K2: nat] :
% 5.46/5.72 ( ( ord_less_nat @ K2 @ N )
% 5.46/5.72 & ( A
% 5.46/5.72 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_eq_0_iff
% 5.46/5.72 thf(fact_8751_pochhammer__eq__0__iff,axiom,
% 5.46/5.72 ! [A: complex,N: nat] :
% 5.46/5.72 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.46/5.72 = zero_zero_complex )
% 5.46/5.72 = ( ? [K2: nat] :
% 5.46/5.72 ( ( ord_less_nat @ K2 @ N )
% 5.46/5.72 & ( A
% 5.46/5.72 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_eq_0_iff
% 5.46/5.72 thf(fact_8752_pochhammer__eq__0__iff,axiom,
% 5.46/5.72 ! [A: rat,N: nat] :
% 5.46/5.72 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.46/5.72 = zero_zero_rat )
% 5.46/5.72 = ( ? [K2: nat] :
% 5.46/5.72 ( ( ord_less_nat @ K2 @ N )
% 5.46/5.72 & ( A
% 5.46/5.72 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_eq_0_iff
% 5.46/5.72 thf(fact_8753_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.46/5.72 != zero_z3403309356797280102nteger ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.72 thf(fact_8754_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.46/5.72 != zero_zero_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.72 thf(fact_8755_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.46/5.72 != zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.72 thf(fact_8756_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.46/5.72 != zero_zero_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.72 thf(fact_8757_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.46/5.72 != zero_zero_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.72 thf(fact_8758_pochhammer__product_H,axiom,
% 5.46/5.72 ! [Z: int,N: nat,M: nat] :
% 5.46/5.72 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.72 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product'
% 5.46/5.72 thf(fact_8759_pochhammer__product_H,axiom,
% 5.46/5.72 ! [Z: real,N: nat,M: nat] :
% 5.46/5.72 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.72 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product'
% 5.46/5.72 thf(fact_8760_pochhammer__product_H,axiom,
% 5.46/5.72 ! [Z: nat,N: nat,M: nat] :
% 5.46/5.72 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.72 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product'
% 5.46/5.72 thf(fact_8761_pochhammer__product_H,axiom,
% 5.46/5.72 ! [Z: complex,N: nat,M: nat] :
% 5.46/5.72 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.72 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product'
% 5.46/5.72 thf(fact_8762_pochhammer__product_H,axiom,
% 5.46/5.72 ! [Z: rat,N: nat,M: nat] :
% 5.46/5.72 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.72 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product'
% 5.46/5.72 thf(fact_8763_floor__split,axiom,
% 5.46/5.72 ! [P: int > $o,T: real] :
% 5.46/5.72 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.46/5.72 = ( ! [I4: int] :
% 5.46/5.72 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I4 ) @ T )
% 5.46/5.72 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) ) )
% 5.46/5.72 => ( P @ I4 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_split
% 5.46/5.72 thf(fact_8764_floor__split,axiom,
% 5.46/5.72 ! [P: int > $o,T: rat] :
% 5.46/5.72 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 5.46/5.72 = ( ! [I4: int] :
% 5.46/5.72 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I4 ) @ T )
% 5.46/5.72 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) ) )
% 5.46/5.72 => ( P @ I4 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_split
% 5.46/5.72 thf(fact_8765_floor__eq__iff,axiom,
% 5.46/5.72 ! [X2: real,A: int] :
% 5.46/5.72 ( ( ( archim6058952711729229775r_real @ X2 )
% 5.46/5.72 = A )
% 5.46/5.72 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X2 )
% 5.46/5.72 & ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_eq_iff
% 5.46/5.72 thf(fact_8766_floor__eq__iff,axiom,
% 5.46/5.72 ! [X2: rat,A: int] :
% 5.46/5.72 ( ( ( archim3151403230148437115or_rat @ X2 )
% 5.46/5.72 = A )
% 5.46/5.72 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X2 )
% 5.46/5.72 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_eq_iff
% 5.46/5.72 thf(fact_8767_floor__unique,axiom,
% 5.46/5.72 ! [Z: int,X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.46/5.72 => ( ( archim6058952711729229775r_real @ X2 )
% 5.46/5.72 = Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_unique
% 5.46/5.72 thf(fact_8768_floor__unique,axiom,
% 5.46/5.72 ! [Z: int,X2: rat] :
% 5.46/5.72 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 )
% 5.46/5.72 => ( ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.46/5.72 => ( ( archim3151403230148437115or_rat @ X2 )
% 5.46/5.72 = Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_unique
% 5.46/5.72 thf(fact_8769_le__mult__floor,axiom,
% 5.46/5.72 ! [A: real,B: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.46/5.72 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_mult_floor
% 5.46/5.72 thf(fact_8770_le__mult__floor,axiom,
% 5.46/5.72 ! [A: rat,B: rat] :
% 5.46/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.46/5.72 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_mult_floor
% 5.46/5.72 thf(fact_8771_less__floor__iff,axiom,
% 5.46/5.72 ! [Z: int,X2: real] :
% 5.46/5.72 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_floor_iff
% 5.46/5.72 thf(fact_8772_less__floor__iff,axiom,
% 5.46/5.72 ! [Z: int,X2: rat] :
% 5.46/5.72 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_floor_iff
% 5.46/5.72 thf(fact_8773_floor__le__iff,axiom,
% 5.46/5.72 ! [X2: real,Z: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.46/5.72 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_iff
% 5.46/5.72 thf(fact_8774_floor__le__iff,axiom,
% 5.46/5.72 ! [X2: rat,Z: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.46/5.72 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_le_iff
% 5.46/5.72 thf(fact_8775_floor__correct,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 )
% 5.46/5.72 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_correct
% 5.46/5.72 thf(fact_8776_floor__correct,axiom,
% 5.46/5.72 ! [X2: rat] :
% 5.46/5.72 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 )
% 5.46/5.72 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_correct
% 5.46/5.72 thf(fact_8777_floor__eq2,axiom,
% 5.46/5.72 ! [N: int,X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.46/5.72 => ( ( archim6058952711729229775r_real @ X2 )
% 5.46/5.72 = N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_eq2
% 5.46/5.72 thf(fact_8778_Suc__times__gbinomial,axiom,
% 5.46/5.72 ! [K: nat,A: real] :
% 5.46/5.72 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.46/5.72 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Suc_times_gbinomial
% 5.46/5.72 thf(fact_8779_Suc__times__gbinomial,axiom,
% 5.46/5.72 ! [K: nat,A: complex] :
% 5.46/5.72 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.46/5.72 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Suc_times_gbinomial
% 5.46/5.72 thf(fact_8780_Suc__times__gbinomial,axiom,
% 5.46/5.72 ! [K: nat,A: rat] :
% 5.46/5.72 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.46/5.72 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Suc_times_gbinomial
% 5.46/5.72 thf(fact_8781_gbinomial__absorption,axiom,
% 5.46/5.72 ! [K: nat,A: real] :
% 5.46/5.72 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.46/5.72 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_absorption
% 5.46/5.72 thf(fact_8782_gbinomial__absorption,axiom,
% 5.46/5.72 ! [K: nat,A: complex] :
% 5.46/5.72 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.46/5.72 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_absorption
% 5.46/5.72 thf(fact_8783_gbinomial__absorption,axiom,
% 5.46/5.72 ! [K: nat,A: rat] :
% 5.46/5.72 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.46/5.72 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_absorption
% 5.46/5.72 thf(fact_8784_floor__divide__real__eq__div,axiom,
% 5.46/5.72 ! [B: int,A: real] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.46/5.72 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.46/5.72 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_real_eq_div
% 5.46/5.72 thf(fact_8785_gbinomial__trinomial__revision,axiom,
% 5.46/5.72 ! [K: nat,M: nat,A: real] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ M )
% 5.46/5.72 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.46/5.72 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_trinomial_revision
% 5.46/5.72 thf(fact_8786_gbinomial__trinomial__revision,axiom,
% 5.46/5.72 ! [K: nat,M: nat,A: complex] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ M )
% 5.46/5.72 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 5.46/5.72 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_trinomial_revision
% 5.46/5.72 thf(fact_8787_gbinomial__trinomial__revision,axiom,
% 5.46/5.72 ! [K: nat,M: nat,A: rat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ M )
% 5.46/5.72 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.46/5.72 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_trinomial_revision
% 5.46/5.72 thf(fact_8788_pochhammer__product,axiom,
% 5.46/5.72 ! [M: nat,N: nat,Z: int] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.72 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 5.46/5.72 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product
% 5.46/5.72 thf(fact_8789_pochhammer__product,axiom,
% 5.46/5.72 ! [M: nat,N: nat,Z: real] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.72 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 5.46/5.72 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product
% 5.46/5.72 thf(fact_8790_pochhammer__product,axiom,
% 5.46/5.72 ! [M: nat,N: nat,Z: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.72 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 5.46/5.72 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product
% 5.46/5.72 thf(fact_8791_pochhammer__product,axiom,
% 5.46/5.72 ! [M: nat,N: nat,Z: complex] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.72 => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 5.46/5.72 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product
% 5.46/5.72 thf(fact_8792_pochhammer__product,axiom,
% 5.46/5.72 ! [M: nat,N: nat,Z: rat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.72 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 5.46/5.72 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_product
% 5.46/5.72 thf(fact_8793_floor__divide__lower,axiom,
% 5.46/5.72 ! [Q2: real,P2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q2 ) ) ) @ Q2 ) @ P2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_lower
% 5.46/5.72 thf(fact_8794_floor__divide__lower,axiom,
% 5.46/5.72 ! [Q2: rat,P2: rat] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.46/5.72 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q2 ) ) ) @ Q2 ) @ P2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_lower
% 5.46/5.72 thf(fact_8795_gbinomial__rec,axiom,
% 5.46/5.72 ! [A: real,K: nat] :
% 5.46/5.72 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.46/5.72 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_rec
% 5.46/5.72 thf(fact_8796_gbinomial__rec,axiom,
% 5.46/5.72 ! [A: complex,K: nat] :
% 5.46/5.72 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.46/5.72 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_rec
% 5.46/5.72 thf(fact_8797_gbinomial__rec,axiom,
% 5.46/5.72 ! [A: rat,K: nat] :
% 5.46/5.72 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.46/5.72 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_rec
% 5.46/5.72 thf(fact_8798_gbinomial__factors,axiom,
% 5.46/5.72 ! [A: real,K: nat] :
% 5.46/5.72 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.46/5.72 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_factors
% 5.46/5.72 thf(fact_8799_gbinomial__factors,axiom,
% 5.46/5.72 ! [A: complex,K: nat] :
% 5.46/5.72 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.46/5.72 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_factors
% 5.46/5.72 thf(fact_8800_gbinomial__factors,axiom,
% 5.46/5.72 ! [A: rat,K: nat] :
% 5.46/5.72 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.46/5.72 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_factors
% 5.46/5.72 thf(fact_8801_gbinomial__negated__upper,axiom,
% 5.46/5.72 ( gbinomial_real
% 5.46/5.72 = ( ^ [A3: real,K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K2 ) @ A3 ) @ one_one_real ) @ K2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_negated_upper
% 5.46/5.72 thf(fact_8802_gbinomial__negated__upper,axiom,
% 5.46/5.72 ( gbinomial_complex
% 5.46/5.72 = ( ^ [A3: complex,K2: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K2 ) @ A3 ) @ one_one_complex ) @ K2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_negated_upper
% 5.46/5.72 thf(fact_8803_gbinomial__negated__upper,axiom,
% 5.46/5.72 ( gbinomial_rat
% 5.46/5.72 = ( ^ [A3: rat,K2: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A3 ) @ one_one_rat ) @ K2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_negated_upper
% 5.46/5.72 thf(fact_8804_gbinomial__index__swap,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K ) )
% 5.46/5.72 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_index_swap
% 5.46/5.72 thf(fact_8805_gbinomial__index__swap,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.46/5.72 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_index_swap
% 5.46/5.72 thf(fact_8806_gbinomial__index__swap,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 5.46/5.72 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_index_swap
% 5.46/5.72 thf(fact_8807_pochhammer__absorb__comp,axiom,
% 5.46/5.72 ! [R: code_integer,K: nat] :
% 5.46/5.72 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R ) @ K ) )
% 5.46/5.72 = ( times_3573771949741848930nteger @ R @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_absorb_comp
% 5.46/5.72 thf(fact_8808_pochhammer__absorb__comp,axiom,
% 5.46/5.72 ! [R: int,K: nat] :
% 5.46/5.72 ( ( times_times_int @ ( minus_minus_int @ R @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R ) @ K ) )
% 5.46/5.72 = ( times_times_int @ R @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R ) @ one_one_int ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_absorb_comp
% 5.46/5.72 thf(fact_8809_pochhammer__absorb__comp,axiom,
% 5.46/5.72 ! [R: real,K: nat] :
% 5.46/5.72 ( ( times_times_real @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R ) @ K ) )
% 5.46/5.72 = ( times_times_real @ R @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R ) @ one_one_real ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_absorb_comp
% 5.46/5.72 thf(fact_8810_pochhammer__absorb__comp,axiom,
% 5.46/5.72 ! [R: complex,K: nat] :
% 5.46/5.72 ( ( times_times_complex @ ( minus_minus_complex @ R @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R ) @ K ) )
% 5.46/5.72 = ( times_times_complex @ R @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R ) @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_absorb_comp
% 5.46/5.72 thf(fact_8811_pochhammer__absorb__comp,axiom,
% 5.46/5.72 ! [R: rat,K: nat] :
% 5.46/5.72 ( ( times_times_rat @ ( minus_minus_rat @ R @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R ) @ K ) )
% 5.46/5.72 = ( times_times_rat @ R @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R ) @ one_one_rat ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_absorb_comp
% 5.46/5.72 thf(fact_8812_floor__divide__upper,axiom,
% 5.46/5.72 ! [Q2: real,P2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.46/5.72 => ( ord_less_real @ P2 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_upper
% 5.46/5.72 thf(fact_8813_floor__divide__upper,axiom,
% 5.46/5.72 ! [Q2: rat,P2: rat] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.46/5.72 => ( ord_less_rat @ P2 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_divide_upper
% 5.46/5.72 thf(fact_8814_pochhammer__same,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.46/5.72 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_same
% 5.46/5.72 thf(fact_8815_pochhammer__same,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.46/5.72 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_same
% 5.46/5.72 thf(fact_8816_pochhammer__same,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.46/5.72 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_same
% 5.46/5.72 thf(fact_8817_pochhammer__same,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.46/5.72 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_same
% 5.46/5.72 thf(fact_8818_pochhammer__same,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.46/5.72 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_same
% 5.46/5.72 thf(fact_8819_round__def,axiom,
% 5.46/5.72 ( archim8280529875227126926d_real
% 5.46/5.72 = ( ^ [X: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % round_def
% 5.46/5.72 thf(fact_8820_round__def,axiom,
% 5.46/5.72 ( archim7778729529865785530nd_rat
% 5.46/5.72 = ( ^ [X: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % round_def
% 5.46/5.72 thf(fact_8821_gbinomial__minus,axiom,
% 5.46/5.72 ! [A: real,K: nat] :
% 5.46/5.72 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.46/5.72 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_minus
% 5.46/5.72 thf(fact_8822_gbinomial__minus,axiom,
% 5.46/5.72 ! [A: complex,K: nat] :
% 5.46/5.72 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.46/5.72 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_minus
% 5.46/5.72 thf(fact_8823_gbinomial__minus,axiom,
% 5.46/5.72 ! [A: rat,K: nat] :
% 5.46/5.72 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.46/5.72 = ( 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 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_minus
% 5.46/5.72 thf(fact_8824_gbinomial__reduce__nat,axiom,
% 5.46/5.72 ! [K: nat,A: complex] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.72 => ( ( gbinomial_complex @ A @ K )
% 5.46/5.72 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_reduce_nat
% 5.46/5.72 thf(fact_8825_gbinomial__reduce__nat,axiom,
% 5.46/5.72 ! [K: nat,A: real] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.72 => ( ( gbinomial_real @ A @ K )
% 5.46/5.72 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_reduce_nat
% 5.46/5.72 thf(fact_8826_gbinomial__reduce__nat,axiom,
% 5.46/5.72 ! [K: nat,A: rat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.72 => ( ( gbinomial_rat @ A @ K )
% 5.46/5.72 = ( 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 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_reduce_nat
% 5.46/5.72 thf(fact_8827_pochhammer__minus_H,axiom,
% 5.46/5.72 ! [B: code_integer,K: nat] :
% 5.46/5.72 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.46/5.72 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus'
% 5.46/5.72 thf(fact_8828_pochhammer__minus_H,axiom,
% 5.46/5.72 ! [B: int,K: nat] :
% 5.46/5.72 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.46/5.72 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus'
% 5.46/5.72 thf(fact_8829_pochhammer__minus_H,axiom,
% 5.46/5.72 ! [B: real,K: nat] :
% 5.46/5.72 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.46/5.72 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus'
% 5.46/5.72 thf(fact_8830_pochhammer__minus_H,axiom,
% 5.46/5.72 ! [B: complex,K: nat] :
% 5.46/5.72 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.46/5.72 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus'
% 5.46/5.72 thf(fact_8831_pochhammer__minus_H,axiom,
% 5.46/5.72 ! [B: rat,K: nat] :
% 5.46/5.72 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.46/5.72 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus'
% 5.46/5.72 thf(fact_8832_pochhammer__minus,axiom,
% 5.46/5.72 ! [B: code_integer,K: nat] :
% 5.46/5.72 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.46/5.72 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus
% 5.46/5.72 thf(fact_8833_pochhammer__minus,axiom,
% 5.46/5.72 ! [B: int,K: nat] :
% 5.46/5.72 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.46/5.72 = ( 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 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus
% 5.46/5.72 thf(fact_8834_pochhammer__minus,axiom,
% 5.46/5.72 ! [B: real,K: nat] :
% 5.46/5.72 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.46/5.72 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus
% 5.46/5.72 thf(fact_8835_pochhammer__minus,axiom,
% 5.46/5.72 ! [B: complex,K: nat] :
% 5.46/5.72 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.46/5.72 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus
% 5.46/5.72 thf(fact_8836_pochhammer__minus,axiom,
% 5.46/5.72 ! [B: rat,K: nat] :
% 5.46/5.72 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.46/5.72 = ( 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 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_minus
% 5.46/5.72 thf(fact_8837_gbinomial__sum__up__index,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( groups2073611262835488442omplex
% 5.46/5.72 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.72 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_sum_up_index
% 5.46/5.72 thf(fact_8838_gbinomial__sum__up__index,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( groups2906978787729119204at_rat
% 5.46/5.72 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.72 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_sum_up_index
% 5.46/5.72 thf(fact_8839_gbinomial__sum__up__index,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( groups6591440286371151544t_real
% 5.46/5.72 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.72 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_sum_up_index
% 5.46/5.72 thf(fact_8840_floor__log__eq__powr__iff,axiom,
% 5.46/5.72 ! [X2: real,B: real,K: int] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.72 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X2 ) )
% 5.46/5.72 = K )
% 5.46/5.72 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X2 )
% 5.46/5.72 & ( ord_less_real @ X2 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_log_eq_powr_iff
% 5.46/5.72 thf(fact_8841_gbinomial__absorption_H,axiom,
% 5.46/5.72 ! [K: nat,A: real] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.72 => ( ( gbinomial_real @ A @ K )
% 5.46/5.72 = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_absorption'
% 5.46/5.72 thf(fact_8842_gbinomial__absorption_H,axiom,
% 5.46/5.72 ! [K: nat,A: complex] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.72 => ( ( gbinomial_complex @ A @ K )
% 5.46/5.72 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_absorption'
% 5.46/5.72 thf(fact_8843_gbinomial__absorption_H,axiom,
% 5.46/5.72 ! [K: nat,A: rat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.72 => ( ( gbinomial_rat @ A @ K )
% 5.46/5.72 = ( 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 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_absorption'
% 5.46/5.72 thf(fact_8844_floor__log2__div2,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.72 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_log2_div2
% 5.46/5.72 thf(fact_8845_fact__double,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.72 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % fact_double
% 5.46/5.72 thf(fact_8846_fact__double,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.72 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % fact_double
% 5.46/5.72 thf(fact_8847_fact__double,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.72 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % fact_double
% 5.46/5.72 thf(fact_8848_floor__log__nat__eq__if,axiom,
% 5.46/5.72 ! [B: nat,N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.46/5.72 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.46/5.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.46/5.72 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.46/5.72 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_log_nat_eq_if
% 5.46/5.72 thf(fact_8849_gbinomial__code,axiom,
% 5.46/5.72 ( gbinomial_complex
% 5.46/5.72 = ( ^ [A3: complex,K2: nat] :
% 5.46/5.72 ( if_complex @ ( K2 = zero_zero_nat ) @ one_one_complex
% 5.46/5.72 @ ( divide1717551699836669952omplex
% 5.46/5.72 @ ( set_fo1517530859248394432omplex
% 5.46/5.72 @ ^ [L: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L ) ) )
% 5.46/5.72 @ zero_zero_nat
% 5.46/5.72 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.46/5.72 @ one_one_complex )
% 5.46/5.72 @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_code
% 5.46/5.72 thf(fact_8850_gbinomial__code,axiom,
% 5.46/5.72 ( gbinomial_rat
% 5.46/5.72 = ( ^ [A3: rat,K2: nat] :
% 5.46/5.72 ( if_rat @ ( K2 = zero_zero_nat ) @ one_one_rat
% 5.46/5.72 @ ( divide_divide_rat
% 5.46/5.72 @ ( set_fo1949268297981939178at_rat
% 5.46/5.72 @ ^ [L: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L ) ) )
% 5.46/5.72 @ zero_zero_nat
% 5.46/5.72 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.46/5.72 @ one_one_rat )
% 5.46/5.72 @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_code
% 5.46/5.72 thf(fact_8851_gbinomial__code,axiom,
% 5.46/5.72 ( gbinomial_real
% 5.46/5.72 = ( ^ [A3: real,K2: nat] :
% 5.46/5.72 ( if_real @ ( K2 = zero_zero_nat ) @ one_one_real
% 5.46/5.72 @ ( divide_divide_real
% 5.46/5.72 @ ( set_fo3111899725591712190t_real
% 5.46/5.72 @ ^ [L: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L ) ) )
% 5.46/5.72 @ zero_zero_nat
% 5.46/5.72 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.46/5.72 @ one_one_real )
% 5.46/5.72 @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_code
% 5.46/5.72 thf(fact_8852_pochhammer__times__pochhammer__half,axiom,
% 5.46/5.72 ! [Z: real,N: nat] :
% 5.46/5.72 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.46/5.72 = ( groups129246275422532515t_real
% 5.46/5.72 @ ^ [K2: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_times_pochhammer_half
% 5.46/5.72 thf(fact_8853_pochhammer__times__pochhammer__half,axiom,
% 5.46/5.72 ! [Z: complex,N: nat] :
% 5.46/5.72 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.46/5.72 = ( groups6464643781859351333omplex
% 5.46/5.72 @ ^ [K2: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_times_pochhammer_half
% 5.46/5.72 thf(fact_8854_pochhammer__times__pochhammer__half,axiom,
% 5.46/5.72 ! [Z: rat,N: nat] :
% 5.46/5.72 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.46/5.72 = ( groups73079841787564623at_rat
% 5.46/5.72 @ ^ [K2: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_times_pochhammer_half
% 5.46/5.72 thf(fact_8855_pochhammer__code,axiom,
% 5.46/5.72 ( comm_s4660882817536571857er_int
% 5.46/5.72 = ( ^ [A3: int,N2: nat] :
% 5.46/5.72 ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 5.46/5.72 @ ( set_fo2581907887559384638at_int
% 5.46/5.72 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.46/5.72 @ zero_zero_nat
% 5.46/5.72 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.72 @ one_one_int ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_code
% 5.46/5.72 thf(fact_8856_pochhammer__code,axiom,
% 5.46/5.72 ( comm_s7457072308508201937r_real
% 5.46/5.72 = ( ^ [A3: real,N2: nat] :
% 5.46/5.72 ( if_real @ ( N2 = zero_zero_nat ) @ one_one_real
% 5.46/5.72 @ ( set_fo3111899725591712190t_real
% 5.46/5.72 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.46/5.72 @ zero_zero_nat
% 5.46/5.72 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.72 @ one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_code
% 5.46/5.72 thf(fact_8857_pochhammer__code,axiom,
% 5.46/5.72 ( comm_s2602460028002588243omplex
% 5.46/5.72 = ( ^ [A3: complex,N2: nat] :
% 5.46/5.72 ( if_complex @ ( N2 = zero_zero_nat ) @ one_one_complex
% 5.46/5.72 @ ( set_fo1517530859248394432omplex
% 5.46/5.72 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.46/5.72 @ zero_zero_nat
% 5.46/5.72 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.72 @ one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_code
% 5.46/5.72 thf(fact_8858_pochhammer__code,axiom,
% 5.46/5.72 ( comm_s4028243227959126397er_rat
% 5.46/5.72 = ( ^ [A3: rat,N2: nat] :
% 5.46/5.72 ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 5.46/5.72 @ ( set_fo1949268297981939178at_rat
% 5.46/5.72 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.46/5.72 @ zero_zero_nat
% 5.46/5.72 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.72 @ one_one_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_code
% 5.46/5.72 thf(fact_8859_pochhammer__code,axiom,
% 5.46/5.72 ( comm_s4663373288045622133er_nat
% 5.46/5.72 = ( ^ [A3: nat,N2: nat] :
% 5.46/5.72 ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 5.46/5.72 @ ( set_fo2584398358068434914at_nat
% 5.46/5.72 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.46/5.72 @ zero_zero_nat
% 5.46/5.72 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.72 @ one_one_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pochhammer_code
% 5.46/5.72 thf(fact_8860_gbinomial__partial__row__sum,axiom,
% 5.46/5.72 ! [A: complex,M: nat] :
% 5.46/5.72 ( ( groups2073611262835488442omplex
% 5.46/5.72 @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.72 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_partial_row_sum
% 5.46/5.72 thf(fact_8861_gbinomial__partial__row__sum,axiom,
% 5.46/5.72 ! [A: rat,M: nat] :
% 5.46/5.72 ( ( groups2906978787729119204at_rat
% 5.46/5.72 @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.72 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_partial_row_sum
% 5.46/5.72 thf(fact_8862_gbinomial__partial__row__sum,axiom,
% 5.46/5.72 ! [A: real,M: nat] :
% 5.46/5.72 ( ( groups6591440286371151544t_real
% 5.46/5.72 @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.72 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % gbinomial_partial_row_sum
% 5.46/5.72 thf(fact_8863_atMost__iff,axiom,
% 5.46/5.72 ! [I: real,K: real] :
% 5.46/5.72 ( ( member_real @ I @ ( set_ord_atMost_real @ K ) )
% 5.46/5.72 = ( ord_less_eq_real @ I @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_iff
% 5.46/5.72 thf(fact_8864_atMost__iff,axiom,
% 5.46/5.72 ! [I: set_nat,K: set_nat] :
% 5.46/5.72 ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 5.46/5.72 = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_iff
% 5.46/5.72 thf(fact_8865_atMost__iff,axiom,
% 5.46/5.72 ! [I: rat,K: rat] :
% 5.46/5.72 ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 5.46/5.72 = ( ord_less_eq_rat @ I @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_iff
% 5.46/5.72 thf(fact_8866_atMost__iff,axiom,
% 5.46/5.72 ! [I: num,K: num] :
% 5.46/5.72 ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 5.46/5.72 = ( ord_less_eq_num @ I @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_iff
% 5.46/5.72 thf(fact_8867_atMost__iff,axiom,
% 5.46/5.72 ! [I: int,K: int] :
% 5.46/5.72 ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 5.46/5.72 = ( ord_less_eq_int @ I @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_iff
% 5.46/5.72 thf(fact_8868_atMost__iff,axiom,
% 5.46/5.72 ! [I: nat,K: nat] :
% 5.46/5.72 ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 5.46/5.72 = ( ord_less_eq_nat @ I @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_iff
% 5.46/5.72 thf(fact_8869_prod_Oneutral__const,axiom,
% 5.46/5.72 ! [A2: set_nat] :
% 5.46/5.72 ( ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [Uu3: nat] : one_one_nat
% 5.46/5.72 @ A2 )
% 5.46/5.72 = one_one_nat ) ).
% 5.46/5.72
% 5.46/5.72 % prod.neutral_const
% 5.46/5.72 thf(fact_8870_prod_Oneutral__const,axiom,
% 5.46/5.72 ! [A2: set_nat] :
% 5.46/5.72 ( ( groups705719431365010083at_int
% 5.46/5.72 @ ^ [Uu3: nat] : one_one_int
% 5.46/5.72 @ A2 )
% 5.46/5.72 = one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % prod.neutral_const
% 5.46/5.72 thf(fact_8871_prod_Oneutral__const,axiom,
% 5.46/5.72 ! [A2: set_int] :
% 5.46/5.72 ( ( groups1705073143266064639nt_int
% 5.46/5.72 @ ^ [Uu3: int] : one_one_int
% 5.46/5.72 @ A2 )
% 5.46/5.72 = one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % prod.neutral_const
% 5.46/5.72 thf(fact_8872_prod_Oempty,axiom,
% 5.46/5.72 ! [G: nat > complex] :
% 5.46/5.72 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8873_prod_Oempty,axiom,
% 5.46/5.72 ! [G: nat > real] :
% 5.46/5.72 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8874_prod_Oempty,axiom,
% 5.46/5.72 ! [G: nat > rat] :
% 5.46/5.72 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.46/5.72 = one_one_rat ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8875_prod_Oempty,axiom,
% 5.46/5.72 ! [G: int > complex] :
% 5.46/5.72 ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8876_prod_Oempty,axiom,
% 5.46/5.72 ! [G: int > real] :
% 5.46/5.72 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8877_prod_Oempty,axiom,
% 5.46/5.72 ! [G: int > rat] :
% 5.46/5.72 ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 5.46/5.72 = one_one_rat ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8878_prod_Oempty,axiom,
% 5.46/5.72 ! [G: int > nat] :
% 5.46/5.72 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.46/5.72 = one_one_nat ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8879_prod_Oempty,axiom,
% 5.46/5.72 ! [G: real > complex] :
% 5.46/5.72 ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8880_prod_Oempty,axiom,
% 5.46/5.72 ! [G: real > real] :
% 5.46/5.72 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8881_prod_Oempty,axiom,
% 5.46/5.72 ! [G: real > rat] :
% 5.46/5.72 ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 5.46/5.72 = one_one_rat ) ).
% 5.46/5.72
% 5.46/5.72 % prod.empty
% 5.46/5.72 thf(fact_8882_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_nat,G: nat > complex] :
% 5.46/5.72 ( ~ ( finite_finite_nat @ A2 )
% 5.46/5.72 => ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.46/5.72 = one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8883_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_int,G: int > complex] :
% 5.46/5.72 ( ~ ( finite_finite_int @ A2 )
% 5.46/5.72 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.46/5.72 = one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8884_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_complex,G: complex > complex] :
% 5.46/5.72 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.46/5.72 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.46/5.72 = one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8885_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_nat,G: nat > real] :
% 5.46/5.72 ( ~ ( finite_finite_nat @ A2 )
% 5.46/5.72 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.46/5.72 = one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8886_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_int,G: int > real] :
% 5.46/5.72 ( ~ ( finite_finite_int @ A2 )
% 5.46/5.72 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.46/5.72 = one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8887_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_complex,G: complex > real] :
% 5.46/5.72 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.46/5.72 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.46/5.72 = one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8888_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_nat,G: nat > rat] :
% 5.46/5.72 ( ~ ( finite_finite_nat @ A2 )
% 5.46/5.72 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.46/5.72 = one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8889_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_int,G: int > rat] :
% 5.46/5.72 ( ~ ( finite_finite_int @ A2 )
% 5.46/5.72 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.46/5.72 = one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8890_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_complex,G: complex > rat] :
% 5.46/5.72 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.46/5.72 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.46/5.72 = one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8891_prod_Oinfinite,axiom,
% 5.46/5.72 ! [A2: set_int,G: int > nat] :
% 5.46/5.72 ( ~ ( finite_finite_int @ A2 )
% 5.46/5.72 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 5.46/5.72 = one_one_nat ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.infinite
% 5.46/5.72 thf(fact_8892_atMost__subset__iff,axiom,
% 5.46/5.72 ! [X2: set_nat,Y2: set_nat] :
% 5.46/5.72 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X2 ) @ ( set_or4236626031148496127et_nat @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_set_nat @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_subset_iff
% 5.46/5.72 thf(fact_8893_atMost__subset__iff,axiom,
% 5.46/5.72 ! [X2: rat,Y2: rat] :
% 5.46/5.72 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X2 ) @ ( set_ord_atMost_rat @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_rat @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_subset_iff
% 5.46/5.72 thf(fact_8894_atMost__subset__iff,axiom,
% 5.46/5.72 ! [X2: num,Y2: num] :
% 5.46/5.72 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X2 ) @ ( set_ord_atMost_num @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_num @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_subset_iff
% 5.46/5.72 thf(fact_8895_atMost__subset__iff,axiom,
% 5.46/5.72 ! [X2: int,Y2: int] :
% 5.46/5.72 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X2 ) @ ( set_ord_atMost_int @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_subset_iff
% 5.46/5.72 thf(fact_8896_atMost__subset__iff,axiom,
% 5.46/5.72 ! [X2: nat,Y2: nat] :
% 5.46/5.72 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X2 ) @ ( set_ord_atMost_nat @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_subset_iff
% 5.46/5.72 thf(fact_8897_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_real,A: real,B: real > complex] :
% 5.46/5.72 ( ( finite_finite_real @ S2 )
% 5.46/5.72 => ( ( ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups713298508707869441omplex
% 5.46/5.72 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups713298508707869441omplex
% 5.46/5.72 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8898_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_nat,A: nat,B: nat > complex] :
% 5.46/5.72 ( ( finite_finite_nat @ S2 )
% 5.46/5.72 => ( ( ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups6464643781859351333omplex
% 5.46/5.72 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups6464643781859351333omplex
% 5.46/5.72 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8899_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_int,A: int,B: int > complex] :
% 5.46/5.72 ( ( finite_finite_int @ S2 )
% 5.46/5.72 => ( ( ( member_int @ A @ S2 )
% 5.46/5.72 => ( ( groups7440179247065528705omplex
% 5.46/5.72 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_int @ A @ S2 )
% 5.46/5.72 => ( ( groups7440179247065528705omplex
% 5.46/5.72 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8900_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_complex,A: complex,B: complex > complex] :
% 5.46/5.72 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.72 => ( ( ( member_complex @ A @ S2 )
% 5.46/5.72 => ( ( groups3708469109370488835omplex
% 5.46/5.72 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_complex @ A @ S2 )
% 5.46/5.72 => ( ( groups3708469109370488835omplex
% 5.46/5.72 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8901_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_real,A: real,B: real > real] :
% 5.46/5.72 ( ( finite_finite_real @ S2 )
% 5.46/5.72 => ( ( ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups1681761925125756287l_real
% 5.46/5.72 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups1681761925125756287l_real
% 5.46/5.72 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8902_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_nat,A: nat,B: nat > real] :
% 5.46/5.72 ( ( finite_finite_nat @ S2 )
% 5.46/5.72 => ( ( ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups129246275422532515t_real
% 5.46/5.72 @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups129246275422532515t_real
% 5.46/5.72 @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8903_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_int,A: int,B: int > real] :
% 5.46/5.72 ( ( finite_finite_int @ S2 )
% 5.46/5.72 => ( ( ( member_int @ A @ S2 )
% 5.46/5.72 => ( ( groups2316167850115554303t_real
% 5.46/5.72 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_int @ A @ S2 )
% 5.46/5.72 => ( ( groups2316167850115554303t_real
% 5.46/5.72 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8904_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_complex,A: complex,B: complex > real] :
% 5.46/5.72 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.72 => ( ( ( member_complex @ A @ S2 )
% 5.46/5.72 => ( ( groups766887009212190081x_real
% 5.46/5.72 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_complex @ A @ S2 )
% 5.46/5.72 => ( ( groups766887009212190081x_real
% 5.46/5.72 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8905_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_real,A: real,B: real > rat] :
% 5.46/5.72 ( ( finite_finite_real @ S2 )
% 5.46/5.72 => ( ( ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups4061424788464935467al_rat
% 5.46/5.72 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups4061424788464935467al_rat
% 5.46/5.72 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8906_prod_Odelta_H,axiom,
% 5.46/5.72 ! [S2: set_nat,A: nat,B: nat > rat] :
% 5.46/5.72 ( ( finite_finite_nat @ S2 )
% 5.46/5.72 => ( ( ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups73079841787564623at_rat
% 5.46/5.72 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups73079841787564623at_rat
% 5.46/5.72 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta'
% 5.46/5.72 thf(fact_8907_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_real,A: real,B: real > complex] :
% 5.46/5.72 ( ( finite_finite_real @ S2 )
% 5.46/5.72 => ( ( ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups713298508707869441omplex
% 5.46/5.72 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups713298508707869441omplex
% 5.46/5.72 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8908_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_nat,A: nat,B: nat > complex] :
% 5.46/5.72 ( ( finite_finite_nat @ S2 )
% 5.46/5.72 => ( ( ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups6464643781859351333omplex
% 5.46/5.72 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups6464643781859351333omplex
% 5.46/5.72 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8909_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_int,A: int,B: int > complex] :
% 5.46/5.72 ( ( finite_finite_int @ S2 )
% 5.46/5.72 => ( ( ( member_int @ A @ S2 )
% 5.46/5.72 => ( ( groups7440179247065528705omplex
% 5.46/5.72 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_int @ A @ S2 )
% 5.46/5.72 => ( ( groups7440179247065528705omplex
% 5.46/5.72 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8910_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_complex,A: complex,B: complex > complex] :
% 5.46/5.72 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.72 => ( ( ( member_complex @ A @ S2 )
% 5.46/5.72 => ( ( groups3708469109370488835omplex
% 5.46/5.72 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_complex @ A @ S2 )
% 5.46/5.72 => ( ( groups3708469109370488835omplex
% 5.46/5.72 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8911_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_real,A: real,B: real > real] :
% 5.46/5.72 ( ( finite_finite_real @ S2 )
% 5.46/5.72 => ( ( ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups1681761925125756287l_real
% 5.46/5.72 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups1681761925125756287l_real
% 5.46/5.72 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8912_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_nat,A: nat,B: nat > real] :
% 5.46/5.72 ( ( finite_finite_nat @ S2 )
% 5.46/5.72 => ( ( ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups129246275422532515t_real
% 5.46/5.72 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups129246275422532515t_real
% 5.46/5.72 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8913_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_int,A: int,B: int > real] :
% 5.46/5.72 ( ( finite_finite_int @ S2 )
% 5.46/5.72 => ( ( ( member_int @ A @ S2 )
% 5.46/5.72 => ( ( groups2316167850115554303t_real
% 5.46/5.72 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_int @ A @ S2 )
% 5.46/5.72 => ( ( groups2316167850115554303t_real
% 5.46/5.72 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8914_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_complex,A: complex,B: complex > real] :
% 5.46/5.72 ( ( finite3207457112153483333omplex @ S2 )
% 5.46/5.72 => ( ( ( member_complex @ A @ S2 )
% 5.46/5.72 => ( ( groups766887009212190081x_real
% 5.46/5.72 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_complex @ A @ S2 )
% 5.46/5.72 => ( ( groups766887009212190081x_real
% 5.46/5.72 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8915_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_real,A: real,B: real > rat] :
% 5.46/5.72 ( ( finite_finite_real @ S2 )
% 5.46/5.72 => ( ( ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups4061424788464935467al_rat
% 5.46/5.72 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_real @ A @ S2 )
% 5.46/5.72 => ( ( groups4061424788464935467al_rat
% 5.46/5.72 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8916_prod_Odelta,axiom,
% 5.46/5.72 ! [S2: set_nat,A: nat,B: nat > rat] :
% 5.46/5.72 ( ( finite_finite_nat @ S2 )
% 5.46/5.72 => ( ( ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups73079841787564623at_rat
% 5.46/5.72 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = ( B @ A ) ) )
% 5.46/5.72 & ( ~ ( member_nat @ A @ S2 )
% 5.46/5.72 => ( ( groups73079841787564623at_rat
% 5.46/5.72 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.46/5.72 @ S2 )
% 5.46/5.72 = one_one_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.delta
% 5.46/5.72 thf(fact_8917_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.46/5.72 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.72 => ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.72 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8918_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_real,X2: real,G: real > real] :
% 5.46/5.72 ( ( finite_finite_real @ A2 )
% 5.46/5.72 => ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.72 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_real @ ( G @ X2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8919_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_nat,X2: nat,G: nat > real] :
% 5.46/5.72 ( ( finite_finite_nat @ A2 )
% 5.46/5.72 => ( ~ ( member_nat @ X2 @ A2 )
% 5.46/5.72 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8920_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_int,X2: int,G: int > real] :
% 5.46/5.72 ( ( finite_finite_int @ A2 )
% 5.46/5.72 => ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.72 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8921_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_complex,X2: complex,G: complex > real] :
% 5.46/5.72 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.72 => ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.72 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8922_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.46/5.72 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.46/5.72 => ( ~ ( member_VEBT_VEBT @ X2 @ A2 )
% 5.46/5.72 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8923_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_real,X2: real,G: real > rat] :
% 5.46/5.72 ( ( finite_finite_real @ A2 )
% 5.46/5.72 => ( ~ ( member_real @ X2 @ A2 )
% 5.46/5.72 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_rat @ ( G @ X2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8924_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_nat,X2: nat,G: nat > rat] :
% 5.46/5.72 ( ( finite_finite_nat @ A2 )
% 5.46/5.72 => ( ~ ( member_nat @ X2 @ A2 )
% 5.46/5.72 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8925_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_int,X2: int,G: int > rat] :
% 5.46/5.72 ( ( finite_finite_int @ A2 )
% 5.46/5.72 => ( ~ ( member_int @ X2 @ A2 )
% 5.46/5.72 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_rat @ ( G @ X2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8926_prod_Oinsert,axiom,
% 5.46/5.72 ! [A2: set_complex,X2: complex,G: complex > rat] :
% 5.46/5.72 ( ( finite3207457112153483333omplex @ A2 )
% 5.46/5.72 => ( ~ ( member_complex @ X2 @ A2 )
% 5.46/5.72 => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X2 @ A2 ) )
% 5.46/5.72 = ( times_times_rat @ ( G @ X2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.insert
% 5.46/5.72 thf(fact_8927_Icc__subset__Iic__iff,axiom,
% 5.46/5.72 ! [L2: set_nat,H2: set_nat,H3: set_nat] :
% 5.46/5.72 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L2 @ H2 ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 5.46/5.72 = ( ~ ( ord_less_eq_set_nat @ L2 @ H2 )
% 5.46/5.72 | ( ord_less_eq_set_nat @ H2 @ H3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Icc_subset_Iic_iff
% 5.46/5.72 thf(fact_8928_Icc__subset__Iic__iff,axiom,
% 5.46/5.72 ! [L2: rat,H2: rat,H3: rat] :
% 5.46/5.72 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L2 @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.46/5.72 = ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.46/5.72 | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Icc_subset_Iic_iff
% 5.46/5.72 thf(fact_8929_Icc__subset__Iic__iff,axiom,
% 5.46/5.72 ! [L2: num,H2: num,H3: num] :
% 5.46/5.72 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L2 @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 5.46/5.72 = ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.46/5.72 | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Icc_subset_Iic_iff
% 5.46/5.72 thf(fact_8930_Icc__subset__Iic__iff,axiom,
% 5.46/5.72 ! [L2: nat,H2: nat,H3: nat] :
% 5.46/5.72 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L2 @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.46/5.72 = ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.46/5.72 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Icc_subset_Iic_iff
% 5.46/5.72 thf(fact_8931_Icc__subset__Iic__iff,axiom,
% 5.46/5.72 ! [L2: int,H2: int,H3: int] :
% 5.46/5.72 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L2 @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 5.46/5.72 = ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.46/5.72 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Icc_subset_Iic_iff
% 5.46/5.72 thf(fact_8932_Icc__subset__Iic__iff,axiom,
% 5.46/5.72 ! [L2: real,H2: real,H3: real] :
% 5.46/5.72 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L2 @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 5.46/5.72 = ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.46/5.72 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Icc_subset_Iic_iff
% 5.46/5.72 thf(fact_8933_sum_OatMost__Suc,axiom,
% 5.46/5.72 ! [G: nat > rat,N: nat] :
% 5.46/5.72 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sum.atMost_Suc
% 5.46/5.72 thf(fact_8934_sum_OatMost__Suc,axiom,
% 5.46/5.72 ! [G: nat > int,N: nat] :
% 5.46/5.72 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sum.atMost_Suc
% 5.46/5.72 thf(fact_8935_sum_OatMost__Suc,axiom,
% 5.46/5.72 ! [G: nat > nat,N: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sum.atMost_Suc
% 5.46/5.72 thf(fact_8936_sum_OatMost__Suc,axiom,
% 5.46/5.72 ! [G: nat > real,N: nat] :
% 5.46/5.72 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sum.atMost_Suc
% 5.46/5.72 thf(fact_8937_prod_OlessThan__Suc,axiom,
% 5.46/5.72 ! [G: nat > real,N: nat] :
% 5.46/5.72 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.lessThan_Suc
% 5.46/5.72 thf(fact_8938_prod_OlessThan__Suc,axiom,
% 5.46/5.72 ! [G: nat > rat,N: nat] :
% 5.46/5.72 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.lessThan_Suc
% 5.46/5.72 thf(fact_8939_prod_OlessThan__Suc,axiom,
% 5.46/5.72 ! [G: nat > nat,N: nat] :
% 5.46/5.72 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.lessThan_Suc
% 5.46/5.72 thf(fact_8940_prod_OlessThan__Suc,axiom,
% 5.46/5.72 ! [G: nat > int,N: nat] :
% 5.46/5.72 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.lessThan_Suc
% 5.46/5.72 thf(fact_8941_prod_OatMost__Suc,axiom,
% 5.46/5.72 ! [G: nat > real,N: nat] :
% 5.46/5.72 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.atMost_Suc
% 5.46/5.72 thf(fact_8942_prod_OatMost__Suc,axiom,
% 5.46/5.72 ! [G: nat > rat,N: nat] :
% 5.46/5.72 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.atMost_Suc
% 5.46/5.72 thf(fact_8943_prod_OatMost__Suc,axiom,
% 5.46/5.72 ! [G: nat > nat,N: nat] :
% 5.46/5.72 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.atMost_Suc
% 5.46/5.72 thf(fact_8944_prod_OatMost__Suc,axiom,
% 5.46/5.72 ! [G: nat > int,N: nat] :
% 5.46/5.72 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.atMost_Suc
% 5.46/5.72 thf(fact_8945_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.72 ! [N: nat,M: nat,G: nat > complex] :
% 5.46/5.72 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = one_one_complex ) )
% 5.46/5.72 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.cl_ivl_Suc
% 5.46/5.72 thf(fact_8946_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.72 ! [N: nat,M: nat,G: nat > real] :
% 5.46/5.72 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = one_one_real ) )
% 5.46/5.72 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.cl_ivl_Suc
% 5.46/5.72 thf(fact_8947_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.72 ! [N: nat,M: nat,G: nat > rat] :
% 5.46/5.72 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = one_one_rat ) )
% 5.46/5.72 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.cl_ivl_Suc
% 5.46/5.72 thf(fact_8948_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.72 ! [N: nat,M: nat,G: nat > nat] :
% 5.46/5.72 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = one_one_nat ) )
% 5.46/5.72 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.cl_ivl_Suc
% 5.46/5.72 thf(fact_8949_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.72 ! [N: nat,M: nat,G: nat > int] :
% 5.46/5.72 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = one_one_int ) )
% 5.46/5.72 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.72 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.cl_ivl_Suc
% 5.46/5.72 thf(fact_8950_prod_Odistrib,axiom,
% 5.46/5.72 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.46/5.72 ( ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [X: nat] : ( times_times_nat @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.72 @ A2 )
% 5.46/5.72 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.distrib
% 5.46/5.72 thf(fact_8951_prod_Odistrib,axiom,
% 5.46/5.72 ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 5.46/5.72 ( ( groups705719431365010083at_int
% 5.46/5.72 @ ^ [X: nat] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.72 @ A2 )
% 5.46/5.72 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.distrib
% 5.46/5.72 thf(fact_8952_prod_Odistrib,axiom,
% 5.46/5.72 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.46/5.72 ( ( groups1705073143266064639nt_int
% 5.46/5.72 @ ^ [X: int] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.72 @ A2 )
% 5.46/5.72 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.distrib
% 5.46/5.72 thf(fact_8953_prod_Oneutral,axiom,
% 5.46/5.72 ! [A2: set_nat,G: nat > nat] :
% 5.46/5.72 ( ! [X3: nat] :
% 5.46/5.72 ( ( member_nat @ X3 @ A2 )
% 5.46/5.72 => ( ( G @ X3 )
% 5.46/5.72 = one_one_nat ) )
% 5.46/5.72 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.46/5.72 = one_one_nat ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.neutral
% 5.46/5.72 thf(fact_8954_prod_Oneutral,axiom,
% 5.46/5.72 ! [A2: set_nat,G: nat > int] :
% 5.46/5.72 ( ! [X3: nat] :
% 5.46/5.72 ( ( member_nat @ X3 @ A2 )
% 5.46/5.72 => ( ( G @ X3 )
% 5.46/5.72 = one_one_int ) )
% 5.46/5.72 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.46/5.72 = one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.neutral
% 5.46/5.72 thf(fact_8955_prod_Oneutral,axiom,
% 5.46/5.72 ! [A2: set_int,G: int > int] :
% 5.46/5.72 ( ! [X3: int] :
% 5.46/5.72 ( ( member_int @ X3 @ A2 )
% 5.46/5.72 => ( ( G @ X3 )
% 5.46/5.72 = one_one_int ) )
% 5.46/5.72 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 5.46/5.72 = one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.neutral
% 5.46/5.72 thf(fact_8956_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: complex > complex,A2: set_complex] :
% 5.46/5.72 ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.46/5.72 != one_one_complex )
% 5.46/5.72 => ~ ! [A5: complex] :
% 5.46/5.72 ( ( member_complex @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_complex ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8957_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: real > complex,A2: set_real] :
% 5.46/5.72 ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.46/5.72 != one_one_complex )
% 5.46/5.72 => ~ ! [A5: real] :
% 5.46/5.72 ( ( member_real @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_complex ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8958_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: nat > complex,A2: set_nat] :
% 5.46/5.72 ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.46/5.72 != one_one_complex )
% 5.46/5.72 => ~ ! [A5: nat] :
% 5.46/5.72 ( ( member_nat @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_complex ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8959_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: int > complex,A2: set_int] :
% 5.46/5.72 ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.46/5.72 != one_one_complex )
% 5.46/5.72 => ~ ! [A5: int] :
% 5.46/5.72 ( ( member_int @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_complex ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8960_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: complex > real,A2: set_complex] :
% 5.46/5.72 ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.46/5.72 != one_one_real )
% 5.46/5.72 => ~ ! [A5: complex] :
% 5.46/5.72 ( ( member_complex @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8961_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: real > real,A2: set_real] :
% 5.46/5.72 ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.46/5.72 != one_one_real )
% 5.46/5.72 => ~ ! [A5: real] :
% 5.46/5.72 ( ( member_real @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8962_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: nat > real,A2: set_nat] :
% 5.46/5.72 ( ( ( groups129246275422532515t_real @ G @ A2 )
% 5.46/5.72 != one_one_real )
% 5.46/5.72 => ~ ! [A5: nat] :
% 5.46/5.72 ( ( member_nat @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8963_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: int > real,A2: set_int] :
% 5.46/5.72 ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.46/5.72 != one_one_real )
% 5.46/5.72 => ~ ! [A5: int] :
% 5.46/5.72 ( ( member_int @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8964_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: complex > rat,A2: set_complex] :
% 5.46/5.72 ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.46/5.72 != one_one_rat )
% 5.46/5.72 => ~ ! [A5: complex] :
% 5.46/5.72 ( ( member_complex @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8965_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.72 ! [G: real > rat,A2: set_real] :
% 5.46/5.72 ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.46/5.72 != one_one_rat )
% 5.46/5.72 => ~ ! [A5: real] :
% 5.46/5.72 ( ( member_real @ A5 @ A2 )
% 5.46/5.72 => ( ( G @ A5 )
% 5.46/5.72 = one_one_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.not_neutral_contains_not_neutral
% 5.46/5.72 thf(fact_8966_prod__power__distrib,axiom,
% 5.46/5.72 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.46/5.72 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N )
% 5.46/5.72 = ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N )
% 5.46/5.72 @ A2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod_power_distrib
% 5.46/5.72 thf(fact_8967_prod__power__distrib,axiom,
% 5.46/5.72 ! [F: nat > int,A2: set_nat,N: nat] :
% 5.46/5.72 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N )
% 5.46/5.72 = ( groups705719431365010083at_int
% 5.46/5.72 @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N )
% 5.46/5.72 @ A2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod_power_distrib
% 5.46/5.72 thf(fact_8968_prod__power__distrib,axiom,
% 5.46/5.72 ! [F: int > int,A2: set_int,N: nat] :
% 5.46/5.72 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N )
% 5.46/5.72 = ( groups1705073143266064639nt_int
% 5.46/5.72 @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N )
% 5.46/5.72 @ A2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod_power_distrib
% 5.46/5.72 thf(fact_8969_mod__prod__eq,axiom,
% 5.46/5.72 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.46/5.72 ( ( modulo_modulo_nat
% 5.46/5.72 @ ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A )
% 5.46/5.72 @ A2 )
% 5.46/5.72 @ A )
% 5.46/5.72 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_prod_eq
% 5.46/5.72 thf(fact_8970_mod__prod__eq,axiom,
% 5.46/5.72 ! [F: nat > int,A: int,A2: set_nat] :
% 5.46/5.72 ( ( modulo_modulo_int
% 5.46/5.72 @ ( groups705719431365010083at_int
% 5.46/5.72 @ ^ [I4: nat] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.46/5.72 @ A2 )
% 5.46/5.72 @ A )
% 5.46/5.72 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_prod_eq
% 5.46/5.72 thf(fact_8971_mod__prod__eq,axiom,
% 5.46/5.72 ! [F: int > int,A: int,A2: set_int] :
% 5.46/5.72 ( ( modulo_modulo_int
% 5.46/5.72 @ ( groups1705073143266064639nt_int
% 5.46/5.72 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.46/5.72 @ A2 )
% 5.46/5.72 @ A )
% 5.46/5.72 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_prod_eq
% 5.46/5.72 thf(fact_8972_prod_OatMost__Suc__shift,axiom,
% 5.46/5.72 ! [G: nat > real,N: nat] :
% 5.46/5.72 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.46/5.72 @ ( groups129246275422532515t_real
% 5.46/5.72 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.atMost_Suc_shift
% 5.46/5.72 thf(fact_8973_prod_OatMost__Suc__shift,axiom,
% 5.46/5.72 ! [G: nat > rat,N: nat] :
% 5.46/5.72 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.46/5.72 @ ( groups73079841787564623at_rat
% 5.46/5.72 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.atMost_Suc_shift
% 5.46/5.72 thf(fact_8974_prod_OatMost__Suc__shift,axiom,
% 5.46/5.72 ! [G: nat > nat,N: nat] :
% 5.46/5.72 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.46/5.72 @ ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.atMost_Suc_shift
% 5.46/5.72 thf(fact_8975_prod_OatMost__Suc__shift,axiom,
% 5.46/5.72 ! [G: nat > int,N: nat] :
% 5.46/5.72 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.46/5.72 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.46/5.72 @ ( groups705719431365010083at_int
% 5.46/5.72 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.atMost_Suc_shift
% 5.46/5.72 thf(fact_8976_prod_Onested__swap_H,axiom,
% 5.46/5.72 ! [A: nat > nat > nat,N: nat] :
% 5.46/5.72 ( ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [I4: nat] : ( groups708209901874060359at_nat @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.72 = ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [J3: nat] :
% 5.46/5.72 ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.46/5.72 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.nested_swap'
% 5.46/5.72 thf(fact_8977_prod_Onested__swap_H,axiom,
% 5.46/5.72 ! [A: nat > nat > int,N: nat] :
% 5.46/5.72 ( ( groups705719431365010083at_int
% 5.46/5.72 @ ^ [I4: nat] : ( groups705719431365010083at_int @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.72 = ( groups705719431365010083at_int
% 5.46/5.72 @ ^ [J3: nat] :
% 5.46/5.72 ( groups705719431365010083at_int
% 5.46/5.72 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.46/5.72 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod.nested_swap'
% 5.46/5.72 thf(fact_8978_atMost__def,axiom,
% 5.46/5.72 ( set_ord_atMost_real
% 5.46/5.72 = ( ^ [U2: real] :
% 5.46/5.72 ( collect_real
% 5.46/5.72 @ ^ [X: real] : ( ord_less_eq_real @ X @ U2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_def
% 5.46/5.72 thf(fact_8979_atMost__def,axiom,
% 5.46/5.72 ( set_or4236626031148496127et_nat
% 5.46/5.72 = ( ^ [U2: set_nat] :
% 5.46/5.72 ( collect_set_nat
% 5.46/5.72 @ ^ [X: set_nat] : ( ord_less_eq_set_nat @ X @ U2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_def
% 5.46/5.72 thf(fact_8980_atMost__def,axiom,
% 5.46/5.72 ( set_ord_atMost_rat
% 5.46/5.72 = ( ^ [U2: rat] :
% 5.46/5.72 ( collect_rat
% 5.46/5.72 @ ^ [X: rat] : ( ord_less_eq_rat @ X @ U2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_def
% 5.46/5.72 thf(fact_8981_atMost__def,axiom,
% 5.46/5.72 ( set_ord_atMost_num
% 5.46/5.72 = ( ^ [U2: num] :
% 5.46/5.72 ( collect_num
% 5.46/5.72 @ ^ [X: num] : ( ord_less_eq_num @ X @ U2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_def
% 5.46/5.72 thf(fact_8982_atMost__def,axiom,
% 5.46/5.72 ( set_ord_atMost_int
% 5.46/5.72 = ( ^ [U2: int] :
% 5.46/5.72 ( collect_int
% 5.46/5.72 @ ^ [X: int] : ( ord_less_eq_int @ X @ U2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_def
% 5.46/5.72 thf(fact_8983_atMost__def,axiom,
% 5.46/5.72 ( set_ord_atMost_nat
% 5.46/5.72 = ( ^ [U2: nat] :
% 5.46/5.72 ( collect_nat
% 5.46/5.72 @ ^ [X: nat] : ( ord_less_eq_nat @ X @ U2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_def
% 5.46/5.72 thf(fact_8984_prod__mono,axiom,
% 5.46/5.72 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.46/5.72 ( ! [I2: complex] :
% 5.46/5.72 ( ( member_complex @ I2 @ A2 )
% 5.46/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I2 ) )
% 5.46/5.72 & ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.46/5.72 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ A2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod_mono
% 5.46/5.72 thf(fact_8985_prod__mono,axiom,
% 5.46/5.72 ! [A2: set_real,F: real > int,G: real > int] :
% 5.46/5.72 ( ! [I2: real] :
% 5.46/5.72 ( ( member_real @ I2 @ A2 )
% 5.46/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I2 ) )
% 5.46/5.72 & ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.46/5.72 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod_mono
% 5.46/5.72 thf(fact_8986_prod__mono,axiom,
% 5.46/5.72 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.46/5.72 ( ! [I2: nat] :
% 5.46/5.72 ( ( member_nat @ I2 @ A2 )
% 5.46/5.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.46/5.72 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.46/5.72 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ A2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod_mono
% 5.46/5.72 thf(fact_8987_prod__mono,axiom,
% 5.46/5.72 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 5.46/5.72 ( ! [I2: nat] :
% 5.46/5.72 ( ( member_nat @ I2 @ A2 )
% 5.46/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I2 ) )
% 5.46/5.72 & ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.46/5.72 => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ G @ A2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod_mono
% 5.46/5.72 thf(fact_8988_prod__mono,axiom,
% 5.46/5.72 ! [A2: set_int,F: int > int,G: int > int] :
% 5.46/5.72 ( ! [I2: int] :
% 5.46/5.72 ( ( member_int @ I2 @ A2 )
% 5.46/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I2 ) )
% 5.46/5.72 & ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.46/5.72 => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ G @ A2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod_mono
% 5.46/5.72 thf(fact_8989_lessThan__Suc__atMost,axiom,
% 5.46/5.72 ! [K: nat] :
% 5.46/5.72 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.46/5.72 = ( set_ord_atMost_nat @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % lessThan_Suc_atMost
% 5.46/5.72 thf(fact_8990_atMost__Suc,axiom,
% 5.46/5.72 ! [K: nat] :
% 5.46/5.72 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.46/5.72 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_Suc
% 5.46/5.72 thf(fact_8991_atMost__nat__numeral,axiom,
% 5.46/5.72 ! [K: num] :
% 5.46/5.72 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.46/5.72 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % atMost_nat_numeral
% 5.46/5.72 thf(fact_8992_atLeast1__atMost__eq__remove0,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.72 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % atLeast1_atMost_eq_remove0
% 5.46/5.72 thf(fact_8993_fact__eq__fact__times,axiom,
% 5.46/5.72 ! [N: nat,M: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.72 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.46/5.72 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.46/5.72 @ ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [X: nat] : X
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % fact_eq_fact_times
% 5.46/5.72 thf(fact_8994_fact__div__fact,axiom,
% 5.46/5.72 ! [N: nat,M: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.72 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.46/5.72 = ( groups708209901874060359at_nat
% 5.46/5.72 @ ^ [X: nat] : X
% 5.46/5.72 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % fact_div_fact
% 5.46/5.72 thf(fact_8995_polynomial__product__nat,axiom,
% 5.46/5.72 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X2: nat] :
% 5.46/5.72 ( ! [I2: nat] :
% 5.46/5.72 ( ( ord_less_nat @ M @ I2 )
% 5.46/5.72 => ( ( A @ I2 )
% 5.46/5.72 = zero_zero_nat ) )
% 5.46/5.72 => ( ! [J2: nat] :
% 5.46/5.72 ( ( ord_less_nat @ N @ J2 )
% 5.46/5.72 => ( ( B @ J2 )
% 5.46/5.72 = zero_zero_nat ) )
% 5.46/5.72 => ( ( times_times_nat
% 5.46/5.72 @ ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( power_power_nat @ X2 @ I4 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.72 @ ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X2 @ J3 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) ) )
% 5.46/5.72 = ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [R5: nat] :
% 5.46/5.72 ( times_times_nat
% 5.46/5.72 @ ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ R5 ) )
% 5.46/5.72 @ ( power_power_nat @ X2 @ R5 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % polynomial_product_nat
% 5.46/5.72 thf(fact_8996_central__binomial__lower__bound,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.72 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % central_binomial_lower_bound
% 5.46/5.72 thf(fact_8997_binomial__Suc__n,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( binomial @ ( suc @ N ) @ N )
% 5.46/5.72 = ( suc @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_Suc_n
% 5.46/5.72 thf(fact_8998_binomial__n__n,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( binomial @ N @ N )
% 5.46/5.72 = one_one_nat ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_n_n
% 5.46/5.72 thf(fact_8999_binomial__1,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.72 = N ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_1
% 5.46/5.72 thf(fact_9000_binomial__0__Suc,axiom,
% 5.46/5.72 ! [K: nat] :
% 5.46/5.72 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.46/5.72 = zero_zero_nat ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_0_Suc
% 5.46/5.72 thf(fact_9001_binomial__eq__0__iff,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ( binomial @ N @ K )
% 5.46/5.72 = zero_zero_nat )
% 5.46/5.72 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_eq_0_iff
% 5.46/5.72 thf(fact_9002_binomial__Suc__Suc,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.46/5.72 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_Suc_Suc
% 5.46/5.72 thf(fact_9003_binomial__n__0,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( binomial @ N @ zero_zero_nat )
% 5.46/5.72 = one_one_nat ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_n_0
% 5.46/5.72 thf(fact_9004_zero__less__binomial__iff,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.46/5.72 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_binomial_iff
% 5.46/5.72 thf(fact_9005_choose__one,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( binomial @ N @ one_one_nat )
% 5.46/5.72 = N ) ).
% 5.46/5.72
% 5.46/5.72 % choose_one
% 5.46/5.72 thf(fact_9006_binomial__eq__0,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_nat @ N @ K )
% 5.46/5.72 => ( ( binomial @ N @ K )
% 5.46/5.72 = zero_zero_nat ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_eq_0
% 5.46/5.72 thf(fact_9007_Suc__times__binomial,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.46/5.72 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Suc_times_binomial
% 5.46/5.72 thf(fact_9008_Suc__times__binomial__eq,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.46/5.72 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Suc_times_binomial_eq
% 5.46/5.72 thf(fact_9009_binomial__symmetric,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( binomial @ N @ K )
% 5.46/5.72 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_symmetric
% 5.46/5.72 thf(fact_9010_choose__mult__lemma,axiom,
% 5.46/5.72 ! [M: nat,R: nat,K: nat] :
% 5.46/5.72 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.46/5.72 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % choose_mult_lemma
% 5.46/5.72 thf(fact_9011_binomial__le__pow,axiom,
% 5.46/5.72 ! [R: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ R @ N )
% 5.46/5.72 => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_le_pow
% 5.46/5.72 thf(fact_9012_zero__less__binomial,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_binomial
% 5.46/5.72 thf(fact_9013_Suc__times__binomial__add,axiom,
% 5.46/5.72 ! [A: nat,B: nat] :
% 5.46/5.72 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.46/5.72 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Suc_times_binomial_add
% 5.46/5.72 thf(fact_9014_binomial__Suc__Suc__eq__times,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.46/5.72 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_Suc_Suc_eq_times
% 5.46/5.72 thf(fact_9015_choose__mult,axiom,
% 5.46/5.72 ! [K: nat,M: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ M )
% 5.46/5.72 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.72 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.46/5.72 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % choose_mult
% 5.46/5.72 thf(fact_9016_binomial__absorb__comp,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.46/5.72 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_absorb_comp
% 5.46/5.72 thf(fact_9017_sum__choose__upper,axiom,
% 5.46/5.72 ! [M: nat,N: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [K2: nat] : ( binomial @ K2 @ M )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.72 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sum_choose_upper
% 5.46/5.72 thf(fact_9018_binomial__absorption,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.46/5.72 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_absorption
% 5.46/5.72 thf(fact_9019_binomial__fact__lemma,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.46/5.72 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_fact_lemma
% 5.46/5.72 thf(fact_9020_prod__int__plus__eq,axiom,
% 5.46/5.72 ! [I: nat,J: nat] :
% 5.46/5.72 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.46/5.72 = ( groups1705073143266064639nt_int
% 5.46/5.72 @ ^ [X: int] : X
% 5.46/5.72 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % prod_int_plus_eq
% 5.46/5.72 thf(fact_9021_sum__choose__lower,axiom,
% 5.46/5.72 ! [R: nat,N: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R @ K2 ) @ K2 )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.72 = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % sum_choose_lower
% 5.46/5.72 thf(fact_9022_choose__rising__sum_I2_J,axiom,
% 5.46/5.72 ! [N: nat,M: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.46/5.72 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.72 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % choose_rising_sum(2)
% 5.46/5.72 thf(fact_9023_choose__rising__sum_I1_J,axiom,
% 5.46/5.72 ! [N: nat,M: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.46/5.72 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.72 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % choose_rising_sum(1)
% 5.46/5.72 thf(fact_9024_binomial__mono,axiom,
% 5.46/5.72 ! [K: nat,K6: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ K6 )
% 5.46/5.72 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.46/5.72 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_mono
% 5.46/5.72 thf(fact_9025_binomial__maximum_H,axiom,
% 5.46/5.72 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_maximum'
% 5.46/5.72 thf(fact_9026_binomial__maximum,axiom,
% 5.46/5.72 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_maximum
% 5.46/5.72 thf(fact_9027_binomial__antimono,axiom,
% 5.46/5.72 ! [K: nat,K6: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ K6 )
% 5.46/5.72 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.46/5.72 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.46/5.72 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_antimono
% 5.46/5.72 thf(fact_9028_binomial__le__pow2,axiom,
% 5.46/5.72 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_le_pow2
% 5.46/5.72 thf(fact_9029_choose__reduce__nat,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.72 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.72 => ( ( binomial @ N @ K )
% 5.46/5.72 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % choose_reduce_nat
% 5.46/5.72 thf(fact_9030_times__binomial__minus1__eq,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.72 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.46/5.72 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % times_binomial_minus1_eq
% 5.46/5.72 thf(fact_9031_binomial__altdef__nat,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( binomial @ N @ K )
% 5.46/5.72 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_altdef_nat
% 5.46/5.72 thf(fact_9032_sum__choose__diagonal,axiom,
% 5.46/5.72 ! [M: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.72 => ( ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.72 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sum_choose_diagonal
% 5.46/5.72 thf(fact_9033_vandermonde,axiom,
% 5.46/5.72 ! [M: nat,N: nat,R: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K2 ) ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ R ) )
% 5.46/5.72 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 5.46/5.72
% 5.46/5.72 % vandermonde
% 5.46/5.72 thf(fact_9034_binomial__less__binomial__Suc,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_less_binomial_Suc
% 5.46/5.72 thf(fact_9035_binomial__strict__mono,axiom,
% 5.46/5.72 ! [K: nat,K6: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_nat @ K @ K6 )
% 5.46/5.72 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.46/5.72 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_strict_mono
% 5.46/5.72 thf(fact_9036_binomial__strict__antimono,axiom,
% 5.46/5.72 ! [K: nat,K6: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_nat @ K @ K6 )
% 5.46/5.72 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.46/5.72 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.46/5.72 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_strict_antimono
% 5.46/5.72 thf(fact_9037_central__binomial__odd,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % central_binomial_odd
% 5.46/5.72 thf(fact_9038_binomial__addition__formula,axiom,
% 5.46/5.72 ! [N: nat,K: nat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.72 => ( ( binomial @ N @ ( suc @ K ) )
% 5.46/5.72 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_addition_formula
% 5.46/5.72 thf(fact_9039_choose__row__sum,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % choose_row_sum
% 5.46/5.72 thf(fact_9040_binomial,axiom,
% 5.46/5.72 ! [A: nat,B: nat,N: nat] :
% 5.46/5.72 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.46/5.72 = ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial
% 5.46/5.72 thf(fact_9041_choose__two,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % choose_two
% 5.46/5.72 thf(fact_9042_choose__square__sum,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.72 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % choose_square_sum
% 5.46/5.72 thf(fact_9043_binomial__r__part__sum,axiom,
% 5.46/5.72 ! [M: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_r_part_sum
% 5.46/5.72 thf(fact_9044_choose__linear__sum,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( groups3542108847815614940at_nat
% 5.46/5.72 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 5.46/5.72 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.72 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % choose_linear_sum
% 5.46/5.72 thf(fact_9045_binomial__code,axiom,
% 5.46/5.72 ( binomial
% 5.46/5.72 = ( ^ [N2: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K2 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % binomial_code
% 5.46/5.72 thf(fact_9046_Maclaurin__sin__bound,axiom,
% 5.46/5.72 ! [X2: real,N: nat] :
% 5.46/5.72 ( ord_less_eq_real
% 5.46/5.72 @ ( abs_abs_real
% 5.46/5.72 @ ( minus_minus_real @ ( sin_real @ X2 )
% 5.46/5.72 @ ( groups6591440286371151544t_real
% 5.46/5.72 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.72 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.46/5.72 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X2 ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Maclaurin_sin_bound
% 5.46/5.72 thf(fact_9047_of__nat__id,axiom,
% 5.46/5.72 ( semiri1316708129612266289at_nat
% 5.46/5.72 = ( ^ [N2: nat] : N2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_nat_id
% 5.46/5.72 thf(fact_9048_real__sqrt__inverse,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( sqrt @ ( inverse_inverse_real @ X2 ) )
% 5.46/5.72 = ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_sqrt_inverse
% 5.46/5.72 thf(fact_9049_real__scaleR__def,axiom,
% 5.46/5.72 real_V1485227260804924795R_real = times_times_real ).
% 5.46/5.72
% 5.46/5.72 % real_scaleR_def
% 5.46/5.72 thf(fact_9050_divide__real__def,axiom,
% 5.46/5.72 ( divide_divide_real
% 5.46/5.72 = ( ^ [X: real,Y: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_real_def
% 5.46/5.72 thf(fact_9051_complex__scaleR,axiom,
% 5.46/5.72 ! [R: real,A: real,B: real] :
% 5.46/5.72 ( ( real_V2046097035970521341omplex @ R @ ( complex2 @ A @ B ) )
% 5.46/5.72 = ( complex2 @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % complex_scaleR
% 5.46/5.72 thf(fact_9052_inverse__powr,axiom,
% 5.46/5.72 ! [Y2: real,A: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ( powr_real @ ( inverse_inverse_real @ Y2 ) @ A )
% 5.46/5.72 = ( inverse_inverse_real @ ( powr_real @ Y2 @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % inverse_powr
% 5.46/5.72 thf(fact_9053_forall__pos__mono__1,axiom,
% 5.46/5.72 ! [P: real > $o,E: real] :
% 5.46/5.72 ( ! [D3: real,E2: real] :
% 5.46/5.72 ( ( ord_less_real @ D3 @ E2 )
% 5.46/5.72 => ( ( P @ D3 )
% 5.46/5.72 => ( P @ E2 ) ) )
% 5.46/5.72 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.72 => ( P @ E ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % forall_pos_mono_1
% 5.46/5.72 thf(fact_9054_forall__pos__mono,axiom,
% 5.46/5.72 ! [P: real > $o,E: real] :
% 5.46/5.72 ( ! [D3: real,E2: real] :
% 5.46/5.72 ( ( ord_less_real @ D3 @ E2 )
% 5.46/5.72 => ( ( P @ D3 )
% 5.46/5.72 => ( P @ E2 ) ) )
% 5.46/5.72 => ( ! [N3: nat] :
% 5.46/5.72 ( ( N3 != zero_zero_nat )
% 5.46/5.72 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.72 => ( P @ E ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % forall_pos_mono
% 5.46/5.72 thf(fact_9055_real__arch__inverse,axiom,
% 5.46/5.72 ! [E: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.72 = ( ? [N2: nat] :
% 5.46/5.72 ( ( N2 != zero_zero_nat )
% 5.46/5.72 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.46/5.72 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_arch_inverse
% 5.46/5.72 thf(fact_9056_sqrt__divide__self__eq,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( divide_divide_real @ ( sqrt @ X2 ) @ X2 )
% 5.46/5.72 = ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sqrt_divide_self_eq
% 5.46/5.72 thf(fact_9057_ln__inverse,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ln_ln_real @ ( inverse_inverse_real @ X2 ) )
% 5.46/5.72 = ( uminus_uminus_real @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ln_inverse
% 5.46/5.72 thf(fact_9058_log__inverse,axiom,
% 5.46/5.72 ! [A: real,X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.72 => ( ( A != one_one_real )
% 5.46/5.72 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( log @ A @ ( inverse_inverse_real @ X2 ) )
% 5.46/5.72 = ( uminus_uminus_real @ ( log @ A @ X2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % log_inverse
% 5.46/5.72 thf(fact_9059_exp__plus__inverse__exp,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % exp_plus_inverse_exp
% 5.46/5.72 thf(fact_9060_plus__inverse__ge__2,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % plus_inverse_ge_2
% 5.46/5.72 thf(fact_9061_real__inv__sqrt__pow2,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( inverse_inverse_real @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_inv_sqrt_pow2
% 5.46/5.72 thf(fact_9062_tan__cot,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.46/5.72 = ( inverse_inverse_real @ ( tan_real @ X2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_cot
% 5.46/5.72 thf(fact_9063_real__le__x__sinh,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ord_less_eq_real @ X2 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_le_x_sinh
% 5.46/5.72 thf(fact_9064_real__le__abs__sinh,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_le_abs_sinh
% 5.46/5.72 thf(fact_9065_exp__two__pi__i,axiom,
% 5.46/5.72 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % exp_two_pi_i
% 5.46/5.72 thf(fact_9066_exp__two__pi__i_H,axiom,
% 5.46/5.72 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % exp_two_pi_i'
% 5.46/5.72 thf(fact_9067_sinh__real__less__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % sinh_real_less_iff
% 5.46/5.72 thf(fact_9068_sinh__real__le__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % sinh_real_le_iff
% 5.46/5.72 thf(fact_9069_sinh__real__neg__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( sinh_real @ X2 ) @ zero_zero_real )
% 5.46/5.72 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % sinh_real_neg_iff
% 5.46/5.72 thf(fact_9070_sinh__real__pos__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X2 ) )
% 5.46/5.72 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % sinh_real_pos_iff
% 5.46/5.72 thf(fact_9071_sinh__real__nonpos__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( sinh_real @ X2 ) @ zero_zero_real )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % sinh_real_nonpos_iff
% 5.46/5.72 thf(fact_9072_sinh__real__nonneg__iff,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % sinh_real_nonneg_iff
% 5.46/5.72 thf(fact_9073_norm__ii,axiom,
% 5.46/5.72 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % norm_ii
% 5.46/5.72 thf(fact_9074_divide__i,axiom,
% 5.46/5.72 ! [X2: complex] :
% 5.46/5.72 ( ( divide1717551699836669952omplex @ X2 @ imaginary_unit )
% 5.46/5.72 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_i
% 5.46/5.72 thf(fact_9075_divide__numeral__i,axiom,
% 5.46/5.72 ! [Z: complex,N: num] :
% 5.46/5.72 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_numeral_i
% 5.46/5.72 thf(fact_9076_power2__i,axiom,
% 5.46/5.72 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_i
% 5.46/5.72 thf(fact_9077_i__even__power,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % i_even_power
% 5.46/5.72 thf(fact_9078_divide__complex__def,axiom,
% 5.46/5.72 ( divide1717551699836669952omplex
% 5.46/5.72 = ( ^ [X: complex,Y: complex] : ( times_times_complex @ X @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_complex_def
% 5.46/5.72 thf(fact_9079_sinh__less__cosh__real,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % sinh_less_cosh_real
% 5.46/5.72 thf(fact_9080_sinh__le__cosh__real,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_eq_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % sinh_le_cosh_real
% 5.46/5.72 thf(fact_9081_cosh__real__pos,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % cosh_real_pos
% 5.46/5.72 thf(fact_9082_cosh__real__nonpos__le__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ Y2 @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cosh_real_nonpos_le_iff
% 5.46/5.72 thf(fact_9083_cosh__real__nonneg__le__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y2 ) )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cosh_real_nonneg_le_iff
% 5.46/5.72 thf(fact_9084_cosh__real__nonneg,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % cosh_real_nonneg
% 5.46/5.72 thf(fact_9085_cosh__real__ge__1,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % cosh_real_ge_1
% 5.46/5.72 thf(fact_9086_cosh__real__nonpos__less__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ Y2 @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cosh_real_nonpos_less_iff
% 5.46/5.72 thf(fact_9087_cosh__real__nonneg__less__iff,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.72 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y2 ) )
% 5.46/5.72 = ( ord_less_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cosh_real_nonneg_less_iff
% 5.46/5.72 thf(fact_9088_cosh__real__strict__mono,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cosh_real_strict_mono
% 5.46/5.72 thf(fact_9089_arcosh__cosh__real,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( arcosh_real @ ( cosh_real @ X2 ) )
% 5.46/5.72 = X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcosh_cosh_real
% 5.46/5.72 thf(fact_9090_Complex__eq__i,axiom,
% 5.46/5.72 ! [X2: real,Y2: real] :
% 5.46/5.72 ( ( ( complex2 @ X2 @ Y2 )
% 5.46/5.72 = imaginary_unit )
% 5.46/5.72 = ( ( X2 = zero_zero_real )
% 5.46/5.72 & ( Y2 = one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Complex_eq_i
% 5.46/5.72 thf(fact_9091_imaginary__unit_Ocode,axiom,
% 5.46/5.72 ( imaginary_unit
% 5.46/5.72 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % imaginary_unit.code
% 5.46/5.72 thf(fact_9092_complex__inverse,axiom,
% 5.46/5.72 ! [A: real,B: real] :
% 5.46/5.72 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.46/5.72 = ( complex2 @ ( divide_divide_real @ A @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B ) @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % complex_inverse
% 5.46/5.72 thf(fact_9093_cmod__unit__one,axiom,
% 5.46/5.72 ! [A: real] :
% 5.46/5.72 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % cmod_unit_one
% 5.46/5.72 thf(fact_9094_cosh__ln__real,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( cosh_real @ ( ln_ln_real @ X2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cosh_ln_real
% 5.46/5.72 thf(fact_9095_sinh__ln__real,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( sinh_real @ ( ln_ln_real @ X2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sinh_ln_real
% 5.46/5.72 thf(fact_9096_Arg__minus__ii,axiom,
% 5.46/5.72 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.46/5.72 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Arg_minus_ii
% 5.46/5.72 thf(fact_9097_csqrt__ii,axiom,
% 5.46/5.72 ( ( csqrt @ imaginary_unit )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % csqrt_ii
% 5.46/5.72 thf(fact_9098_Arg__ii,axiom,
% 5.46/5.72 ( ( arg @ imaginary_unit )
% 5.46/5.72 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Arg_ii
% 5.46/5.72 thf(fact_9099_cis__minus__pi__half,axiom,
% 5.46/5.72 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.46/5.72
% 5.46/5.72 % cis_minus_pi_half
% 5.46/5.72 thf(fact_9100_norm__cis,axiom,
% 5.46/5.72 ! [A: real] :
% 5.46/5.72 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % norm_cis
% 5.46/5.72 thf(fact_9101_power2__csqrt,axiom,
% 5.46/5.72 ! [Z: complex] :
% 5.46/5.72 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = Z ) ).
% 5.46/5.72
% 5.46/5.72 % power2_csqrt
% 5.46/5.72 thf(fact_9102_cis__pi__half,axiom,
% 5.46/5.72 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = imaginary_unit ) ).
% 5.46/5.72
% 5.46/5.72 % cis_pi_half
% 5.46/5.72 thf(fact_9103_cis__2pi,axiom,
% 5.46/5.72 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % cis_2pi
% 5.46/5.72 thf(fact_9104_cis__divide,axiom,
% 5.46/5.72 ! [A: real,B: real] :
% 5.46/5.72 ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 5.46/5.72 = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cis_divide
% 5.46/5.72 thf(fact_9105_cis__mult,axiom,
% 5.46/5.72 ! [A: real,B: real] :
% 5.46/5.72 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.46/5.72 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cis_mult
% 5.46/5.72 thf(fact_9106_DeMoivre,axiom,
% 5.46/5.72 ! [A: real,N: nat] :
% 5.46/5.72 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.46/5.72 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % DeMoivre
% 5.46/5.72 thf(fact_9107_of__real__sqrt,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X2 ) )
% 5.46/5.72 = ( csqrt @ ( real_V4546457046886955230omplex @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_real_sqrt
% 5.46/5.72 thf(fact_9108_Arg__bounded,axiom,
% 5.46/5.72 ! [Z: complex] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.46/5.72 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.46/5.72
% 5.46/5.72 % Arg_bounded
% 5.46/5.72 thf(fact_9109_bij__betw__roots__unity,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.72 => ( bij_betw_nat_complex
% 5.46/5.72 @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.72 @ ( set_ord_lessThan_nat @ N )
% 5.46/5.72 @ ( collect_complex
% 5.46/5.72 @ ^ [Z4: complex] :
% 5.46/5.72 ( ( power_power_complex @ Z4 @ N )
% 5.46/5.72 = one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % bij_betw_roots_unity
% 5.46/5.72 thf(fact_9110_cot__less__zero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ ( cot_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cot_less_zero
% 5.46/5.72 thf(fact_9111_cot__periodic,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( cot_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.72 = ( cot_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % cot_periodic
% 5.46/5.72 thf(fact_9112_arctan__def,axiom,
% 5.46/5.72 ( arctan
% 5.46/5.72 = ( ^ [Y: real] :
% 5.46/5.72 ( the_real
% 5.46/5.72 @ ^ [X: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.46/5.72 & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 & ( ( tan_real @ X )
% 5.46/5.72 = Y ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arctan_def
% 5.46/5.72 thf(fact_9113_cot__npi,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.46/5.72 = zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % cot_npi
% 5.46/5.72 thf(fact_9114_ln__neg__is__const,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.72 => ( ( ln_ln_real @ X2 )
% 5.46/5.72 = ( the_real
% 5.46/5.72 @ ^ [X: real] : $false ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ln_neg_is_const
% 5.46/5.72 thf(fact_9115_arccos__def,axiom,
% 5.46/5.72 ( arccos
% 5.46/5.72 = ( ^ [Y: real] :
% 5.46/5.72 ( the_real
% 5.46/5.72 @ ^ [X: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.46/5.72 & ( ord_less_eq_real @ X @ pi )
% 5.46/5.72 & ( ( cos_real @ X )
% 5.46/5.72 = Y ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arccos_def
% 5.46/5.72 thf(fact_9116_pi__half,axiom,
% 5.46/5.72 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( the_real
% 5.46/5.72 @ ^ [X: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.46/5.72 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.72 & ( ( cos_real @ X )
% 5.46/5.72 = zero_zero_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pi_half
% 5.46/5.72 thf(fact_9117_pi__def,axiom,
% 5.46/5.72 ( pi
% 5.46/5.72 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.46/5.72 @ ( the_real
% 5.46/5.72 @ ^ [X: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.46/5.72 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.72 & ( ( cos_real @ X )
% 5.46/5.72 = zero_zero_real ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pi_def
% 5.46/5.72 thf(fact_9118_cot__gt__zero,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % cot_gt_zero
% 5.46/5.72 thf(fact_9119_tan__cot_H,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.46/5.72 = ( cot_real @ X2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % tan_cot'
% 5.46/5.72 thf(fact_9120_arcsin__def,axiom,
% 5.46/5.72 ( arcsin
% 5.46/5.72 = ( ^ [Y: real] :
% 5.46/5.72 ( the_real
% 5.46/5.72 @ ^ [X: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.46/5.72 & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.72 & ( ( sin_real @ X )
% 5.46/5.72 = Y ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % arcsin_def
% 5.46/5.72 thf(fact_9121_signed__take__bit__eq__take__bit__minus,axiom,
% 5.46/5.72 ( bit_ri631733984087533419it_int
% 5.46/5.72 = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K2 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_eq_take_bit_minus
% 5.46/5.72 thf(fact_9122_modulo__int__unfold,axiom,
% 5.46/5.72 ! [L2: int,K: int,N: nat,M: nat] :
% 5.46/5.72 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 | ( ( sgn_sgn_int @ K )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 | ( N = zero_zero_nat ) )
% 5.46/5.72 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.72 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.46/5.72 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 | ( ( sgn_sgn_int @ K )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 | ( N = zero_zero_nat ) )
% 5.46/5.72 => ( ( ( ( sgn_sgn_int @ K )
% 5.46/5.72 = ( sgn_sgn_int @ L2 ) )
% 5.46/5.72 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.72 = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.46/5.72 & ( ( ( sgn_sgn_int @ K )
% 5.46/5.72 != ( sgn_sgn_int @ L2 ) )
% 5.46/5.72 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.72 = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.46/5.72 @ ( minus_minus_int
% 5.46/5.72 @ ( semiri1314217659103216013at_int
% 5.46/5.72 @ ( times_times_nat @ N
% 5.46/5.72 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.72 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.46/5.72 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % modulo_int_unfold
% 5.46/5.72 thf(fact_9123_powr__int,axiom,
% 5.46/5.72 ! [X2: real,I: int] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.72 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.46/5.72 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.46/5.72 = ( power_power_real @ X2 @ ( nat2 @ I ) ) ) )
% 5.46/5.72 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.46/5.72 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.46/5.72 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % powr_int
% 5.46/5.72 thf(fact_9124_nat__numeral,axiom,
% 5.46/5.72 ! [K: num] :
% 5.46/5.72 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.46/5.72 = ( numeral_numeral_nat @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_numeral
% 5.46/5.72 thf(fact_9125_nat__1,axiom,
% 5.46/5.72 ( ( nat2 @ one_one_int )
% 5.46/5.72 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_1
% 5.46/5.72 thf(fact_9126_zless__nat__conj,axiom,
% 5.46/5.72 ! [W: int,Z: int] :
% 5.46/5.72 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.46/5.72 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.72 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zless_nat_conj
% 5.46/5.72 thf(fact_9127_nat__neg__numeral,axiom,
% 5.46/5.72 ! [K: num] :
% 5.46/5.72 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.72 = zero_zero_nat ) ).
% 5.46/5.72
% 5.46/5.72 % nat_neg_numeral
% 5.46/5.72 thf(fact_9128_signed__take__bit__nonnegative__iff,axiom,
% 5.46/5.72 ! [N: nat,K: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.46/5.72 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_nonnegative_iff
% 5.46/5.72 thf(fact_9129_signed__take__bit__negative__iff,axiom,
% 5.46/5.72 ! [N: nat,K: int] :
% 5.46/5.72 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.72 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_negative_iff
% 5.46/5.72 thf(fact_9130_zero__less__nat__eq,axiom,
% 5.46/5.72 ! [Z: int] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.46/5.72 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_nat_eq
% 5.46/5.72 thf(fact_9131_diff__nat__numeral,axiom,
% 5.46/5.72 ! [V: num,V3: num] :
% 5.46/5.72 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.46/5.72 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diff_nat_numeral
% 5.46/5.72 thf(fact_9132_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.46/5.72 ! [W: num,N: nat] :
% 5.46/5.72 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.46/5.72 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % bit_minus_numeral_Bit0_Suc_iff
% 5.46/5.72 thf(fact_9133_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.46/5.72 ! [W: num,N: nat] :
% 5.46/5.72 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.46/5.72 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % bit_minus_numeral_Bit1_Suc_iff
% 5.46/5.72 thf(fact_9134_nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.72 ! [Y2: int,X2: num,N: nat] :
% 5.46/5.72 ( ( ( nat2 @ Y2 )
% 5.46/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.46/5.72 = ( Y2
% 5.46/5.72 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_eq_numeral_power_cancel_iff
% 5.46/5.72 thf(fact_9135_numeral__power__eq__nat__cancel__iff,axiom,
% 5.46/5.72 ! [X2: num,N: nat,Y2: int] :
% 5.46/5.72 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.46/5.72 = ( nat2 @ Y2 ) )
% 5.46/5.72 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.46/5.72 = Y2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_power_eq_nat_cancel_iff
% 5.46/5.72 thf(fact_9136_nat__ceiling__le__eq,axiom,
% 5.46/5.72 ! [X2: real,A: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) @ A )
% 5.46/5.72 = ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_ceiling_le_eq
% 5.46/5.72 thf(fact_9137_one__less__nat__eq,axiom,
% 5.46/5.72 ! [Z: int] :
% 5.46/5.72 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.46/5.72 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_less_nat_eq
% 5.46/5.72 thf(fact_9138_bit__minus__numeral__int_I1_J,axiom,
% 5.46/5.72 ! [W: num,N: num] :
% 5.46/5.72 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.72 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % bit_minus_numeral_int(1)
% 5.46/5.72 thf(fact_9139_bit__minus__numeral__int_I2_J,axiom,
% 5.46/5.72 ! [W: num,N: num] :
% 5.46/5.72 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.72 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % bit_minus_numeral_int(2)
% 5.46/5.72 thf(fact_9140_nat__numeral__diff__1,axiom,
% 5.46/5.72 ! [V: num] :
% 5.46/5.72 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.46/5.72 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_numeral_diff_1
% 5.46/5.72 thf(fact_9141_nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.72 ! [A: int,X2: num,N: nat] :
% 5.46/5.72 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.46/5.72 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_less_numeral_power_cancel_iff
% 5.46/5.72 thf(fact_9142_numeral__power__less__nat__cancel__iff,axiom,
% 5.46/5.72 ! [X2: num,N: nat,A: int] :
% 5.46/5.72 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 5.46/5.72 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_power_less_nat_cancel_iff
% 5.46/5.72 thf(fact_9143_nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.72 ! [A: int,X2: num,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.46/5.72 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_le_numeral_power_cancel_iff
% 5.46/5.72 thf(fact_9144_numeral__power__le__nat__cancel__iff,axiom,
% 5.46/5.72 ! [X2: num,N: nat,A: int] :
% 5.46/5.72 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 5.46/5.72 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_power_le_nat_cancel_iff
% 5.46/5.72 thf(fact_9145_bit__and__int__iff,axiom,
% 5.46/5.72 ! [K: int,L2: int,N: nat] :
% 5.46/5.72 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 5.46/5.72 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.46/5.72 & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % bit_and_int_iff
% 5.46/5.72 thf(fact_9146_nat__numeral__as__int,axiom,
% 5.46/5.72 ( numeral_numeral_nat
% 5.46/5.72 = ( ^ [I4: num] : ( nat2 @ ( numeral_numeral_int @ I4 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_numeral_as_int
% 5.46/5.72 thf(fact_9147_nat__mono,axiom,
% 5.46/5.72 ! [X2: int,Y2: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ X2 @ Y2 )
% 5.46/5.72 => ( ord_less_eq_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_mono
% 5.46/5.72 thf(fact_9148_nat__one__as__int,axiom,
% 5.46/5.72 ( one_one_nat
% 5.46/5.72 = ( nat2 @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_one_as_int
% 5.46/5.72 thf(fact_9149_div__eq__sgn__abs,axiom,
% 5.46/5.72 ! [K: int,L2: int] :
% 5.46/5.72 ( ( ( sgn_sgn_int @ K )
% 5.46/5.72 = ( sgn_sgn_int @ L2 ) )
% 5.46/5.72 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.72 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % div_eq_sgn_abs
% 5.46/5.72 thf(fact_9150_unset__bit__nat__def,axiom,
% 5.46/5.72 ( bit_se4205575877204974255it_nat
% 5.46/5.72 = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % unset_bit_nat_def
% 5.46/5.72 thf(fact_9151_nat__mask__eq,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.72 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_mask_eq
% 5.46/5.72 thf(fact_9152_nat__mono__iff,axiom,
% 5.46/5.72 ! [Z: int,W: int] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.72 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.46/5.72 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_mono_iff
% 5.46/5.72 thf(fact_9153_zless__nat__eq__int__zless,axiom,
% 5.46/5.72 ! [M: nat,Z: int] :
% 5.46/5.72 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.46/5.72 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.46/5.72
% 5.46/5.72 % zless_nat_eq_int_zless
% 5.46/5.72 thf(fact_9154_nat__le__iff,axiom,
% 5.46/5.72 ! [X2: int,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ ( nat2 @ X2 ) @ N )
% 5.46/5.72 = ( ord_less_eq_int @ X2 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_le_iff
% 5.46/5.72 thf(fact_9155_bit__not__int__iff_H,axiom,
% 5.46/5.72 ! [K: int,N: nat] :
% 5.46/5.72 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.46/5.72 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % bit_not_int_iff'
% 5.46/5.72 thf(fact_9156_nat__int__add,axiom,
% 5.46/5.72 ! [A: nat,B: nat] :
% 5.46/5.72 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.46/5.72 = ( plus_plus_nat @ A @ B ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_int_add
% 5.46/5.72 thf(fact_9157_sgn__mod,axiom,
% 5.46/5.72 ! [L2: int,K: int] :
% 5.46/5.72 ( ( L2 != zero_zero_int )
% 5.46/5.72 => ( ~ ( dvd_dvd_int @ L2 @ K )
% 5.46/5.72 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.46/5.72 = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % sgn_mod
% 5.46/5.72 thf(fact_9158_int__minus,axiom,
% 5.46/5.72 ! [N: nat,M: nat] :
% 5.46/5.72 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.72 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % int_minus
% 5.46/5.72 thf(fact_9159_nat__abs__mult__distrib,axiom,
% 5.46/5.72 ! [W: int,Z: int] :
% 5.46/5.72 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.46/5.72 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_abs_mult_distrib
% 5.46/5.72 thf(fact_9160_real__nat__ceiling__ge,axiom,
% 5.46/5.72 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_nat_ceiling_ge
% 5.46/5.72 thf(fact_9161_and__nat__def,axiom,
% 5.46/5.72 ( bit_se727722235901077358nd_nat
% 5.46/5.72 = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % and_nat_def
% 5.46/5.72 thf(fact_9162_nat__plus__as__int,axiom,
% 5.46/5.72 ( plus_plus_nat
% 5.46/5.72 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_plus_as_int
% 5.46/5.72 thf(fact_9163_nat__times__as__int,axiom,
% 5.46/5.72 ( times_times_nat
% 5.46/5.72 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_times_as_int
% 5.46/5.72 thf(fact_9164_nat__minus__as__int,axiom,
% 5.46/5.72 ( minus_minus_nat
% 5.46/5.72 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_minus_as_int
% 5.46/5.72 thf(fact_9165_nat__div__as__int,axiom,
% 5.46/5.72 ( divide_divide_nat
% 5.46/5.72 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_div_as_int
% 5.46/5.72 thf(fact_9166_nat__mod__as__int,axiom,
% 5.46/5.72 ( modulo_modulo_nat
% 5.46/5.72 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_mod_as_int
% 5.46/5.72 thf(fact_9167_zsgn__def,axiom,
% 5.46/5.72 ( sgn_sgn_int
% 5.46/5.72 = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zsgn_def
% 5.46/5.72 thf(fact_9168_nat__less__eq__zless,axiom,
% 5.46/5.72 ! [W: int,Z: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.46/5.72 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.46/5.72 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_less_eq_zless
% 5.46/5.72 thf(fact_9169_nat__le__eq__zle,axiom,
% 5.46/5.72 ! [W: int,Z: int] :
% 5.46/5.72 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.46/5.72 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.46/5.72 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.46/5.72 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_le_eq_zle
% 5.46/5.72 thf(fact_9170_split__nat,axiom,
% 5.46/5.72 ! [P: nat > $o,I: int] :
% 5.46/5.72 ( ( P @ ( nat2 @ I ) )
% 5.46/5.72 = ( ! [N2: nat] :
% 5.46/5.72 ( ( I
% 5.46/5.72 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.46/5.72 => ( P @ N2 ) )
% 5.46/5.72 & ( ( ord_less_int @ I @ zero_zero_int )
% 5.46/5.72 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % split_nat
% 5.46/5.72 thf(fact_9171_le__nat__iff,axiom,
% 5.46/5.72 ! [K: int,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.72 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.46/5.72 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_nat_iff
% 5.46/5.72 thf(fact_9172_nat__add__distrib,axiom,
% 5.46/5.72 ! [Z: int,Z7: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.46/5.72 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.46/5.72 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_add_distrib
% 5.46/5.72 thf(fact_9173_div__sgn__abs__cancel,axiom,
% 5.46/5.72 ! [V: int,K: int,L2: int] :
% 5.46/5.72 ( ( V != zero_zero_int )
% 5.46/5.72 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L2 ) ) )
% 5.46/5.72 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % div_sgn_abs_cancel
% 5.46/5.72 thf(fact_9174_bit__imp__take__bit__positive,axiom,
% 5.46/5.72 ! [N: nat,M: nat,K: int] :
% 5.46/5.72 ( ( ord_less_nat @ N @ M )
% 5.46/5.72 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.46/5.72 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % bit_imp_take_bit_positive
% 5.46/5.72 thf(fact_9175_Suc__as__int,axiom,
% 5.46/5.72 ( suc
% 5.46/5.72 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Suc_as_int
% 5.46/5.72 thf(fact_9176_nat__mult__distrib,axiom,
% 5.46/5.72 ! [Z: int,Z7: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.72 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.46/5.72 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_mult_distrib
% 5.46/5.72 thf(fact_9177_nat__diff__distrib,axiom,
% 5.46/5.72 ! [Z7: int,Z: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.46/5.72 => ( ( ord_less_eq_int @ Z7 @ Z )
% 5.46/5.72 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 5.46/5.72 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_diff_distrib
% 5.46/5.72 thf(fact_9178_nat__diff__distrib_H,axiom,
% 5.46/5.72 ! [X2: int,Y2: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.72 => ( ( nat2 @ ( minus_minus_int @ X2 @ Y2 ) )
% 5.46/5.72 = ( minus_minus_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_diff_distrib'
% 5.46/5.72 thf(fact_9179_nat__abs__triangle__ineq,axiom,
% 5.46/5.72 ! [K: int,L2: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L2 ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_abs_triangle_ineq
% 5.46/5.72 thf(fact_9180_nat__div__distrib_H,axiom,
% 5.46/5.72 ! [Y2: int,X2: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.72 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_div_distrib'
% 5.46/5.72 thf(fact_9181_nat__div__distrib,axiom,
% 5.46/5.72 ! [X2: int,Y2: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.72 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y2 ) )
% 5.46/5.72 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_div_distrib
% 5.46/5.72 thf(fact_9182_div__dvd__sgn__abs,axiom,
% 5.46/5.72 ! [L2: int,K: int] :
% 5.46/5.72 ( ( dvd_dvd_int @ L2 @ K )
% 5.46/5.72 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.72 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L2 ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % div_dvd_sgn_abs
% 5.46/5.72 thf(fact_9183_bit__concat__bit__iff,axiom,
% 5.46/5.72 ! [M: nat,K: int,L2: int,N: nat] :
% 5.46/5.72 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 5.46/5.72 = ( ( ( ord_less_nat @ N @ M )
% 5.46/5.72 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.46/5.72 | ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.72 & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % bit_concat_bit_iff
% 5.46/5.72 thf(fact_9184_nat__power__eq,axiom,
% 5.46/5.72 ! [Z: int,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.72 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.46/5.72 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_power_eq
% 5.46/5.72 thf(fact_9185_nat__floor__neg,axiom,
% 5.46/5.72 ! [X2: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.46/5.72 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = zero_zero_nat ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_floor_neg
% 5.46/5.72 thf(fact_9186_nat__mod__distrib,axiom,
% 5.46/5.72 ! [X2: int,Y2: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.72 => ( ( nat2 @ ( modulo_modulo_int @ X2 @ Y2 ) )
% 5.46/5.72 = ( modulo_modulo_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_mod_distrib
% 5.46/5.72 thf(fact_9187_div__abs__eq__div__nat,axiom,
% 5.46/5.72 ! [K: int,L2: int] :
% 5.46/5.72 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.46/5.72 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % div_abs_eq_div_nat
% 5.46/5.72 thf(fact_9188_floor__eq3,axiom,
% 5.46/5.72 ! [N: nat,X2: real] :
% 5.46/5.72 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.46/5.72 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.46/5.72 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.72 = N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % floor_eq3
% 5.46/5.72 thf(fact_9189_le__nat__floor,axiom,
% 5.46/5.72 ! [X2: nat,A: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ A )
% 5.46/5.72 => ( ord_less_eq_nat @ X2 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_nat_floor
% 5.46/5.72 thf(fact_9190_mod__abs__eq__div__nat,axiom,
% 5.46/5.72 ! [K: int,L2: int] :
% 5.46/5.72 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.46/5.72 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_abs_eq_div_nat
% 5.46/5.72 thf(fact_9191_take__bit__nat__eq,axiom,
% 5.46/5.72 ! [K: int,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.72 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.46/5.72 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % take_bit_nat_eq
% 5.46/5.72 thf(fact_9192_nat__take__bit__eq,axiom,
% 5.46/5.72 ! [K: int,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.72 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.46/5.72 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nat_take_bit_eq
% 5.46/5.72 thf(fact_9193_divide__int__def,axiom,
% 5.46/5.73 ( divide_divide_int
% 5.46/5.73 = ( ^ [K2: int,L: int] :
% 5.46/5.73 ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 5.46/5.73 @ ( if_int
% 5.46/5.73 @ ( ( sgn_sgn_int @ K2 )
% 5.46/5.73 = ( sgn_sgn_int @ L ) )
% 5.46/5.73 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 5.46/5.73 @ ( uminus_uminus_int
% 5.46/5.73 @ ( semiri1314217659103216013at_int
% 5.46/5.73 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 5.46/5.73 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ~ ( dvd_dvd_int @ L @ K2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divide_int_def
% 5.46/5.73 thf(fact_9194_modulo__int__def,axiom,
% 5.46/5.73 ( modulo_modulo_int
% 5.46/5.73 = ( ^ [K2: int,L: int] :
% 5.46/5.73 ( if_int @ ( L = zero_zero_int ) @ K2
% 5.46/5.73 @ ( if_int
% 5.46/5.73 @ ( ( sgn_sgn_int @ K2 )
% 5.46/5.73 = ( sgn_sgn_int @ L ) )
% 5.46/5.73 @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 5.46/5.73 @ ( times_times_int @ ( sgn_sgn_int @ L )
% 5.46/5.73 @ ( minus_minus_int
% 5.46/5.73 @ ( times_times_int @ ( abs_abs_int @ L )
% 5.46/5.73 @ ( zero_n2684676970156552555ol_int
% 5.46/5.73 @ ~ ( dvd_dvd_int @ L @ K2 ) ) )
% 5.46/5.73 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % modulo_int_def
% 5.46/5.73 thf(fact_9195_signed__take__bit__eq__concat__bit,axiom,
% 5.46/5.73 ( bit_ri631733984087533419it_int
% 5.46/5.73 = ( ^ [N2: nat,K2: int] : ( bit_concat_bit @ N2 @ K2 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % signed_take_bit_eq_concat_bit
% 5.46/5.73 thf(fact_9196_nat__2,axiom,
% 5.46/5.73 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_2
% 5.46/5.73 thf(fact_9197_int__bit__bound,axiom,
% 5.46/5.73 ! [K: int] :
% 5.46/5.73 ~ ! [N3: nat] :
% 5.46/5.73 ( ! [M2: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ N3 @ M2 )
% 5.46/5.73 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.46/5.73 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.46/5.73 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.46/5.73 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.46/5.73 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_bit_bound
% 5.46/5.73 thf(fact_9198_Suc__nat__eq__nat__zadd1,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.73 => ( ( suc @ ( nat2 @ Z ) )
% 5.46/5.73 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_nat_eq_nat_zadd1
% 5.46/5.73 thf(fact_9199_nat__less__iff,axiom,
% 5.46/5.73 ! [W: int,M: nat] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.46/5.73 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.46/5.73 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_less_iff
% 5.46/5.73 thf(fact_9200_nat__mult__distrib__neg,axiom,
% 5.46/5.73 ! [Z: int,Z7: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.46/5.73 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.46/5.73 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_mult_distrib_neg
% 5.46/5.73 thf(fact_9201_nat__abs__int__diff,axiom,
% 5.46/5.73 ! [A: nat,B: nat] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ A @ B )
% 5.46/5.73 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.46/5.73 = ( minus_minus_nat @ B @ A ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.46/5.73 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.46/5.73 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_abs_int_diff
% 5.46/5.73 thf(fact_9202_floor__eq4,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.46/5.73 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.46/5.73 = N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % floor_eq4
% 5.46/5.73 thf(fact_9203_diff__nat__eq__if,axiom,
% 5.46/5.73 ! [Z7: int,Z: int] :
% 5.46/5.73 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 5.46/5.73 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.46/5.73 = ( nat2 @ Z ) ) )
% 5.46/5.73 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 5.46/5.73 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.46/5.73 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_nat_eq_if
% 5.46/5.73 thf(fact_9204_bit__int__def,axiom,
% 5.46/5.73 ( bit_se1146084159140164899it_int
% 5.46/5.73 = ( ^ [K2: int,N2: nat] :
% 5.46/5.73 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_int_def
% 5.46/5.73 thf(fact_9205_eucl__rel__int__remainderI,axiom,
% 5.46/5.73 ! [R: int,L2: int,K: int,Q2: int] :
% 5.46/5.73 ( ( ( sgn_sgn_int @ R )
% 5.46/5.73 = ( sgn_sgn_int @ L2 ) )
% 5.46/5.73 => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 5.46/5.73 => ( ( K
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R ) )
% 5.46/5.73 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % eucl_rel_int_remainderI
% 5.46/5.73 thf(fact_9206_eucl__rel__int_Osimps,axiom,
% 5.46/5.73 ( eucl_rel_int
% 5.46/5.73 = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 5.46/5.73 ( ? [K2: int] :
% 5.46/5.73 ( ( A1 = K2 )
% 5.46/5.73 & ( A22 = zero_zero_int )
% 5.46/5.73 & ( A32
% 5.46/5.73 = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 5.46/5.73 | ? [L: int,K2: int,Q4: int] :
% 5.46/5.73 ( ( A1 = K2 )
% 5.46/5.73 & ( A22 = L )
% 5.46/5.73 & ( A32
% 5.46/5.73 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.46/5.73 & ( L != zero_zero_int )
% 5.46/5.73 & ( K2
% 5.46/5.73 = ( times_times_int @ Q4 @ L ) ) )
% 5.46/5.73 | ? [R5: int,L: int,K2: int,Q4: int] :
% 5.46/5.73 ( ( A1 = K2 )
% 5.46/5.73 & ( A22 = L )
% 5.46/5.73 & ( A32
% 5.46/5.73 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.46/5.73 & ( ( sgn_sgn_int @ R5 )
% 5.46/5.73 = ( sgn_sgn_int @ L ) )
% 5.46/5.73 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 5.46/5.73 & ( K2
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R5 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % eucl_rel_int.simps
% 5.46/5.73 thf(fact_9207_eucl__rel__int_Ocases,axiom,
% 5.46/5.73 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 5.46/5.73 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 5.46/5.73 => ( ( ( A23 = zero_zero_int )
% 5.46/5.73 => ( A33
% 5.46/5.73 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.46/5.73 => ( ! [Q3: int] :
% 5.46/5.73 ( ( A33
% 5.46/5.73 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.46/5.73 => ( ( A23 != zero_zero_int )
% 5.46/5.73 => ( A12
% 5.46/5.73 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 5.46/5.73 => ~ ! [R3: int,Q3: int] :
% 5.46/5.73 ( ( A33
% 5.46/5.73 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.46/5.73 => ( ( ( sgn_sgn_int @ R3 )
% 5.46/5.73 = ( sgn_sgn_int @ A23 ) )
% 5.46/5.73 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A23 ) )
% 5.46/5.73 => ( A12
% 5.46/5.73 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % eucl_rel_int.cases
% 5.46/5.73 thf(fact_9208_div__noneq__sgn__abs,axiom,
% 5.46/5.73 ! [L2: int,K: int] :
% 5.46/5.73 ( ( L2 != zero_zero_int )
% 5.46/5.73 => ( ( ( sgn_sgn_int @ K )
% 5.46/5.73 != ( sgn_sgn_int @ L2 ) )
% 5.46/5.73 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.73 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) )
% 5.46/5.73 @ ( zero_n2684676970156552555ol_int
% 5.46/5.73 @ ~ ( dvd_dvd_int @ L2 @ K ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % div_noneq_sgn_abs
% 5.46/5.73 thf(fact_9209_even__nat__iff,axiom,
% 5.46/5.73 ! [K: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.73 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.46/5.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_nat_iff
% 5.46/5.73 thf(fact_9210_set__bit__eq,axiom,
% 5.46/5.73 ( bit_se7879613467334960850it_int
% 5.46/5.73 = ( ^ [N2: nat,K2: int] :
% 5.46/5.73 ( plus_plus_int @ K2
% 5.46/5.73 @ ( times_times_int
% 5.46/5.73 @ ( zero_n2684676970156552555ol_int
% 5.46/5.73 @ ~ ( bit_se1146084159140164899it_int @ K2 @ N2 ) )
% 5.46/5.73 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % set_bit_eq
% 5.46/5.73 thf(fact_9211_unset__bit__eq,axiom,
% 5.46/5.73 ( bit_se4203085406695923979it_int
% 5.46/5.73 = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ K2 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % unset_bit_eq
% 5.46/5.73 thf(fact_9212_take__bit__Suc__from__most,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_from_most
% 5.46/5.73 thf(fact_9213_powr__real__of__int,axiom,
% 5.46/5.73 ! [X2: real,N: int] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.46/5.73 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.46/5.73 = ( power_power_real @ X2 @ ( nat2 @ N ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.46/5.73 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.46/5.73 = ( inverse_inverse_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % powr_real_of_int
% 5.46/5.73 thf(fact_9214_divide__int__unfold,axiom,
% 5.46/5.73 ! [L2: int,K: int,N: nat,M: nat] :
% 5.46/5.73 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.46/5.73 = zero_zero_int )
% 5.46/5.73 | ( ( sgn_sgn_int @ K )
% 5.46/5.73 = zero_zero_int )
% 5.46/5.73 | ( N = zero_zero_nat ) )
% 5.46/5.73 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.73 = zero_zero_int ) )
% 5.46/5.73 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.46/5.73 = zero_zero_int )
% 5.46/5.73 | ( ( sgn_sgn_int @ K )
% 5.46/5.73 = zero_zero_int )
% 5.46/5.73 | ( N = zero_zero_nat ) )
% 5.46/5.73 => ( ( ( ( sgn_sgn_int @ K )
% 5.46/5.73 = ( sgn_sgn_int @ L2 ) )
% 5.46/5.73 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.73 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.46/5.73 & ( ( ( sgn_sgn_int @ K )
% 5.46/5.73 != ( sgn_sgn_int @ L2 ) )
% 5.46/5.73 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.73 = ( uminus_uminus_int
% 5.46/5.73 @ ( semiri1314217659103216013at_int
% 5.46/5.73 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.46/5.73 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divide_int_unfold
% 5.46/5.73 thf(fact_9215_bij__betw__nth__root__unity,axiom,
% 5.46/5.73 ! [C: complex,N: nat] :
% 5.46/5.73 ( ( C != zero_zero_complex )
% 5.46/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.46/5.73 @ ( collect_complex
% 5.46/5.73 @ ^ [Z4: complex] :
% 5.46/5.73 ( ( power_power_complex @ Z4 @ N )
% 5.46/5.73 = one_one_complex ) )
% 5.46/5.73 @ ( collect_complex
% 5.46/5.73 @ ^ [Z4: complex] :
% 5.46/5.73 ( ( power_power_complex @ Z4 @ N )
% 5.46/5.73 = C ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bij_betw_nth_root_unity
% 5.46/5.73 thf(fact_9216_or__int__unfold,axiom,
% 5.46/5.73 ( bit_se1409905431419307370or_int
% 5.46/5.73 = ( ^ [K2: int,L: int] :
% 5.46/5.73 ( if_int
% 5.46/5.73 @ ( ( K2
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 | ( L
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.46/5.73 @ ( uminus_uminus_int @ one_one_int )
% 5.46/5.73 @ ( if_int @ ( K2 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_int_unfold
% 5.46/5.73 thf(fact_9217_zero__le__sgn__iff,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X2 ) )
% 5.46/5.73 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_le_sgn_iff
% 5.46/5.73 thf(fact_9218_sgn__le__0__iff,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X2 ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % sgn_le_0_iff
% 5.46/5.73 thf(fact_9219_real__root__zero,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( root @ N @ zero_zero_real )
% 5.46/5.73 = zero_zero_real ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_zero
% 5.46/5.73 thf(fact_9220_real__root__Suc__0,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( root @ ( suc @ zero_zero_nat ) @ X2 )
% 5.46/5.73 = X2 ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_Suc_0
% 5.46/5.73 thf(fact_9221_real__root__eq__iff,axiom,
% 5.46/5.73 ! [N: nat,X2: real,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ( root @ N @ X2 )
% 5.46/5.73 = ( root @ N @ Y2 ) )
% 5.46/5.73 = ( X2 = Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_eq_iff
% 5.46/5.73 thf(fact_9222_root__0,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( root @ zero_zero_nat @ X2 )
% 5.46/5.73 = zero_zero_real ) ).
% 5.46/5.73
% 5.46/5.73 % root_0
% 5.46/5.73 thf(fact_9223_or__nonnegative__int__iff,axiom,
% 5.46/5.73 ! [K: int,L2: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 5.46/5.73 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.73 & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_nonnegative_int_iff
% 5.46/5.73 thf(fact_9224_or__negative__int__iff,axiom,
% 5.46/5.73 ! [K: int,L2: int] :
% 5.46/5.73 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.73 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.73 | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_negative_int_iff
% 5.46/5.73 thf(fact_9225_real__root__eq__0__iff,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ( root @ N @ X2 )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 = ( X2 = zero_zero_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_eq_0_iff
% 5.46/5.73 thf(fact_9226_real__root__less__iff,axiom,
% 5.46/5.73 ! [N: nat,X2: real,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) )
% 5.46/5.73 = ( ord_less_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_less_iff
% 5.46/5.73 thf(fact_9227_real__root__le__iff,axiom,
% 5.46/5.73 ! [N: nat,X2: real,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) )
% 5.46/5.73 = ( ord_less_eq_real @ X2 @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_le_iff
% 5.46/5.73 thf(fact_9228_real__root__eq__1__iff,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ( root @ N @ X2 )
% 5.46/5.73 = one_one_real )
% 5.46/5.73 = ( X2 = one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_eq_1_iff
% 5.46/5.73 thf(fact_9229_real__root__one,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( root @ N @ one_one_real )
% 5.46/5.73 = one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_one
% 5.46/5.73 thf(fact_9230_real__root__gt__0__iff,axiom,
% 5.46/5.73 ! [N: nat,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_gt_0_iff
% 5.46/5.73 thf(fact_9231_real__root__lt__0__iff,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_real @ X2 @ zero_zero_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_lt_0_iff
% 5.46/5.73 thf(fact_9232_real__root__ge__0__iff,axiom,
% 5.46/5.73 ! [N: nat,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 5.46/5.73 = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_ge_0_iff
% 5.46/5.73 thf(fact_9233_real__root__le__0__iff,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_le_0_iff
% 5.46/5.73 thf(fact_9234_real__root__lt__1__iff,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.46/5.73 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_lt_1_iff
% 5.46/5.73 thf(fact_9235_real__root__gt__1__iff,axiom,
% 5.46/5.73 ! [N: nat,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y2 ) )
% 5.46/5.73 = ( ord_less_real @ one_one_real @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_gt_1_iff
% 5.46/5.73 thf(fact_9236_real__root__le__1__iff,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.46/5.73 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_le_1_iff
% 5.46/5.73 thf(fact_9237_real__root__ge__1__iff,axiom,
% 5.46/5.73 ! [N: nat,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y2 ) )
% 5.46/5.73 = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_ge_1_iff
% 5.46/5.73 thf(fact_9238_or__minus__numerals_I6_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_minus_numerals(6)
% 5.46/5.73 thf(fact_9239_or__minus__numerals_I2_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_minus_numerals(2)
% 5.46/5.73 thf(fact_9240_real__root__pow__pos2,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.46/5.73 = X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_pow_pos2
% 5.46/5.73 thf(fact_9241_bit__or__int__iff,axiom,
% 5.46/5.73 ! [K: int,L2: int,N: nat] :
% 5.46/5.73 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 5.46/5.73 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.46/5.73 | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_or_int_iff
% 5.46/5.73 thf(fact_9242_sgn__root,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( sgn_sgn_real @ ( root @ N @ X2 ) )
% 5.46/5.73 = ( sgn_sgn_real @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sgn_root
% 5.46/5.73 thf(fact_9243_real__root__inverse,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( root @ N @ ( inverse_inverse_real @ X2 ) )
% 5.46/5.73 = ( inverse_inverse_real @ ( root @ N @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_inverse
% 5.46/5.73 thf(fact_9244_real__root__divide,axiom,
% 5.46/5.73 ! [N: nat,X2: real,Y2: real] :
% 5.46/5.73 ( ( root @ N @ ( divide_divide_real @ X2 @ Y2 ) )
% 5.46/5.73 = ( divide_divide_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_divide
% 5.46/5.73 thf(fact_9245_real__root__commute,axiom,
% 5.46/5.73 ! [M: nat,N: nat,X2: real] :
% 5.46/5.73 ( ( root @ M @ ( root @ N @ X2 ) )
% 5.46/5.73 = ( root @ N @ ( root @ M @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_commute
% 5.46/5.73 thf(fact_9246_real__root__minus,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( root @ N @ ( uminus_uminus_real @ X2 ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( root @ N @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_minus
% 5.46/5.73 thf(fact_9247_real__root__mult__exp,axiom,
% 5.46/5.73 ! [M: nat,N: nat,X2: real] :
% 5.46/5.73 ( ( root @ ( times_times_nat @ M @ N ) @ X2 )
% 5.46/5.73 = ( root @ M @ ( root @ N @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_mult_exp
% 5.46/5.73 thf(fact_9248_real__root__mult,axiom,
% 5.46/5.73 ! [N: nat,X2: real,Y2: real] :
% 5.46/5.73 ( ( root @ N @ ( times_times_real @ X2 @ Y2 ) )
% 5.46/5.73 = ( times_times_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_mult
% 5.46/5.73 thf(fact_9249_not__bit__Suc__0__Suc,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % not_bit_Suc_0_Suc
% 5.46/5.73 thf(fact_9250_bit__Suc__0__iff,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.73 = ( N = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_Suc_0_iff
% 5.46/5.73 thf(fact_9251_real__root__pos__pos__le,axiom,
% 5.46/5.73 ! [X2: real,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_pos_pos_le
% 5.46/5.73 thf(fact_9252_OR__lower,axiom,
% 5.46/5.73 ! [X2: int,Y2: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.73 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % OR_lower
% 5.46/5.73 thf(fact_9253_or__greater__eq,axiom,
% 5.46/5.73 ! [L2: int,K: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.46/5.73 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_greater_eq
% 5.46/5.73 thf(fact_9254_real__sgn__eq,axiom,
% 5.46/5.73 ( sgn_sgn_real
% 5.46/5.73 = ( ^ [X: real] : ( divide_divide_real @ X @ ( abs_abs_real @ X ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sgn_eq
% 5.46/5.73 thf(fact_9255_plus__and__or,axiom,
% 5.46/5.73 ! [X2: int,Y2: int] :
% 5.46/5.73 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X2 @ Y2 ) @ ( bit_se1409905431419307370or_int @ X2 @ Y2 ) )
% 5.46/5.73 = ( plus_plus_int @ X2 @ Y2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % plus_and_or
% 5.46/5.73 thf(fact_9256_root__sgn__power,axiom,
% 5.46/5.73 ! [N: nat,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) ) )
% 5.46/5.73 = Y2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % root_sgn_power
% 5.46/5.73 thf(fact_9257_sgn__power__root,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X2 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X2 ) ) @ N ) )
% 5.46/5.73 = X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % sgn_power_root
% 5.46/5.73 thf(fact_9258_pow_Osimps_I1_J,axiom,
% 5.46/5.73 ! [X2: num] :
% 5.46/5.73 ( ( pow @ X2 @ one )
% 5.46/5.73 = X2 ) ).
% 5.46/5.73
% 5.46/5.73 % pow.simps(1)
% 5.46/5.73 thf(fact_9259_split__root,axiom,
% 5.46/5.73 ! [P: real > $o,N: nat,X2: real] :
% 5.46/5.73 ( ( P @ ( root @ N @ X2 ) )
% 5.46/5.73 = ( ( ( N = zero_zero_nat )
% 5.46/5.73 => ( P @ zero_zero_real ) )
% 5.46/5.73 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ! [Y: real] :
% 5.46/5.73 ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.46/5.73 = X2 )
% 5.46/5.73 => ( P @ Y ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_root
% 5.46/5.73 thf(fact_9260_not__bit__Suc__0__numeral,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % not_bit_Suc_0_numeral
% 5.46/5.73 thf(fact_9261_real__root__less__mono,axiom,
% 5.46/5.73 ! [N: nat,X2: real,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.73 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_less_mono
% 5.46/5.73 thf(fact_9262_real__root__le__mono,axiom,
% 5.46/5.73 ! [N: nat,X2: real,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.46/5.73 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_le_mono
% 5.46/5.73 thf(fact_9263_real__root__power,axiom,
% 5.46/5.73 ! [N: nat,X2: real,K: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( root @ N @ ( power_power_real @ X2 @ K ) )
% 5.46/5.73 = ( power_power_real @ ( root @ N @ X2 ) @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_power
% 5.46/5.73 thf(fact_9264_real__root__abs,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( root @ N @ ( abs_abs_real @ X2 ) )
% 5.46/5.73 = ( abs_abs_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_abs
% 5.46/5.73 thf(fact_9265_sgn__eq,axiom,
% 5.46/5.73 ( sgn_sgn_complex
% 5.46/5.73 = ( ^ [Z4: complex] : ( divide1717551699836669952omplex @ Z4 @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ Z4 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sgn_eq
% 5.46/5.73 thf(fact_9266_real__root__gt__zero,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_gt_zero
% 5.46/5.73 thf(fact_9267_real__root__strict__decreasing,axiom,
% 5.46/5.73 ! [N: nat,N4: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_nat @ N @ N4 )
% 5.46/5.73 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.73 => ( ord_less_real @ ( root @ N4 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_strict_decreasing
% 5.46/5.73 thf(fact_9268_sqrt__def,axiom,
% 5.46/5.73 ( sqrt
% 5.46/5.73 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqrt_def
% 5.46/5.73 thf(fact_9269_sgn__real__def,axiom,
% 5.46/5.73 ( sgn_sgn_real
% 5.46/5.73 = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sgn_real_def
% 5.46/5.73 thf(fact_9270_root__abs__power,axiom,
% 5.46/5.73 ! [N: nat,Y2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y2 @ N ) ) )
% 5.46/5.73 = ( abs_abs_real @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % root_abs_power
% 5.46/5.73 thf(fact_9271_bit__nat__iff,axiom,
% 5.46/5.73 ! [K: int,N: nat] :
% 5.46/5.73 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.46/5.73 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.73 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_nat_iff
% 5.46/5.73 thf(fact_9272_real__root__pos__pos,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_pos_pos
% 5.46/5.73 thf(fact_9273_real__root__strict__increasing,axiom,
% 5.46/5.73 ! [N: nat,N4: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_nat @ N @ N4 )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.73 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N4 @ X2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_strict_increasing
% 5.46/5.73 thf(fact_9274_real__root__decreasing,axiom,
% 5.46/5.73 ! [N: nat,N4: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.46/5.73 => ( ord_less_eq_real @ ( root @ N4 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_decreasing
% 5.46/5.73 thf(fact_9275_real__root__pow__pos,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.46/5.73 = X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_pow_pos
% 5.46/5.73 thf(fact_9276_real__root__pos__unique,axiom,
% 5.46/5.73 ! [N: nat,Y2: real,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.46/5.73 => ( ( ( power_power_real @ Y2 @ N )
% 5.46/5.73 = X2 )
% 5.46/5.73 => ( ( root @ N @ X2 )
% 5.46/5.73 = Y2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_pos_unique
% 5.46/5.73 thf(fact_9277_real__root__power__cancel,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.46/5.73 = X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_power_cancel
% 5.46/5.73 thf(fact_9278_odd__real__root__pow,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.46/5.73 = X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % odd_real_root_pow
% 5.46/5.73 thf(fact_9279_odd__real__root__unique,axiom,
% 5.46/5.73 ! [N: nat,Y2: real,X2: real] :
% 5.46/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( ( ( power_power_real @ Y2 @ N )
% 5.46/5.73 = X2 )
% 5.46/5.73 => ( ( root @ N @ X2 )
% 5.46/5.73 = Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % odd_real_root_unique
% 5.46/5.73 thf(fact_9280_odd__real__root__power__cancel,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.46/5.73 = X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % odd_real_root_power_cancel
% 5.46/5.73 thf(fact_9281_sgn__power__injE,axiom,
% 5.46/5.73 ! [A: real,N: nat,X2: real,B: real] :
% 5.46/5.73 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.46/5.73 = X2 )
% 5.46/5.73 => ( ( X2
% 5.46/5.73 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.46/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( A = B ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sgn_power_injE
% 5.46/5.73 thf(fact_9282_real__root__increasing,axiom,
% 5.46/5.73 ! [N: nat,N4: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.73 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N4 @ X2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_root_increasing
% 5.46/5.73 thf(fact_9283_bit__nat__def,axiom,
% 5.46/5.73 ( bit_se1148574629649215175it_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] :
% 5.46/5.73 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_nat_def
% 5.46/5.73 thf(fact_9284_cis__Arg__unique,axiom,
% 5.46/5.73 ! [Z: complex,X2: real] :
% 5.46/5.73 ( ( ( sgn_sgn_complex @ Z )
% 5.46/5.73 = ( cis @ X2 ) )
% 5.46/5.73 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.46/5.73 => ( ( arg @ Z )
% 5.46/5.73 = X2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cis_Arg_unique
% 5.46/5.73 thf(fact_9285_log__root,axiom,
% 5.46/5.73 ! [N: nat,A: real,B: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.73 => ( ( log @ B @ ( root @ N @ A ) )
% 5.46/5.73 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % log_root
% 5.46/5.73 thf(fact_9286_log__base__root,axiom,
% 5.46/5.73 ! [N: nat,B: real,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.73 => ( ( log @ ( root @ N @ B ) @ X2 )
% 5.46/5.73 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % log_base_root
% 5.46/5.73 thf(fact_9287_ln__root,axiom,
% 5.46/5.73 ! [N: nat,B: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.46/5.73 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.46/5.73 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_root
% 5.46/5.73 thf(fact_9288_OR__upper,axiom,
% 5.46/5.73 ! [X2: int,N: nat,Y2: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.73 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X2 @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % OR_upper
% 5.46/5.73 thf(fact_9289_Arg__correct,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( Z != zero_zero_complex )
% 5.46/5.73 => ( ( ( sgn_sgn_complex @ Z )
% 5.46/5.73 = ( cis @ ( arg @ Z ) ) )
% 5.46/5.73 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.46/5.73 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Arg_correct
% 5.46/5.73 thf(fact_9290_root__powr__inverse,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ( root @ N @ X2 )
% 5.46/5.73 = ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % root_powr_inverse
% 5.46/5.73 thf(fact_9291_or__int__rec,axiom,
% 5.46/5.73 ( bit_se1409905431419307370or_int
% 5.46/5.73 = ( ^ [K2: int,L: int] :
% 5.46/5.73 ( plus_plus_int
% 5.46/5.73 @ ( zero_n2684676970156552555ol_int
% 5.46/5.73 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.46/5.73 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.46/5.73 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_int_rec
% 5.46/5.73 thf(fact_9292_arctan__inverse,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( X2 != zero_zero_real )
% 5.46/5.73 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X2 ) )
% 5.46/5.73 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % arctan_inverse
% 5.46/5.73 thf(fact_9293_or__minus__numerals_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_minus_numerals(5)
% 5.46/5.73 thf(fact_9294_or__minus__numerals_I1_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_minus_numerals(1)
% 5.46/5.73 thf(fact_9295_Arg__def,axiom,
% 5.46/5.73 ( arg
% 5.46/5.73 = ( ^ [Z4: complex] :
% 5.46/5.73 ( if_real @ ( Z4 = zero_zero_complex ) @ zero_zero_real
% 5.46/5.73 @ ( fChoice_real
% 5.46/5.73 @ ^ [A3: real] :
% 5.46/5.73 ( ( ( sgn_sgn_complex @ Z4 )
% 5.46/5.73 = ( cis @ A3 ) )
% 5.46/5.73 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 5.46/5.73 & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Arg_def
% 5.46/5.73 thf(fact_9296_cis__multiple__2pi,axiom,
% 5.46/5.73 ! [N: real] :
% 5.46/5.73 ( ( member_real @ N @ ring_1_Ints_real )
% 5.46/5.73 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.46/5.73 = one_one_complex ) ) ).
% 5.46/5.73
% 5.46/5.73 % cis_multiple_2pi
% 5.46/5.73 thf(fact_9297_or__nat__numerals_I2_J,axiom,
% 5.46/5.73 ! [Y2: num] :
% 5.46/5.73 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_nat_numerals(2)
% 5.46/5.73 thf(fact_9298_or__nat__numerals_I4_J,axiom,
% 5.46/5.73 ! [X2: num] :
% 5.46/5.73 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_nat_numerals(4)
% 5.46/5.73 thf(fact_9299_or__nat__numerals_I1_J,axiom,
% 5.46/5.73 ! [Y2: num] :
% 5.46/5.73 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_nat_numerals(1)
% 5.46/5.73 thf(fact_9300_or__nat__numerals_I3_J,axiom,
% 5.46/5.73 ! [X2: num] :
% 5.46/5.73 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_nat_numerals(3)
% 5.46/5.73 thf(fact_9301_or__minus__numerals_I8_J,axiom,
% 5.46/5.73 ! [N: num,M: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_minus_numerals(8)
% 5.46/5.73 thf(fact_9302_or__minus__numerals_I4_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_minus_numerals(4)
% 5.46/5.73 thf(fact_9303_or__minus__numerals_I7_J,axiom,
% 5.46/5.73 ! [N: num,M: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_minus_numerals(7)
% 5.46/5.73 thf(fact_9304_or__minus__numerals_I3_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_minus_numerals(3)
% 5.46/5.73 thf(fact_9305_or__not__num__neg_Osimps_I1_J,axiom,
% 5.46/5.73 ( ( bit_or_not_num_neg @ one @ one )
% 5.46/5.73 = one ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.simps(1)
% 5.46/5.73 thf(fact_9306_or__not__num__neg_Osimps_I4_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.46/5.73 = ( bit0 @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.simps(4)
% 5.46/5.73 thf(fact_9307_or__not__num__neg_Osimps_I6_J,axiom,
% 5.46/5.73 ! [N: num,M: num] :
% 5.46/5.73 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.46/5.73 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.simps(6)
% 5.46/5.73 thf(fact_9308_or__not__num__neg_Osimps_I3_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.46/5.73 = ( bit1 @ M ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.simps(3)
% 5.46/5.73 thf(fact_9309_or__not__num__neg_Osimps_I7_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.46/5.73 = one ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.simps(7)
% 5.46/5.73 thf(fact_9310_or__not__num__neg_Osimps_I5_J,axiom,
% 5.46/5.73 ! [N: num,M: num] :
% 5.46/5.73 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.46/5.73 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.simps(5)
% 5.46/5.73 thf(fact_9311_or__not__num__neg_Osimps_I9_J,axiom,
% 5.46/5.73 ! [N: num,M: num] :
% 5.46/5.73 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 5.46/5.73 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.simps(9)
% 5.46/5.73 thf(fact_9312_or__nat__def,axiom,
% 5.46/5.73 ( bit_se1412395901928357646or_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_nat_def
% 5.46/5.73 thf(fact_9313_or__not__num__neg_Osimps_I2_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.46/5.73 = ( bit1 @ M ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.simps(2)
% 5.46/5.73 thf(fact_9314_or__not__num__neg_Osimps_I8_J,axiom,
% 5.46/5.73 ! [N: num,M: num] :
% 5.46/5.73 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.46/5.73 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.simps(8)
% 5.46/5.73 thf(fact_9315_sin__times__pi__eq__0,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ( sin_real @ ( times_times_real @ X2 @ pi ) )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 = ( member_real @ X2 @ ring_1_Ints_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % sin_times_pi_eq_0
% 5.46/5.73 thf(fact_9316_or__not__num__neg_Oelims,axiom,
% 5.46/5.73 ! [X2: num,Xa2: num,Y2: num] :
% 5.46/5.73 ( ( ( bit_or_not_num_neg @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2 != one ) ) )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ! [M4: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( bit1 @ M4 ) ) ) )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ! [M4: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( bit1 @ M4 ) ) ) )
% 5.46/5.73 => ( ( ? [N3: num] :
% 5.46/5.73 ( X2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( bit0 @ one ) ) ) )
% 5.46/5.73 => ( ! [N3: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ! [M4: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.46/5.73 => ( ! [N3: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ! [M4: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.46/5.73 => ( ( ? [N3: num] :
% 5.46/5.73 ( X2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2 != one ) ) )
% 5.46/5.73 => ( ! [N3: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ! [M4: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.46/5.73 => ~ ! [N3: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ! [M4: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_num_neg.elims
% 5.46/5.73 thf(fact_9317_sin__integer__2pi,axiom,
% 5.46/5.73 ! [N: real] :
% 5.46/5.73 ( ( member_real @ N @ ring_1_Ints_real )
% 5.46/5.73 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.46/5.73 = zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % sin_integer_2pi
% 5.46/5.73 thf(fact_9318_cos__integer__2pi,axiom,
% 5.46/5.73 ! [N: real] :
% 5.46/5.73 ( ( member_real @ N @ ring_1_Ints_real )
% 5.46/5.73 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.46/5.73 = one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % cos_integer_2pi
% 5.46/5.73 thf(fact_9319_or__Suc__0__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_Suc_0_eq
% 5.46/5.73 thf(fact_9320_Suc__0__or__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.73 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_0_or_eq
% 5.46/5.73 thf(fact_9321_or__nat__rec,axiom,
% 5.46/5.73 ( bit_se1412395901928357646or_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] :
% 5.46/5.73 ( plus_plus_nat
% 5.46/5.73 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 5.46/5.73 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.73 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_nat_rec
% 5.46/5.73 thf(fact_9322_or__nat__unfold,axiom,
% 5.46/5.73 ( bit_se1412395901928357646or_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_nat_unfold
% 5.46/5.73 thf(fact_9323_setceilmax,axiom,
% 5.46/5.73 ! [S: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 5.46/5.73 ( ( vEBT_invar_vebt @ S @ M )
% 5.46/5.73 => ( ! [X3: vEBT_VEBT] :
% 5.46/5.73 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.46/5.73 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.46/5.73 => ( ( M
% 5.46/5.73 = ( suc @ N ) )
% 5.46/5.73 => ( ! [X3: vEBT_VEBT] :
% 5.46/5.73 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.46/5.73 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X3 ) )
% 5.46/5.73 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.46/5.73 => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S ) )
% 5.46/5.73 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 5.46/5.73 => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 5.46/5.73 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % setceilmax
% 5.46/5.73 thf(fact_9324_xor__Suc__0__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.73 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_Suc_0_eq
% 5.46/5.73 thf(fact_9325_Suc__0__xor__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.73 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.73 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_0_xor_eq
% 5.46/5.73 thf(fact_9326_horner__sum__of__bool__2__less,axiom,
% 5.46/5.73 ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % horner_sum_of_bool_2_less
% 5.46/5.73 thf(fact_9327_height__compose__list,axiom,
% 5.46/5.73 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.46/5.73 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.73 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % height_compose_list
% 5.46/5.73 thf(fact_9328_max__ins__scaled,axiom,
% 5.46/5.73 ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % max_ins_scaled
% 5.46/5.73 thf(fact_9329_height__i__max,axiom,
% 5.46/5.73 ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 5.46/5.73 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.46/5.73 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % height_i_max
% 5.46/5.73 thf(fact_9330_max__idx__list,axiom,
% 5.46/5.73 ! [I: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 5.46/5.73 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.46/5.73 => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % max_idx_list
% 5.46/5.73 thf(fact_9331_xor__nat__numerals_I4_J,axiom,
% 5.46/5.73 ! [X2: num] :
% 5.46/5.73 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_nat_numerals(4)
% 5.46/5.73 thf(fact_9332_xor__nat__numerals_I3_J,axiom,
% 5.46/5.73 ! [X2: num] :
% 5.46/5.73 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_nat_numerals(3)
% 5.46/5.73 thf(fact_9333_xor__nat__numerals_I2_J,axiom,
% 5.46/5.73 ! [Y2: num] :
% 5.46/5.73 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_nat_numerals(2)
% 5.46/5.73 thf(fact_9334_xor__nat__numerals_I1_J,axiom,
% 5.46/5.73 ! [Y2: num] :
% 5.46/5.73 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_nat_numerals(1)
% 5.46/5.73 thf(fact_9335_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 5.46/5.73 ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.46/5.73 ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu @ Deg @ TreeList @ Summary ) )
% 5.46/5.73 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % VEBT_internal.height.simps(2)
% 5.46/5.73 thf(fact_9336_VEBT__internal_Oheight_Oelims,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.46/5.73 ( ( ( vEBT_VEBT_height @ X2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( ? [A5: $o,B5: $o] :
% 5.46/5.73 ( X2
% 5.46/5.73 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.73 => ( Y2 != zero_zero_nat ) )
% 5.46/5.73 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % VEBT_internal.height.elims
% 5.46/5.73 thf(fact_9337_divide__nat__def,axiom,
% 5.46/5.73 ( divide_divide_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] :
% 5.46/5.73 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.46/5.73 @ ( lattic8265883725875713057ax_nat
% 5.46/5.73 @ ( collect_nat
% 5.46/5.73 @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N2 ) @ M3 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divide_nat_def
% 5.46/5.73 thf(fact_9338_xor__nat__unfold,axiom,
% 5.46/5.73 ( bit_se6528837805403552850or_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_nat_unfold
% 5.46/5.73 thf(fact_9339_xor__nat__rec,axiom,
% 5.46/5.73 ( bit_se6528837805403552850or_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] :
% 5.46/5.73 ( plus_plus_nat
% 5.46/5.73 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.46/5.73 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.46/5.73 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_nat_rec
% 5.46/5.73 thf(fact_9340_bij__betw__Suc,axiom,
% 5.46/5.73 ! [M7: set_nat,N4: set_nat] :
% 5.46/5.73 ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 5.46/5.73 = ( ( image_nat_nat @ suc @ M7 )
% 5.46/5.73 = N4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % bij_betw_Suc
% 5.46/5.73 thf(fact_9341_image__Suc__atLeastAtMost,axiom,
% 5.46/5.73 ! [I: nat,J: nat] :
% 5.46/5.73 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.46/5.73 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % image_Suc_atLeastAtMost
% 5.46/5.73 thf(fact_9342_xor__nonnegative__int__iff,axiom,
% 5.46/5.73 ! [K: int,L2: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 5.46/5.73 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_nonnegative_int_iff
% 5.46/5.73 thf(fact_9343_xor__negative__int__iff,axiom,
% 5.46/5.73 ! [K: int,L2: int] :
% 5.46/5.73 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.73 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.73 != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_negative_int_iff
% 5.46/5.73 thf(fact_9344_bit__xor__int__iff,axiom,
% 5.46/5.73 ! [K: int,L2: int,N: nat] :
% 5.46/5.73 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 5.46/5.73 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.46/5.73 != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_xor_int_iff
% 5.46/5.73 thf(fact_9345_zero__notin__Suc__image,axiom,
% 5.46/5.73 ! [A2: set_nat] :
% 5.46/5.73 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_notin_Suc_image
% 5.46/5.73 thf(fact_9346_XOR__lower,axiom,
% 5.46/5.73 ! [X2: int,Y2: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.46/5.73 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % XOR_lower
% 5.46/5.73 thf(fact_9347_xor__nat__def,axiom,
% 5.46/5.73 ( bit_se6528837805403552850or_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_nat_def
% 5.46/5.73 thf(fact_9348_image__Suc__lessThan,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % image_Suc_lessThan
% 5.46/5.73 thf(fact_9349_image__Suc__atMost,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.73 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % image_Suc_atMost
% 5.46/5.73 thf(fact_9350_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.46/5.73 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeast0_atMost_Suc_eq_insert_0
% 5.46/5.73 thf(fact_9351_lessThan__Suc__eq__insert__0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.46/5.73 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lessThan_Suc_eq_insert_0
% 5.46/5.73 thf(fact_9352_atMost__Suc__eq__insert__0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.46/5.73 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % atMost_Suc_eq_insert_0
% 5.46/5.73 thf(fact_9353_XOR__upper,axiom,
% 5.46/5.73 ! [X2: int,N: nat,Y2: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.46/5.73 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X2 @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % XOR_upper
% 5.46/5.73 thf(fact_9354_xor__int__rec,axiom,
% 5.46/5.73 ( bit_se6526347334894502574or_int
% 5.46/5.73 = ( ^ [K2: int,L: int] :
% 5.46/5.73 ( plus_plus_int
% 5.46/5.73 @ ( zero_n2684676970156552555ol_int
% 5.46/5.73 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 5.46/5.73 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.46/5.73 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_int_rec
% 5.46/5.73 thf(fact_9355_xor__int__unfold,axiom,
% 5.46/5.73 ( bit_se6526347334894502574or_int
% 5.46/5.73 = ( ^ [K2: int,L: int] :
% 5.46/5.73 ( if_int
% 5.46/5.73 @ ( K2
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 @ ( bit_ri7919022796975470100ot_int @ L )
% 5.46/5.73 @ ( if_int
% 5.46/5.73 @ ( L
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 @ ( bit_ri7919022796975470100ot_int @ K2 )
% 5.46/5.73 @ ( if_int @ ( K2 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_int_unfold
% 5.46/5.73 thf(fact_9356_push__bit__nonnegative__int__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % push_bit_nonnegative_int_iff
% 5.46/5.73 thf(fact_9357_push__bit__negative__int__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.73 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % push_bit_negative_int_iff
% 5.46/5.73 thf(fact_9358_concat__bit__of__zero__1,axiom,
% 5.46/5.73 ! [N: nat,L2: int] :
% 5.46/5.73 ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 5.46/5.73 = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_of_zero_1
% 5.46/5.73 thf(fact_9359_not__negative__int__iff,axiom,
% 5.46/5.73 ! [K: int] :
% 5.46/5.73 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % not_negative_int_iff
% 5.46/5.73 thf(fact_9360_not__nonnegative__int__iff,axiom,
% 5.46/5.73 ! [K: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.46/5.73 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % not_nonnegative_int_iff
% 5.46/5.73 thf(fact_9361_push__bit__of__Suc__0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % push_bit_of_Suc_0
% 5.46/5.73 thf(fact_9362_and__minus__minus__numerals,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_minus_minus_numerals
% 5.46/5.73 thf(fact_9363_or__minus__minus__numerals,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_minus_minus_numerals
% 5.46/5.73 thf(fact_9364_unset__bit__int__def,axiom,
% 5.46/5.73 ( bit_se4203085406695923979it_int
% 5.46/5.73 = ( ^ [N2: nat,K2: int] : ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % unset_bit_int_def
% 5.46/5.73 thf(fact_9365_push__bit__nat__eq,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 5.46/5.73 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % push_bit_nat_eq
% 5.46/5.73 thf(fact_9366_bit__not__int__iff,axiom,
% 5.46/5.73 ! [K: int,N: nat] :
% 5.46/5.73 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 5.46/5.73 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_not_int_iff
% 5.46/5.73 thf(fact_9367_or__int__def,axiom,
% 5.46/5.73 ( bit_se1409905431419307370or_int
% 5.46/5.73 = ( ^ [K2: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_int_def
% 5.46/5.73 thf(fact_9368_flip__bit__nat__def,axiom,
% 5.46/5.73 ( bit_se2161824704523386999it_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % flip_bit_nat_def
% 5.46/5.73 thf(fact_9369_set__bit__nat__def,axiom,
% 5.46/5.73 ( bit_se7882103937844011126it_nat
% 5.46/5.73 = ( ^ [M3: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % set_bit_nat_def
% 5.46/5.73 thf(fact_9370_not__int__def,axiom,
% 5.46/5.73 ( bit_ri7919022796975470100ot_int
% 5.46/5.73 = ( ^ [K2: int] : ( minus_minus_int @ ( uminus_uminus_int @ K2 ) @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % not_int_def
% 5.46/5.73 thf(fact_9371_and__not__numerals_I1_J,axiom,
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_numerals(1)
% 5.46/5.73 thf(fact_9372_or__not__numerals_I1_J,axiom,
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_numerals(1)
% 5.46/5.73 thf(fact_9373_bit__push__bit__iff__int,axiom,
% 5.46/5.73 ! [M: nat,K: int,N: nat] :
% 5.46/5.73 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.46/5.73 = ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.73 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_push_bit_iff_int
% 5.46/5.73 thf(fact_9374_bit__push__bit__iff__nat,axiom,
% 5.46/5.73 ! [M: nat,Q2: nat,N: nat] :
% 5.46/5.73 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 5.46/5.73 = ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.73 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_push_bit_iff_nat
% 5.46/5.73 thf(fact_9375_concat__bit__eq,axiom,
% 5.46/5.73 ( bit_concat_bit
% 5.46/5.73 = ( ^ [N2: nat,K2: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_eq
% 5.46/5.73 thf(fact_9376_xor__int__def,axiom,
% 5.46/5.73 ( bit_se6526347334894502574or_int
% 5.46/5.73 = ( ^ [K2: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ L ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_int_def
% 5.46/5.73 thf(fact_9377_concat__bit__def,axiom,
% 5.46/5.73 ( bit_concat_bit
% 5.46/5.73 = ( ^ [N2: nat,K2: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_def
% 5.46/5.73 thf(fact_9378_set__bit__int__def,axiom,
% 5.46/5.73 ( bit_se7879613467334960850it_int
% 5.46/5.73 = ( ^ [N2: nat,K2: int] : ( bit_se1409905431419307370or_int @ K2 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % set_bit_int_def
% 5.46/5.73 thf(fact_9379_flip__bit__int__def,axiom,
% 5.46/5.73 ( bit_se2159334234014336723it_int
% 5.46/5.73 = ( ^ [N2: nat,K2: int] : ( bit_se6526347334894502574or_int @ K2 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % flip_bit_int_def
% 5.46/5.73 thf(fact_9380_not__int__div__2,axiom,
% 5.46/5.73 ! [K: int] :
% 5.46/5.73 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % not_int_div_2
% 5.46/5.73 thf(fact_9381_even__not__iff__int,axiom,
% 5.46/5.73 ! [K: int] :
% 5.46/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.46/5.73 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_not_iff_int
% 5.46/5.73 thf(fact_9382_and__not__numerals_I4_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.73 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_numerals(4)
% 5.46/5.73 thf(fact_9383_and__not__numerals_I2_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_numerals(2)
% 5.46/5.73 thf(fact_9384_or__not__numerals_I2_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_numerals(2)
% 5.46/5.73 thf(fact_9385_or__not__numerals_I4_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_numerals(4)
% 5.46/5.73 thf(fact_9386_bit__minus__int__iff,axiom,
% 5.46/5.73 ! [K: int,N: nat] :
% 5.46/5.73 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.46/5.73 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_minus_int_iff
% 5.46/5.73 thf(fact_9387_int__numeral__or__not__num__neg,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_numeral_or_not_num_neg
% 5.46/5.73 thf(fact_9388_int__numeral__not__or__num__neg,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_numeral_not_or_num_neg
% 5.46/5.73 thf(fact_9389_numeral__or__not__num__eq,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_or_not_num_eq
% 5.46/5.73 thf(fact_9390_and__not__numerals_I5_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_numerals(5)
% 5.46/5.73 thf(fact_9391_and__not__numerals_I7_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.73 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_numerals(7)
% 5.46/5.73 thf(fact_9392_or__not__numerals_I3_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_numerals(3)
% 5.46/5.73 thf(fact_9393_and__not__numerals_I3_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_numerals(3)
% 5.46/5.73 thf(fact_9394_or__not__numerals_I7_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_numerals(7)
% 5.46/5.73 thf(fact_9395_push__bit__int__def,axiom,
% 5.46/5.73 ( bit_se545348938243370406it_int
% 5.46/5.73 = ( ^ [N2: nat,K2: int] : ( times_times_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % push_bit_int_def
% 5.46/5.73 thf(fact_9396_push__bit__nat__def,axiom,
% 5.46/5.73 ( bit_se547839408752420682it_nat
% 5.46/5.73 = ( ^ [N2: nat,M3: nat] : ( times_times_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % push_bit_nat_def
% 5.46/5.73 thf(fact_9397_and__not__numerals_I9_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_numerals(9)
% 5.46/5.73 thf(fact_9398_and__not__numerals_I6_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_numerals(6)
% 5.46/5.73 thf(fact_9399_or__not__numerals_I6_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_numerals(6)
% 5.46/5.73 thf(fact_9400_push__bit__minus__one,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % push_bit_minus_one
% 5.46/5.73 thf(fact_9401_or__not__numerals_I5_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_numerals(5)
% 5.46/5.73 thf(fact_9402_and__not__numerals_I8_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_numerals(8)
% 5.46/5.73 thf(fact_9403_or__not__numerals_I8_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_numerals(8)
% 5.46/5.73 thf(fact_9404_or__not__numerals_I9_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % or_not_numerals(9)
% 5.46/5.73 thf(fact_9405_not__int__rec,axiom,
% 5.46/5.73 ( bit_ri7919022796975470100ot_int
% 5.46/5.73 = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % not_int_rec
% 5.46/5.73 thf(fact_9406_VEBT__internal_Oheight_Opelims,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.46/5.73 ( ( ( vEBT_VEBT_height @ X2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X2 )
% 5.46/5.73 => ( ! [A5: $o,B5: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.73 => ( ( Y2 = zero_zero_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.46/5.73 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.73 => ( ( Y2
% 5.46/5.73 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % VEBT_internal.height.pelims
% 5.46/5.73 thf(fact_9407_vebt__maxt_Opelims,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT,Y2: option_nat] :
% 5.46/5.73 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X2 )
% 5.46/5.73 => ( ! [A5: $o,B5: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.73 => ( ( ( B5
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.73 & ( ~ B5
% 5.46/5.73 => ( ( A5
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.73 & ( ~ A5
% 5.46/5.73 => ( Y2 = none_nat ) ) ) ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.46/5.73 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.73 => ( ( Y2 = none_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.46/5.73 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.46/5.73 => ( ( Y2
% 5.46/5.73 = ( some_nat @ Ma2 ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % vebt_maxt.pelims
% 5.46/5.73 thf(fact_9408_vebt__mint_Opelims,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT,Y2: option_nat] :
% 5.46/5.73 ( ( ( vEBT_vebt_mint @ X2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X2 )
% 5.46/5.73 => ( ! [A5: $o,B5: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.73 => ( ( ( A5
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.73 & ( ~ A5
% 5.46/5.73 => ( ( B5
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.73 & ( ~ B5
% 5.46/5.73 => ( Y2 = none_nat ) ) ) ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.46/5.73 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.73 => ( ( Y2 = none_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.46/5.73 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.46/5.73 => ( ( Y2
% 5.46/5.73 = ( some_nat @ Mi2 ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % vebt_mint.pelims
% 5.46/5.73 thf(fact_9409_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.46/5.73 ( ( ( vEBT_T_m_i_n_t @ X2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X2 )
% 5.46/5.73 => ( ! [A5: $o,B5: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.73 => ( ( Y2
% 5.46/5.73 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.46/5.73 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.73 => ( ( Y2 = one_one_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.46/5.73 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.46/5.73 => ( ( Y2 = one_one_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.pelims
% 5.46/5.73 thf(fact_9410_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.46/5.73 ( ( ( vEBT_T_m_a_x_t @ X2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ X2 )
% 5.46/5.73 => ( ! [A5: $o,B5: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.73 => ( ( Y2
% 5.46/5.73 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B5 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.46/5.73 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.46/5.73 => ( ( Y2 = one_one_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.46/5.73 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.46/5.73 => ( ( Y2 = one_one_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.pelims
% 5.46/5.73 thf(fact_9411_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Opelims,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT,Y2: nat] :
% 5.46/5.73 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ X2 )
% 5.46/5.73 => ( ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.73 => ( ( Y2 = one_one_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.46/5.73 => ( ! [Uv2: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.46/5.73 => ( ( Y2 = one_one_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.46/5.73 => ( ! [Uu2: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.46/5.73 => ( ( Y2 = one_one_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.46/5.73 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.46/5.73 => ( ( Y2 = one_one_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.46/5.73 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.46/5.73 => ( ( Y2 = one_one_nat )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.pelims
% 5.46/5.73 thf(fact_9412_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT,Y2: $o] :
% 5.46/5.73 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.46/5.73 => ( ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.46/5.73 => ( ! [Uv2: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.46/5.73 => ( ~ Y2
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.46/5.73 => ( ! [Uu2: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.46/5.73 => ( ~ Y2
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.46/5.73 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.46/5.73 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.46/5.73 => ( ~ Y2
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % VEBT_internal.minNull.pelims(1)
% 5.46/5.73 thf(fact_9413_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT] :
% 5.46/5.73 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.46/5.73 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.46/5.73 => ( ! [Uv2: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.46/5.73 => ( ! [Uu2: $o] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.46/5.73 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % VEBT_internal.minNull.pelims(3)
% 5.46/5.73 thf(fact_9414_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.46/5.73 ! [X2: vEBT_VEBT] :
% 5.46/5.73 ( ( vEBT_VEBT_minNull @ X2 )
% 5.46/5.73 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.46/5.73 => ( ( ( X2
% 5.46/5.73 = ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.46/5.73 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.46/5.73 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % VEBT_internal.minNull.pelims(2)
% 5.46/5.73 thf(fact_9415_Cauchy__iff2,axiom,
% 5.46/5.73 ( topolo4055970368930404560y_real
% 5.46/5.73 = ( ^ [X5: nat > real] :
% 5.46/5.73 ! [J3: nat] :
% 5.46/5.73 ? [M8: nat] :
% 5.46/5.73 ! [M3: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ M8 @ M3 )
% 5.46/5.73 => ! [N2: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ M8 @ N2 )
% 5.46/5.73 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X5 @ M3 ) @ ( X5 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Cauchy_iff2
% 5.46/5.73 thf(fact_9416_Sum__Ico__nat,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( groups3542108847815614940at_nat
% 5.46/5.73 @ ^ [X: nat] : X
% 5.46/5.73 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.46/5.73 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Sum_Ico_nat
% 5.46/5.73 thf(fact_9417_VEBT_Osize_I3_J,axiom,
% 5.46/5.73 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.46/5.73 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.46/5.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % VEBT.size(3)
% 5.46/5.73 thf(fact_9418_image__Suc__atLeastLessThan,axiom,
% 5.46/5.73 ! [I: nat,J: nat] :
% 5.46/5.73 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 5.46/5.73 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % image_Suc_atLeastLessThan
% 5.46/5.73 thf(fact_9419_atLeastLessThan__singleton,axiom,
% 5.46/5.73 ! [M: nat] :
% 5.46/5.73 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.46/5.73 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeastLessThan_singleton
% 5.46/5.73 thf(fact_9420_ex__nat__less__eq,axiom,
% 5.46/5.73 ! [N: nat,P: nat > $o] :
% 5.46/5.73 ( ( ? [M3: nat] :
% 5.46/5.73 ( ( ord_less_nat @ M3 @ N )
% 5.46/5.73 & ( P @ M3 ) ) )
% 5.46/5.73 = ( ? [X: nat] :
% 5.46/5.73 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.46/5.73 & ( P @ X ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ex_nat_less_eq
% 5.46/5.73 thf(fact_9421_all__nat__less__eq,axiom,
% 5.46/5.73 ! [N: nat,P: nat > $o] :
% 5.46/5.73 ( ( ! [M3: nat] :
% 5.46/5.73 ( ( ord_less_nat @ M3 @ N )
% 5.46/5.73 => ( P @ M3 ) ) )
% 5.46/5.73 = ( ! [X: nat] :
% 5.46/5.73 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.46/5.73 => ( P @ X ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % all_nat_less_eq
% 5.46/5.73 thf(fact_9422_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.46/5.73 ! [L2: nat,U: nat] :
% 5.46/5.73 ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 5.46/5.73 = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeastLessThanSuc_atLeastAtMost
% 5.46/5.73 thf(fact_9423_atLeast0__lessThan__Suc,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.46/5.73 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeast0_lessThan_Suc
% 5.46/5.73 thf(fact_9424_atLeastLessThanSuc,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.73 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.46/5.73 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.46/5.73 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.46/5.73 = bot_bot_set_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeastLessThanSuc
% 5.46/5.73 thf(fact_9425_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.46/5.73 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeast0_lessThan_Suc_eq_insert_0
% 5.46/5.73 thf(fact_9426_prod__Suc__Suc__fact,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.46/5.73 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % prod_Suc_Suc_fact
% 5.46/5.73 thf(fact_9427_prod__Suc__fact,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.46/5.73 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % prod_Suc_fact
% 5.46/5.73 thf(fact_9428_atLeastLessThan__nat__numeral,axiom,
% 5.46/5.73 ! [M: nat,K: num] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.46/5.73 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.46/5.73 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.46/5.73 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.46/5.73 = bot_bot_set_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeastLessThan_nat_numeral
% 5.46/5.73 thf(fact_9429_image__minus__const__atLeastLessThan__nat,axiom,
% 5.46/5.73 ! [C: nat,Y2: nat,X2: nat] :
% 5.46/5.73 ( ( ( ord_less_nat @ C @ Y2 )
% 5.46/5.73 => ( ( image_nat_nat
% 5.46/5.73 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.46/5.73 @ ( set_or4665077453230672383an_nat @ X2 @ Y2 ) )
% 5.46/5.73 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y2 @ C ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_nat @ C @ Y2 )
% 5.46/5.73 => ( ( ( ord_less_nat @ X2 @ Y2 )
% 5.46/5.73 => ( ( image_nat_nat
% 5.46/5.73 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.46/5.73 @ ( set_or4665077453230672383an_nat @ X2 @ Y2 ) )
% 5.46/5.73 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.46/5.73 & ( ~ ( ord_less_nat @ X2 @ Y2 )
% 5.46/5.73 => ( ( image_nat_nat
% 5.46/5.73 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.46/5.73 @ ( set_or4665077453230672383an_nat @ X2 @ Y2 ) )
% 5.46/5.73 = bot_bot_set_nat ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % image_minus_const_atLeastLessThan_nat
% 5.46/5.73 thf(fact_9430_atLeast1__lessThan__eq__remove0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.73 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeast1_lessThan_eq_remove0
% 5.46/5.73 thf(fact_9431_sum__power2,axiom,
% 5.46/5.73 ! [K: nat] :
% 5.46/5.73 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.46/5.73 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % sum_power2
% 5.46/5.73 thf(fact_9432_Chebyshev__sum__upper__nat,axiom,
% 5.46/5.73 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.46/5.73 ( ! [I2: nat,J2: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.46/5.73 => ( ( ord_less_nat @ J2 @ N )
% 5.46/5.73 => ( ord_less_eq_nat @ ( A @ I2 ) @ ( A @ J2 ) ) ) )
% 5.46/5.73 => ( ! [I2: nat,J2: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.46/5.73 => ( ( ord_less_nat @ J2 @ N )
% 5.46/5.73 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I2 ) ) ) )
% 5.46/5.73 => ( ord_less_eq_nat
% 5.46/5.73 @ ( times_times_nat @ N
% 5.46/5.73 @ ( groups3542108847815614940at_nat
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( B @ I4 ) )
% 5.46/5.73 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.73 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Chebyshev_sum_upper_nat
% 5.46/5.73 thf(fact_9433_image__add__int__atLeastLessThan,axiom,
% 5.46/5.73 ! [L2: int,U: int] :
% 5.46/5.73 ( ( image_int_int
% 5.46/5.73 @ ^ [X: int] : ( plus_plus_int @ X @ L2 )
% 5.46/5.73 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 5.46/5.73 = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 5.46/5.73
% 5.46/5.73 % image_add_int_atLeastLessThan
% 5.46/5.73 thf(fact_9434_VEBT_Osize__gen_I1_J,axiom,
% 5.46/5.73 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.46/5.73 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.46/5.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % VEBT.size_gen(1)
% 5.46/5.73 thf(fact_9435_valid__eq2,axiom,
% 5.46/5.73 ! [T: vEBT_VEBT,D2: nat] :
% 5.46/5.73 ( ( vEBT_VEBT_valid @ T @ D2 )
% 5.46/5.73 => ( vEBT_invar_vebt @ T @ D2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % valid_eq2
% 5.46/5.73 thf(fact_9436_valid__eq1,axiom,
% 5.46/5.73 ! [T: vEBT_VEBT,D2: nat] :
% 5.46/5.73 ( ( vEBT_invar_vebt @ T @ D2 )
% 5.46/5.73 => ( vEBT_VEBT_valid @ T @ D2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % valid_eq1
% 5.46/5.73 thf(fact_9437_valid__eq,axiom,
% 5.46/5.73 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.46/5.73
% 5.46/5.73 % valid_eq
% 5.46/5.73 thf(fact_9438_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.46/5.73 ! [Uu: $o,Uv: $o,D2: nat] :
% 5.46/5.73 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D2 )
% 5.46/5.73 = ( D2 = one_one_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % VEBT_internal.valid'.simps(1)
% 5.46/5.73 thf(fact_9439_Code__Target__Int_Opositive__def,axiom,
% 5.46/5.73 code_Target_positive = numeral_numeral_int ).
% 5.46/5.73
% 5.46/5.73 % Code_Target_Int.positive_def
% 5.46/5.73 thf(fact_9440_csqrt_Osimps_I1_J,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( re @ ( csqrt @ Z ) )
% 5.46/5.73 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % csqrt.simps(1)
% 5.46/5.73 thf(fact_9441_complex__Re__numeral,axiom,
% 5.46/5.73 ! [V: num] :
% 5.46/5.73 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.46/5.73 = ( numeral_numeral_real @ V ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_Re_numeral
% 5.46/5.73 thf(fact_9442_Re__divide__of__nat,axiom,
% 5.46/5.73 ! [Z: complex,N: nat] :
% 5.46/5.73 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.46/5.73 = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_divide_of_nat
% 5.46/5.73 thf(fact_9443_Re__divide__of__real,axiom,
% 5.46/5.73 ! [Z: complex,R: real] :
% 5.46/5.73 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 5.46/5.73 = ( divide_divide_real @ ( re @ Z ) @ R ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_divide_of_real
% 5.46/5.73 thf(fact_9444_Re__sgn,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( re @ ( sgn_sgn_complex @ Z ) )
% 5.46/5.73 = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_sgn
% 5.46/5.73 thf(fact_9445_Re__divide__numeral,axiom,
% 5.46/5.73 ! [Z: complex,W: num] :
% 5.46/5.73 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.73 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_divide_numeral
% 5.46/5.73 thf(fact_9446_complex__Re__le__cmod,axiom,
% 5.46/5.73 ! [X2: complex] : ( ord_less_eq_real @ ( re @ X2 ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_Re_le_cmod
% 5.46/5.73 thf(fact_9447_one__complex_Osimps_I1_J,axiom,
% 5.46/5.73 ( ( re @ one_one_complex )
% 5.46/5.73 = one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % one_complex.simps(1)
% 5.46/5.73 thf(fact_9448_plus__complex_Osimps_I1_J,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( re @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.46/5.73 = ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % plus_complex.simps(1)
% 5.46/5.73 thf(fact_9449_scaleR__complex_Osimps_I1_J,axiom,
% 5.46/5.73 ! [R: real,X2: complex] :
% 5.46/5.73 ( ( re @ ( real_V2046097035970521341omplex @ R @ X2 ) )
% 5.46/5.73 = ( times_times_real @ R @ ( re @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % scaleR_complex.simps(1)
% 5.46/5.73 thf(fact_9450_minus__complex_Osimps_I1_J,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( re @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.46/5.73 = ( minus_minus_real @ ( re @ X2 ) @ ( re @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_complex.simps(1)
% 5.46/5.73 thf(fact_9451_abs__Re__le__cmod,axiom,
% 5.46/5.73 ! [X2: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % abs_Re_le_cmod
% 5.46/5.73 thf(fact_9452_Re__csqrt,axiom,
% 5.46/5.73 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_csqrt
% 5.46/5.73 thf(fact_9453_cmod__plus__Re__le__0__iff,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.46/5.73 = ( ( re @ Z )
% 5.46/5.73 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cmod_plus_Re_le_0_iff
% 5.46/5.73 thf(fact_9454_cos__n__Re__cis__pow__n,axiom,
% 5.46/5.73 ! [N: nat,A: real] :
% 5.46/5.73 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.46/5.73 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cos_n_Re_cis_pow_n
% 5.46/5.73 thf(fact_9455_csqrt_Ocode,axiom,
% 5.46/5.73 ( csqrt
% 5.46/5.73 = ( ^ [Z4: complex] :
% 5.46/5.73 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.73 @ ( times_times_real
% 5.46/5.73 @ ( if_real
% 5.46/5.73 @ ( ( im @ Z4 )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 @ one_one_real
% 5.46/5.73 @ ( sgn_sgn_real @ ( im @ Z4 ) ) )
% 5.46/5.73 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % csqrt.code
% 5.46/5.73 thf(fact_9456_csqrt_Osimps_I2_J,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( im @ ( csqrt @ Z ) )
% 5.46/5.73 = ( times_times_real
% 5.46/5.73 @ ( if_real
% 5.46/5.73 @ ( ( im @ Z )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 @ one_one_real
% 5.46/5.73 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.46/5.73 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % csqrt.simps(2)
% 5.46/5.73 thf(fact_9457_csqrt__of__real__nonpos,axiom,
% 5.46/5.73 ! [X2: complex] :
% 5.46/5.73 ( ( ( im @ X2 )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 => ( ( ord_less_eq_real @ ( re @ X2 ) @ zero_zero_real )
% 5.46/5.73 => ( ( csqrt @ X2 )
% 5.46/5.73 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X2 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % csqrt_of_real_nonpos
% 5.46/5.73 thf(fact_9458_Im__divide__of__real,axiom,
% 5.46/5.73 ! [Z: complex,R: real] :
% 5.46/5.73 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 5.46/5.73 = ( divide_divide_real @ ( im @ Z ) @ R ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_divide_of_real
% 5.46/5.73 thf(fact_9459_Im__sgn,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( im @ ( sgn_sgn_complex @ Z ) )
% 5.46/5.73 = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_sgn
% 5.46/5.73 thf(fact_9460_Re__power__real,axiom,
% 5.46/5.73 ! [X2: complex,N: nat] :
% 5.46/5.73 ( ( ( im @ X2 )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 => ( ( re @ ( power_power_complex @ X2 @ N ) )
% 5.46/5.73 = ( power_power_real @ ( re @ X2 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_power_real
% 5.46/5.73 thf(fact_9461_Im__divide__numeral,axiom,
% 5.46/5.73 ! [Z: complex,W: num] :
% 5.46/5.73 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.73 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_divide_numeral
% 5.46/5.73 thf(fact_9462_Im__divide__of__nat,axiom,
% 5.46/5.73 ! [Z: complex,N: nat] :
% 5.46/5.73 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.46/5.73 = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_divide_of_nat
% 5.46/5.73 thf(fact_9463_csqrt__of__real__nonneg,axiom,
% 5.46/5.73 ! [X2: complex] :
% 5.46/5.73 ( ( ( im @ X2 )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X2 ) )
% 5.46/5.73 => ( ( csqrt @ X2 )
% 5.46/5.73 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % csqrt_of_real_nonneg
% 5.46/5.73 thf(fact_9464_csqrt__minus,axiom,
% 5.46/5.73 ! [X2: complex] :
% 5.46/5.73 ( ( ( ord_less_real @ ( im @ X2 ) @ zero_zero_real )
% 5.46/5.73 | ( ( ( im @ X2 )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X2 ) ) ) )
% 5.46/5.73 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.46/5.73 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % csqrt_minus
% 5.46/5.73 thf(fact_9465_imaginary__unit_Osimps_I2_J,axiom,
% 5.46/5.73 ( ( im @ imaginary_unit )
% 5.46/5.73 = one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % imaginary_unit.simps(2)
% 5.46/5.73 thf(fact_9466_plus__complex_Osimps_I2_J,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( im @ ( plus_plus_complex @ X2 @ Y2 ) )
% 5.46/5.73 = ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % plus_complex.simps(2)
% 5.46/5.73 thf(fact_9467_scaleR__complex_Osimps_I2_J,axiom,
% 5.46/5.73 ! [R: real,X2: complex] :
% 5.46/5.73 ( ( im @ ( real_V2046097035970521341omplex @ R @ X2 ) )
% 5.46/5.73 = ( times_times_real @ R @ ( im @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % scaleR_complex.simps(2)
% 5.46/5.73 thf(fact_9468_minus__complex_Osimps_I2_J,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( im @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.46/5.73 = ( minus_minus_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_complex.simps(2)
% 5.46/5.73 thf(fact_9469_abs__Im__le__cmod,axiom,
% 5.46/5.73 ! [X2: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % abs_Im_le_cmod
% 5.46/5.73 thf(fact_9470_times__complex_Osimps_I2_J,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( im @ ( times_times_complex @ X2 @ Y2 ) )
% 5.46/5.73 = ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y2 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % times_complex.simps(2)
% 5.46/5.73 thf(fact_9471_cmod__Re__le__iff,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( ( im @ X2 )
% 5.46/5.73 = ( im @ Y2 ) )
% 5.46/5.73 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 5.46/5.73 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X2 ) ) @ ( abs_abs_real @ ( re @ Y2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cmod_Re_le_iff
% 5.46/5.73 thf(fact_9472_cmod__Im__le__iff,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( ( re @ X2 )
% 5.46/5.73 = ( re @ Y2 ) )
% 5.46/5.73 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 5.46/5.73 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X2 ) ) @ ( abs_abs_real @ ( im @ Y2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cmod_Im_le_iff
% 5.46/5.73 thf(fact_9473_times__complex_Osimps_I1_J,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( re @ ( times_times_complex @ X2 @ Y2 ) )
% 5.46/5.73 = ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % times_complex.simps(1)
% 5.46/5.73 thf(fact_9474_plus__complex_Ocode,axiom,
% 5.46/5.73 ( plus_plus_complex
% 5.46/5.73 = ( ^ [X: complex,Y: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X ) @ ( re @ Y ) ) @ ( plus_plus_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % plus_complex.code
% 5.46/5.73 thf(fact_9475_scaleR__complex_Ocode,axiom,
% 5.46/5.73 ( real_V2046097035970521341omplex
% 5.46/5.73 = ( ^ [R5: real,X: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X ) ) @ ( times_times_real @ R5 @ ( im @ X ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % scaleR_complex.code
% 5.46/5.73 thf(fact_9476_minus__complex_Ocode,axiom,
% 5.46/5.73 ( minus_minus_complex
% 5.46/5.73 = ( ^ [X: complex,Y: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X ) @ ( re @ Y ) ) @ ( minus_minus_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_complex.code
% 5.46/5.73 thf(fact_9477_csqrt__principal,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.46/5.73 | ( ( ( re @ ( csqrt @ Z ) )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % csqrt_principal
% 5.46/5.73 thf(fact_9478_cmod__le,axiom,
% 5.46/5.73 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cmod_le
% 5.46/5.73 thf(fact_9479_sin__n__Im__cis__pow__n,axiom,
% 5.46/5.73 ! [N: nat,A: real] :
% 5.46/5.73 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.46/5.73 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sin_n_Im_cis_pow_n
% 5.46/5.73 thf(fact_9480_Re__exp,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( re @ ( exp_complex @ Z ) )
% 5.46/5.73 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_exp
% 5.46/5.73 thf(fact_9481_Im__exp,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( im @ ( exp_complex @ Z ) )
% 5.46/5.73 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_exp
% 5.46/5.73 thf(fact_9482_times__complex_Ocode,axiom,
% 5.46/5.73 ( times_times_complex
% 5.46/5.73 = ( ^ [X: complex,Y: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % times_complex.code
% 5.46/5.73 thf(fact_9483_cmod__power2,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cmod_power2
% 5.46/5.73 thf(fact_9484_Im__power2,axiom,
% 5.46/5.73 ! [X2: complex] :
% 5.46/5.73 ( ( im @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X2 ) ) @ ( im @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_power2
% 5.46/5.73 thf(fact_9485_Re__power2,axiom,
% 5.46/5.73 ! [X2: complex] :
% 5.46/5.73 ( ( re @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = ( minus_minus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_power2
% 5.46/5.73 thf(fact_9486_complex__eq__0,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( Z = zero_zero_complex )
% 5.46/5.73 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_eq_0
% 5.46/5.73 thf(fact_9487_norm__complex__def,axiom,
% 5.46/5.73 ( real_V1022390504157884413omplex
% 5.46/5.73 = ( ^ [Z4: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % norm_complex_def
% 5.46/5.73 thf(fact_9488_inverse__complex_Osimps_I1_J,axiom,
% 5.46/5.73 ! [X2: complex] :
% 5.46/5.73 ( ( re @ ( invers8013647133539491842omplex @ X2 ) )
% 5.46/5.73 = ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % inverse_complex.simps(1)
% 5.46/5.73 thf(fact_9489_complex__neq__0,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( Z != zero_zero_complex )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_neq_0
% 5.46/5.73 thf(fact_9490_Re__divide,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( re @ ( divide1717551699836669952omplex @ X2 @ Y2 ) )
% 5.46/5.73 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_divide
% 5.46/5.73 thf(fact_9491_csqrt__unique,axiom,
% 5.46/5.73 ! [W: complex,Z: complex] :
% 5.46/5.73 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = Z )
% 5.46/5.73 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.46/5.73 | ( ( ( re @ W )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.46/5.73 => ( ( csqrt @ Z )
% 5.46/5.73 = W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % csqrt_unique
% 5.46/5.73 thf(fact_9492_csqrt__square,axiom,
% 5.46/5.73 ! [B: complex] :
% 5.46/5.73 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.46/5.73 | ( ( ( re @ B )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.46/5.73 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = B ) ) ).
% 5.46/5.73
% 5.46/5.73 % csqrt_square
% 5.46/5.73 thf(fact_9493_inverse__complex_Osimps_I2_J,axiom,
% 5.46/5.73 ! [X2: complex] :
% 5.46/5.73 ( ( im @ ( invers8013647133539491842omplex @ X2 ) )
% 5.46/5.73 = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % inverse_complex.simps(2)
% 5.46/5.73 thf(fact_9494_Im__divide,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( im @ ( divide1717551699836669952omplex @ X2 @ Y2 ) )
% 5.46/5.73 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_divide
% 5.46/5.73 thf(fact_9495_complex__abs__le__norm,axiom,
% 5.46/5.73 ! [Z: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_abs_le_norm
% 5.46/5.73 thf(fact_9496_complex__unit__circle,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( Z != zero_zero_complex )
% 5.46/5.73 => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_unit_circle
% 5.46/5.73 thf(fact_9497_inverse__complex_Ocode,axiom,
% 5.46/5.73 ( invers8013647133539491842omplex
% 5.46/5.73 = ( ^ [X: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % inverse_complex.code
% 5.46/5.73 thf(fact_9498_Complex__divide,axiom,
% 5.46/5.73 ( divide1717551699836669952omplex
% 5.46/5.73 = ( ^ [X: complex,Y: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Complex_divide
% 5.46/5.73 thf(fact_9499_Im__Reals__divide,axiom,
% 5.46/5.73 ! [R: complex,Z: complex] :
% 5.46/5.73 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.46/5.73 => ( ( im @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.46/5.73 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_Reals_divide
% 5.46/5.73 thf(fact_9500_Re__Reals__divide,axiom,
% 5.46/5.73 ! [R: complex,Z: complex] :
% 5.46/5.73 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.46/5.73 => ( ( re @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.46/5.73 = ( divide_divide_real @ ( times_times_real @ ( re @ R ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_Reals_divide
% 5.46/5.73 thf(fact_9501_Re__divide__Reals,axiom,
% 5.46/5.73 ! [R: complex,Z: complex] :
% 5.46/5.73 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.46/5.73 => ( ( re @ ( divide1717551699836669952omplex @ Z @ R ) )
% 5.46/5.73 = ( divide_divide_real @ ( re @ Z ) @ ( re @ R ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_divide_Reals
% 5.46/5.73 thf(fact_9502_Im__divide__Reals,axiom,
% 5.46/5.73 ! [R: complex,Z: complex] :
% 5.46/5.73 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.46/5.73 => ( ( im @ ( divide1717551699836669952omplex @ Z @ R ) )
% 5.46/5.73 = ( divide_divide_real @ ( im @ Z ) @ ( re @ R ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_divide_Reals
% 5.46/5.73 thf(fact_9503_complex__diff__cnj,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.46/5.73 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_diff_cnj
% 5.46/5.73 thf(fact_9504_complex__mult__cnj,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.46/5.73 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_mult_cnj
% 5.46/5.73 thf(fact_9505_complex__cnj__divide,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( cnj @ ( divide1717551699836669952omplex @ X2 @ Y2 ) )
% 5.46/5.73 = ( divide1717551699836669952omplex @ ( cnj @ X2 ) @ ( cnj @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_cnj_divide
% 5.46/5.73 thf(fact_9506_complex__cnj__diff,axiom,
% 5.46/5.73 ! [X2: complex,Y2: complex] :
% 5.46/5.73 ( ( cnj @ ( minus_minus_complex @ X2 @ Y2 ) )
% 5.46/5.73 = ( minus_minus_complex @ ( cnj @ X2 ) @ ( cnj @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_cnj_diff
% 5.46/5.73 thf(fact_9507_Re__complex__div__eq__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.46/5.73 = zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_complex_div_eq_0
% 5.46/5.73 thf(fact_9508_Im__complex__div__eq__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.46/5.73 = zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_complex_div_eq_0
% 5.46/5.73 thf(fact_9509_Re__complex__div__lt__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_complex_div_lt_0
% 5.46/5.73 thf(fact_9510_Re__complex__div__gt__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_complex_div_gt_0
% 5.46/5.73 thf(fact_9511_Re__complex__div__ge__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.46/5.73 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_complex_div_ge_0
% 5.46/5.73 thf(fact_9512_Re__complex__div__le__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % Re_complex_div_le_0
% 5.46/5.73 thf(fact_9513_Im__complex__div__lt__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_complex_div_lt_0
% 5.46/5.73 thf(fact_9514_Im__complex__div__gt__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_complex_div_gt_0
% 5.46/5.73 thf(fact_9515_Im__complex__div__ge__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.46/5.73 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_complex_div_ge_0
% 5.46/5.73 thf(fact_9516_Im__complex__div__le__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % Im_complex_div_le_0
% 5.46/5.73 thf(fact_9517_complex__mod__mult__cnj,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.46/5.73 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_mod_mult_cnj
% 5.46/5.73 thf(fact_9518_complex__div__gt__0,axiom,
% 5.46/5.73 ! [A: complex,B: complex] :
% 5.46/5.73 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.46/5.73 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_div_gt_0
% 5.46/5.73 thf(fact_9519_complex__norm__square,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_norm_square
% 5.46/5.73 thf(fact_9520_complex__add__cnj,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.46/5.73 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_add_cnj
% 5.46/5.73 thf(fact_9521_complex__div__cnj,axiom,
% 5.46/5.73 ( divide1717551699836669952omplex
% 5.46/5.73 = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % complex_div_cnj
% 5.46/5.73 thf(fact_9522_cnj__add__mult__eq__Re,axiom,
% 5.46/5.73 ! [Z: complex,W: complex] :
% 5.46/5.73 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.46/5.73 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cnj_add_mult_eq_Re
% 5.46/5.73 thf(fact_9523_divmod__step__integer__def,axiom,
% 5.46/5.73 ( unique4921790084139445826nteger
% 5.46/5.73 = ( ^ [L: num] :
% 5.46/5.73 ( produc6916734918728496179nteger
% 5.46/5.73 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divmod_step_integer_def
% 5.46/5.73 thf(fact_9524_card__Collect__less__nat,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( finite_card_nat
% 5.46/5.73 @ ( collect_nat
% 5.46/5.73 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 5.46/5.73 = N ) ).
% 5.46/5.73
% 5.46/5.73 % card_Collect_less_nat
% 5.46/5.73 thf(fact_9525_card__atMost,axiom,
% 5.46/5.73 ! [U: nat] :
% 5.46/5.73 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.46/5.73 = ( suc @ U ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_atMost
% 5.46/5.73 thf(fact_9526_card__atLeastLessThan,axiom,
% 5.46/5.73 ! [L2: nat,U: nat] :
% 5.46/5.73 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) )
% 5.46/5.73 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_atLeastLessThan
% 5.46/5.73 thf(fact_9527_card__Collect__le__nat,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( finite_card_nat
% 5.46/5.73 @ ( collect_nat
% 5.46/5.73 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 5.46/5.73 = ( suc @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_Collect_le_nat
% 5.46/5.73 thf(fact_9528_card__atLeastAtMost,axiom,
% 5.46/5.73 ! [L2: nat,U: nat] :
% 5.46/5.73 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.46/5.73 = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_atLeastAtMost
% 5.46/5.73 thf(fact_9529_card__atLeastLessThan__int,axiom,
% 5.46/5.73 ! [L2: int,U: int] :
% 5.46/5.73 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L2 @ U ) )
% 5.46/5.73 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_atLeastLessThan_int
% 5.46/5.73 thf(fact_9530_card__atLeastAtMost__int,axiom,
% 5.46/5.73 ! [L2: int,U: int] :
% 5.46/5.73 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.46/5.73 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_atLeastAtMost_int
% 5.46/5.73 thf(fact_9531_sgn__integer__code,axiom,
% 5.46/5.73 ( sgn_sgn_Code_integer
% 5.46/5.73 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sgn_integer_code
% 5.46/5.73 thf(fact_9532_divmod__integer_H__def,axiom,
% 5.46/5.73 ( unique3479559517661332726nteger
% 5.46/5.73 = ( ^ [M3: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divmod_integer'_def
% 5.46/5.73 thf(fact_9533_minus__integer__code_I1_J,axiom,
% 5.46/5.73 ! [K: code_integer] :
% 5.46/5.73 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 5.46/5.73 = K ) ).
% 5.46/5.73
% 5.46/5.73 % minus_integer_code(1)
% 5.46/5.73 thf(fact_9534_minus__integer__code_I2_J,axiom,
% 5.46/5.73 ! [L2: code_integer] :
% 5.46/5.73 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ L2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_integer_code(2)
% 5.46/5.73 thf(fact_9535_card__less,axiom,
% 5.46/5.73 ! [M7: set_nat,I: nat] :
% 5.46/5.73 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.46/5.73 => ( ( finite_card_nat
% 5.46/5.73 @ ( collect_nat
% 5.46/5.73 @ ^ [K2: nat] :
% 5.46/5.73 ( ( member_nat @ K2 @ M7 )
% 5.46/5.73 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 5.46/5.73 != zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_less
% 5.46/5.73 thf(fact_9536_card__less__Suc,axiom,
% 5.46/5.73 ! [M7: set_nat,I: nat] :
% 5.46/5.73 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.46/5.73 => ( ( suc
% 5.46/5.73 @ ( finite_card_nat
% 5.46/5.73 @ ( collect_nat
% 5.46/5.73 @ ^ [K2: nat] :
% 5.46/5.73 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.46/5.73 & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 5.46/5.73 = ( finite_card_nat
% 5.46/5.73 @ ( collect_nat
% 5.46/5.73 @ ^ [K2: nat] :
% 5.46/5.73 ( ( member_nat @ K2 @ M7 )
% 5.46/5.73 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_less_Suc
% 5.46/5.73 thf(fact_9537_card__less__Suc2,axiom,
% 5.46/5.73 ! [M7: set_nat,I: nat] :
% 5.46/5.73 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.46/5.73 => ( ( finite_card_nat
% 5.46/5.73 @ ( collect_nat
% 5.46/5.73 @ ^ [K2: nat] :
% 5.46/5.73 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.46/5.73 & ( ord_less_nat @ K2 @ I ) ) ) )
% 5.46/5.73 = ( finite_card_nat
% 5.46/5.73 @ ( collect_nat
% 5.46/5.73 @ ^ [K2: nat] :
% 5.46/5.73 ( ( member_nat @ K2 @ M7 )
% 5.46/5.73 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_less_Suc2
% 5.46/5.73 thf(fact_9538_one__natural_Orsp,axiom,
% 5.46/5.73 one_one_nat = one_one_nat ).
% 5.46/5.73
% 5.46/5.73 % one_natural.rsp
% 5.46/5.73 thf(fact_9539_subset__card__intvl__is__intvl,axiom,
% 5.46/5.73 ! [A2: set_nat,K: nat] :
% 5.46/5.73 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.46/5.73 => ( A2
% 5.46/5.73 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % subset_card_intvl_is_intvl
% 5.46/5.73 thf(fact_9540_card__le__Suc__Max,axiom,
% 5.46/5.73 ! [S2: set_nat] :
% 5.46/5.73 ( ( finite_finite_nat @ S2 )
% 5.46/5.73 => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_le_Suc_Max
% 5.46/5.73 thf(fact_9541_subset__eq__atLeast0__lessThan__card,axiom,
% 5.46/5.73 ! [N4: set_nat,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.46/5.73 => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % subset_eq_atLeast0_lessThan_card
% 5.46/5.73 thf(fact_9542_card__sum__le__nat__sum,axiom,
% 5.46/5.73 ! [S2: set_nat] :
% 5.46/5.73 ( ord_less_eq_nat
% 5.46/5.73 @ ( groups3542108847815614940at_nat
% 5.46/5.73 @ ^ [X: nat] : X
% 5.46/5.73 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 5.46/5.73 @ ( groups3542108847815614940at_nat
% 5.46/5.73 @ ^ [X: nat] : X
% 5.46/5.73 @ S2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_sum_le_nat_sum
% 5.46/5.73 thf(fact_9543_card__nth__roots,axiom,
% 5.46/5.73 ! [C: complex,N: nat] :
% 5.46/5.73 ( ( C != zero_zero_complex )
% 5.46/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( finite_card_complex
% 5.46/5.73 @ ( collect_complex
% 5.46/5.73 @ ^ [Z4: complex] :
% 5.46/5.73 ( ( power_power_complex @ Z4 @ N )
% 5.46/5.73 = C ) ) )
% 5.46/5.73 = N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_nth_roots
% 5.46/5.73 thf(fact_9544_card__roots__unity__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( finite_card_complex
% 5.46/5.73 @ ( collect_complex
% 5.46/5.73 @ ^ [Z4: complex] :
% 5.46/5.73 ( ( power_power_complex @ Z4 @ N )
% 5.46/5.73 = one_one_complex ) ) )
% 5.46/5.73 = N ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_roots_unity_eq
% 5.46/5.73 thf(fact_9545_integer__of__int__code,axiom,
% 5.46/5.73 ( code_integer_of_int
% 5.46/5.73 = ( ^ [K2: int] :
% 5.46/5.73 ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.46/5.73 @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.46/5.73 @ ( if_Code_integer
% 5.46/5.73 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = zero_zero_int )
% 5.46/5.73 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.73 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % integer_of_int_code
% 5.46/5.73 thf(fact_9546_abs__integer__code,axiom,
% 5.46/5.73 ( abs_abs_Code_integer
% 5.46/5.73 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % abs_integer_code
% 5.46/5.73 thf(fact_9547_less__integer_Oabs__eq,axiom,
% 5.46/5.73 ! [Xa2: int,X2: int] :
% 5.46/5.73 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.46/5.73 = ( ord_less_int @ Xa2 @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_integer.abs_eq
% 5.46/5.73 thf(fact_9548_less__integer__code_I1_J,axiom,
% 5.46/5.73 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.46/5.73
% 5.46/5.73 % less_integer_code(1)
% 5.46/5.73 thf(fact_9549_divide__integer_Oabs__eq,axiom,
% 5.46/5.73 ! [Xa2: int,X2: int] :
% 5.46/5.73 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.46/5.73 = ( code_integer_of_int @ ( divide_divide_int @ Xa2 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divide_integer.abs_eq
% 5.46/5.73 thf(fact_9550_modulo__integer_Oabs__eq,axiom,
% 5.46/5.73 ! [Xa2: int,X2: int] :
% 5.46/5.73 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.46/5.73 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa2 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % modulo_integer.abs_eq
% 5.46/5.73 thf(fact_9551_minus__integer_Oabs__eq,axiom,
% 5.46/5.73 ! [Xa2: int,X2: int] :
% 5.46/5.73 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.46/5.73 = ( code_integer_of_int @ ( minus_minus_int @ Xa2 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_integer.abs_eq
% 5.46/5.73 thf(fact_9552_floor__real__def,axiom,
% 5.46/5.73 ( archim6058952711729229775r_real
% 5.46/5.73 = ( ^ [X: real] :
% 5.46/5.73 ( the_int
% 5.46/5.73 @ ^ [Z4: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z4 ) @ X )
% 5.46/5.73 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % floor_real_def
% 5.46/5.73 thf(fact_9553_floor__rat__def,axiom,
% 5.46/5.73 ( archim3151403230148437115or_rat
% 5.46/5.73 = ( ^ [X: rat] :
% 5.46/5.73 ( the_int
% 5.46/5.73 @ ^ [Z4: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X )
% 5.46/5.73 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % floor_rat_def
% 5.46/5.73 thf(fact_9554_integer__of__num_I3_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.46/5.73 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.46/5.73
% 5.46/5.73 % integer_of_num(3)
% 5.46/5.73 thf(fact_9555_less__eq__rat__def,axiom,
% 5.46/5.73 ( ord_less_eq_rat
% 5.46/5.73 = ( ^ [X: rat,Y: rat] :
% 5.46/5.73 ( ( ord_less_rat @ X @ Y )
% 5.46/5.73 | ( X = Y ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_eq_rat_def
% 5.46/5.73 thf(fact_9556_obtain__pos__sum,axiom,
% 5.46/5.73 ! [R: rat] :
% 5.46/5.73 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.46/5.73 => ~ ! [S3: rat] :
% 5.46/5.73 ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 5.46/5.73 => ! [T5: rat] :
% 5.46/5.73 ( ( ord_less_rat @ zero_zero_rat @ T5 )
% 5.46/5.73 => ( R
% 5.46/5.73 != ( plus_plus_rat @ S3 @ T5 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % obtain_pos_sum
% 5.46/5.73 thf(fact_9557_sgn__rat__def,axiom,
% 5.46/5.73 ( sgn_sgn_rat
% 5.46/5.73 = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sgn_rat_def
% 5.46/5.73 thf(fact_9558_abs__rat__def,axiom,
% 5.46/5.73 ( abs_abs_rat
% 5.46/5.73 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % abs_rat_def
% 5.46/5.73 thf(fact_9559_integer__of__num__triv_I1_J,axiom,
% 5.46/5.73 ( ( code_integer_of_num @ one )
% 5.46/5.73 = one_one_Code_integer ) ).
% 5.46/5.73
% 5.46/5.73 % integer_of_num_triv(1)
% 5.46/5.73 thf(fact_9560_integer__of__num_I2_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.46/5.73 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % integer_of_num(2)
% 5.46/5.73 thf(fact_9561_integer__of__num__triv_I2_J,axiom,
% 5.46/5.73 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.46/5.73 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % integer_of_num_triv(2)
% 5.46/5.73 thf(fact_9562_normalize__negative,axiom,
% 5.46/5.73 ! [Q2: int,P2: int] :
% 5.46/5.73 ( ( ord_less_int @ Q2 @ zero_zero_int )
% 5.46/5.73 => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.46/5.73 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P2 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % normalize_negative
% 5.46/5.73 thf(fact_9563_int__of__integer__code,axiom,
% 5.46/5.73 ( code_int_of_integer
% 5.46/5.73 = ( ^ [K2: code_integer] :
% 5.46/5.73 ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 5.46/5.73 @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.46/5.73 @ ( produc1553301316500091796er_int
% 5.46/5.73 @ ^ [L: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ one_one_int ) )
% 5.46/5.73 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_of_integer_code
% 5.46/5.73 thf(fact_9564_bit__cut__integer__def,axiom,
% 5.46/5.73 ( code_bit_cut_integer
% 5.46/5.73 = ( ^ [K2: code_integer] :
% 5.46/5.73 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.73 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_cut_integer_def
% 5.46/5.73 thf(fact_9565_int__of__integer__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.46/5.73 = ( numeral_numeral_int @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_of_integer_numeral
% 5.46/5.73 thf(fact_9566_minus__integer_Orep__eq,axiom,
% 5.46/5.73 ! [X2: code_integer,Xa2: code_integer] :
% 5.46/5.73 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X2 @ Xa2 ) )
% 5.46/5.73 = ( minus_minus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_integer.rep_eq
% 5.46/5.73 thf(fact_9567_divide__integer_Orep__eq,axiom,
% 5.46/5.73 ! [X2: code_integer,Xa2: code_integer] :
% 5.46/5.73 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X2 @ Xa2 ) )
% 5.46/5.73 = ( divide_divide_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divide_integer.rep_eq
% 5.46/5.73 thf(fact_9568_modulo__integer_Orep__eq,axiom,
% 5.46/5.73 ! [X2: code_integer,Xa2: code_integer] :
% 5.46/5.73 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X2 @ Xa2 ) )
% 5.46/5.73 = ( modulo_modulo_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % modulo_integer.rep_eq
% 5.46/5.73 thf(fact_9569_diff__rat__def,axiom,
% 5.46/5.73 ( minus_minus_rat
% 5.46/5.73 = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_rat_def
% 5.46/5.73 thf(fact_9570_integer__less__iff,axiom,
% 5.46/5.73 ( ord_le6747313008572928689nteger
% 5.46/5.73 = ( ^ [K2: code_integer,L: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % integer_less_iff
% 5.46/5.73 thf(fact_9571_less__integer_Orep__eq,axiom,
% 5.46/5.73 ( ord_le6747313008572928689nteger
% 5.46/5.73 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_integer.rep_eq
% 5.46/5.73 thf(fact_9572_normalize__denom__pos,axiom,
% 5.46/5.73 ! [R: product_prod_int_int,P2: int,Q2: int] :
% 5.46/5.73 ( ( ( normalize @ R )
% 5.46/5.73 = ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.46/5.73 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % normalize_denom_pos
% 5.46/5.73 thf(fact_9573_divmod__integer__def,axiom,
% 5.46/5.73 ( code_divmod_integer
% 5.46/5.73 = ( ^ [K2: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K2 @ L ) @ ( modulo364778990260209775nteger @ K2 @ L ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divmod_integer_def
% 5.46/5.73 thf(fact_9574_num__of__integer__code,axiom,
% 5.46/5.73 ( code_num_of_integer
% 5.46/5.73 = ( ^ [K2: code_integer] :
% 5.46/5.73 ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 5.46/5.73 @ ( produc7336495610019696514er_num
% 5.46/5.73 @ ^ [L: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ one ) )
% 5.46/5.73 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % num_of_integer_code
% 5.46/5.73 thf(fact_9575_bit__cut__integer__code,axiom,
% 5.46/5.73 ( code_bit_cut_integer
% 5.46/5.73 = ( ^ [K2: code_integer] :
% 5.46/5.73 ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.46/5.73 @ ( produc9125791028180074456eger_o
% 5.46/5.73 @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 5.46/5.73 @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bit_cut_integer_code
% 5.46/5.73 thf(fact_9576_nat__of__integer__code,axiom,
% 5.46/5.73 ( code_nat_of_integer
% 5.46/5.73 = ( ^ [K2: code_integer] :
% 5.46/5.73 ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.46/5.73 @ ( produc1555791787009142072er_nat
% 5.46/5.73 @ ^ [L: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ one_one_nat ) )
% 5.46/5.73 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_of_integer_code
% 5.46/5.73 thf(fact_9577_nat__of__integer__code__post_I3_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.46/5.73 = ( numeral_numeral_nat @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_of_integer_code_post(3)
% 5.46/5.73 thf(fact_9578_nat__of__integer__code__post_I2_J,axiom,
% 5.46/5.73 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % nat_of_integer_code_post(2)
% 5.46/5.73 thf(fact_9579_divmod__abs__def,axiom,
% 5.46/5.73 ( code_divmod_abs
% 5.46/5.73 = ( ^ [K2: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divmod_abs_def
% 5.46/5.73 thf(fact_9580_divmod__integer__code,axiom,
% 5.46/5.73 ( code_divmod_integer
% 5.46/5.73 = ( ^ [K2: code_integer,L: code_integer] :
% 5.46/5.73 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.46/5.73 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 5.46/5.73 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L )
% 5.46/5.73 @ ( produc6916734918728496179nteger
% 5.46/5.73 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S6 ) ) )
% 5.46/5.73 @ ( code_divmod_abs @ K2 @ L ) ) )
% 5.46/5.73 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.46/5.73 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.46/5.73 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L )
% 5.46/5.73 @ ( produc6916734918728496179nteger
% 5.46/5.73 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S6 ) ) )
% 5.46/5.73 @ ( code_divmod_abs @ K2 @ L ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divmod_integer_code
% 5.46/5.73 thf(fact_9581_rat__minus__code,axiom,
% 5.46/5.73 ! [P2: rat,Q2: rat] :
% 5.46/5.73 ( ( quotient_of @ ( minus_minus_rat @ P2 @ Q2 ) )
% 5.46/5.73 = ( produc4245557441103728435nt_int
% 5.46/5.73 @ ^ [A3: int,C3: int] :
% 5.46/5.73 ( produc4245557441103728435nt_int
% 5.46/5.73 @ ^ [B2: int,D: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D ) ) )
% 5.46/5.73 @ ( quotient_of @ Q2 ) )
% 5.46/5.73 @ ( quotient_of @ P2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % rat_minus_code
% 5.46/5.73 thf(fact_9582_quotient__of__number_I3_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.46/5.73 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % quotient_of_number(3)
% 5.46/5.73 thf(fact_9583_quotient__of__number_I5_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.46/5.73 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % quotient_of_number(5)
% 5.46/5.73 thf(fact_9584_nat_Odisc__eq__case_I2_J,axiom,
% 5.46/5.73 ! [Nat: nat] :
% 5.46/5.73 ( ( Nat != zero_zero_nat )
% 5.46/5.73 = ( case_nat_o @ $false
% 5.46/5.73 @ ^ [Uu3: nat] : $true
% 5.46/5.73 @ Nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat.disc_eq_case(2)
% 5.46/5.73 thf(fact_9585_nat_Odisc__eq__case_I1_J,axiom,
% 5.46/5.73 ! [Nat: nat] :
% 5.46/5.73 ( ( Nat = zero_zero_nat )
% 5.46/5.73 = ( case_nat_o @ $true
% 5.46/5.73 @ ^ [Uu3: nat] : $false
% 5.46/5.73 @ Nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat.disc_eq_case(1)
% 5.46/5.73 thf(fact_9586_quotient__of__div,axiom,
% 5.46/5.73 ! [R: rat,N: int,D2: int] :
% 5.46/5.73 ( ( ( quotient_of @ R )
% 5.46/5.73 = ( product_Pair_int_int @ N @ D2 ) )
% 5.46/5.73 => ( R
% 5.46/5.73 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % quotient_of_div
% 5.46/5.73 thf(fact_9587_less__eq__nat_Osimps_I2_J,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.46/5.73 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_eq_nat.simps(2)
% 5.46/5.73 thf(fact_9588_quotient__of__denom__pos,axiom,
% 5.46/5.73 ! [R: rat,P2: int,Q2: int] :
% 5.46/5.73 ( ( ( quotient_of @ R )
% 5.46/5.73 = ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.46/5.73 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % quotient_of_denom_pos
% 5.46/5.73 thf(fact_9589_max__Suc1,axiom,
% 5.46/5.73 ! [N: nat,M: nat] :
% 5.46/5.73 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.46/5.73 = ( case_nat_nat @ ( suc @ N )
% 5.46/5.73 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ N @ M5 ) )
% 5.46/5.73 @ M ) ) ).
% 5.46/5.73
% 5.46/5.73 % max_Suc1
% 5.46/5.73 thf(fact_9590_max__Suc2,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.46/5.73 = ( case_nat_nat @ ( suc @ N )
% 5.46/5.73 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ M5 @ N ) )
% 5.46/5.73 @ M ) ) ).
% 5.46/5.73
% 5.46/5.73 % max_Suc2
% 5.46/5.73 thf(fact_9591_diff__Suc,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.46/5.73 = ( case_nat_nat @ zero_zero_nat
% 5.46/5.73 @ ^ [K2: nat] : K2
% 5.46/5.73 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_Suc
% 5.46/5.73 thf(fact_9592_rat__less__code,axiom,
% 5.46/5.73 ( ord_less_rat
% 5.46/5.73 = ( ^ [P5: rat,Q4: rat] :
% 5.46/5.73 ( produc4947309494688390418_int_o
% 5.46/5.73 @ ^ [A3: int,C3: int] :
% 5.46/5.73 ( produc4947309494688390418_int_o
% 5.46/5.73 @ ^ [B2: int,D: int] : ( ord_less_int @ ( times_times_int @ A3 @ D ) @ ( times_times_int @ C3 @ B2 ) )
% 5.46/5.73 @ ( quotient_of @ Q4 ) )
% 5.46/5.73 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % rat_less_code
% 5.46/5.73 thf(fact_9593_rat__divide__code,axiom,
% 5.46/5.73 ! [P2: rat,Q2: rat] :
% 5.46/5.73 ( ( quotient_of @ ( divide_divide_rat @ P2 @ Q2 ) )
% 5.46/5.73 = ( produc4245557441103728435nt_int
% 5.46/5.73 @ ^ [A3: int,C3: int] :
% 5.46/5.73 ( produc4245557441103728435nt_int
% 5.46/5.73 @ ^ [B2: int,D: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D ) @ ( times_times_int @ C3 @ B2 ) ) )
% 5.46/5.73 @ ( quotient_of @ Q2 ) )
% 5.46/5.73 @ ( quotient_of @ P2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % rat_divide_code
% 5.46/5.73 thf(fact_9594_rat__floor__code,axiom,
% 5.46/5.73 ( archim3151403230148437115or_rat
% 5.46/5.73 = ( ^ [P5: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P5 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % rat_floor_code
% 5.46/5.73 thf(fact_9595_divide__rat__def,axiom,
% 5.46/5.73 ( divide_divide_rat
% 5.46/5.73 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divide_rat_def
% 5.46/5.73 thf(fact_9596_pred__def,axiom,
% 5.46/5.73 ( pred
% 5.46/5.73 = ( case_nat_nat @ zero_zero_nat
% 5.46/5.73 @ ^ [X24: nat] : X24 ) ) ).
% 5.46/5.73
% 5.46/5.73 % pred_def
% 5.46/5.73 thf(fact_9597_Frct__code__post_I5_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.73 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Frct_code_post(5)
% 5.46/5.73 thf(fact_9598_Frct__code__post_I6_J,axiom,
% 5.46/5.73 ! [K: num,L2: num] :
% 5.46/5.73 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 5.46/5.73 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Frct_code_post(6)
% 5.46/5.73 thf(fact_9599_drop__bit__numeral__minus__bit1,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.73 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_numeral_minus_bit1
% 5.46/5.73 thf(fact_9600_drop__bit__nonnegative__int__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_nonnegative_int_iff
% 5.46/5.73 thf(fact_9601_drop__bit__negative__int__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.73 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_negative_int_iff
% 5.46/5.73 thf(fact_9602_drop__bit__minus__one,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_minus_one
% 5.46/5.73 thf(fact_9603_drop__bit__Suc__minus__bit0,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.73 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_Suc_minus_bit0
% 5.46/5.73 thf(fact_9604_drop__bit__numeral__minus__bit0,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.73 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_numeral_minus_bit0
% 5.46/5.73 thf(fact_9605_drop__bit__Suc__minus__bit1,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.73 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_Suc_minus_bit1
% 5.46/5.73 thf(fact_9606_drop__bit__push__bit__int,axiom,
% 5.46/5.73 ! [M: nat,N: nat,K: int] :
% 5.46/5.73 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.46/5.73 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_push_bit_int
% 5.46/5.73 thf(fact_9607_drop__bit__int__def,axiom,
% 5.46/5.73 ( bit_se8568078237143864401it_int
% 5.46/5.73 = ( ^ [N2: nat,K2: int] : ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_int_def
% 5.46/5.73 thf(fact_9608_Frct__code__post_I4_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.46/5.73 = ( numeral_numeral_rat @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % Frct_code_post(4)
% 5.46/5.73 thf(fact_9609_prod__decode__aux_Osimps,axiom,
% 5.46/5.73 ( nat_prod_decode_aux
% 5.46/5.73 = ( ^ [K2: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K2 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K2 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M3 @ ( suc @ K2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % prod_decode_aux.simps
% 5.46/5.73 thf(fact_9610_prod__decode__aux_Oelims,axiom,
% 5.46/5.73 ! [X2: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 5.46/5.73 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % prod_decode_aux.elims
% 5.46/5.73 thf(fact_9611_Suc__0__mod__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.73 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_0_mod_numeral
% 5.46/5.73 thf(fact_9612_drop__bit__of__Suc__0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_of_Suc_0
% 5.46/5.73 thf(fact_9613_snd__divmod__nat,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.46/5.73 = ( modulo_modulo_nat @ M @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % snd_divmod_nat
% 5.46/5.73 thf(fact_9614_drop__bit__nat__eq,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 5.46/5.73 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_nat_eq
% 5.46/5.73 thf(fact_9615_drop__bit__nat__def,axiom,
% 5.46/5.73 ( bit_se8570568707652914677it_nat
% 5.46/5.73 = ( ^ [N2: nat,M3: nat] : ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % drop_bit_nat_def
% 5.46/5.73 thf(fact_9616_Suc__0__div__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.73 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_0_div_numeral
% 5.46/5.73 thf(fact_9617_finite__enumerate,axiom,
% 5.46/5.73 ! [S2: set_nat] :
% 5.46/5.73 ( ( finite_finite_nat @ S2 )
% 5.46/5.73 => ? [R3: nat > nat] :
% 5.46/5.73 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 5.46/5.73 & ! [N7: nat] :
% 5.46/5.73 ( ( ord_less_nat @ N7 @ ( finite_card_nat @ S2 ) )
% 5.46/5.73 => ( member_nat @ ( R3 @ N7 ) @ S2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % finite_enumerate
% 5.46/5.73 thf(fact_9618_divmod__integer__eq__cases,axiom,
% 5.46/5.73 ( code_divmod_integer
% 5.46/5.73 = ( ^ [K2: code_integer,L: code_integer] :
% 5.46/5.73 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.46/5.73 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.46/5.73 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 5.46/5.73 @ ( if_Pro6119634080678213985nteger
% 5.46/5.73 @ ( ( sgn_sgn_Code_integer @ K2 )
% 5.46/5.73 = ( sgn_sgn_Code_integer @ L ) )
% 5.46/5.73 @ ( code_divmod_abs @ K2 @ L )
% 5.46/5.73 @ ( produc6916734918728496179nteger
% 5.46/5.73 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S6 ) ) )
% 5.46/5.73 @ ( code_divmod_abs @ K2 @ L ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divmod_integer_eq_cases
% 5.46/5.73 thf(fact_9619_snd__divmod__integer,axiom,
% 5.46/5.73 ! [K: code_integer,L2: code_integer] :
% 5.46/5.73 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L2 ) )
% 5.46/5.73 = ( modulo364778990260209775nteger @ K @ L2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % snd_divmod_integer
% 5.46/5.73 thf(fact_9620_snd__divmod__abs,axiom,
% 5.46/5.73 ! [K: code_integer,L2: code_integer] :
% 5.46/5.73 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L2 ) )
% 5.46/5.73 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % snd_divmod_abs
% 5.46/5.73 thf(fact_9621_fst__divmod__nat,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.46/5.73 = ( divide_divide_nat @ M @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % fst_divmod_nat
% 5.46/5.73 thf(fact_9622_quotient__of__denom__pos_H,axiom,
% 5.46/5.73 ! [R: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % quotient_of_denom_pos'
% 5.46/5.73 thf(fact_9623_minus__one__mod__numeral,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_one_mod_numeral
% 5.46/5.73 thf(fact_9624_one__mod__minus__numeral,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_mod_minus_numeral
% 5.46/5.73 thf(fact_9625_minus__numeral__mod__numeral,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_numeral_mod_numeral
% 5.46/5.73 thf(fact_9626_fst__divmod__integer,axiom,
% 5.46/5.73 ! [K: code_integer,L2: code_integer] :
% 5.46/5.73 ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L2 ) )
% 5.46/5.73 = ( divide6298287555418463151nteger @ K @ L2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % fst_divmod_integer
% 5.46/5.73 thf(fact_9627_fst__divmod__abs,axiom,
% 5.46/5.73 ! [K: code_integer,L2: code_integer] :
% 5.46/5.73 ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L2 ) )
% 5.46/5.73 = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % fst_divmod_abs
% 5.46/5.73 thf(fact_9628_numeral__mod__minus__numeral,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_mod_minus_numeral
% 5.46/5.73 thf(fact_9629_card_Ocomp__fun__commute__on,axiom,
% 5.46/5.73 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.46/5.73 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.46/5.73
% 5.46/5.73 % card.comp_fun_commute_on
% 5.46/5.73 thf(fact_9630_Divides_Oadjust__mod__def,axiom,
% 5.46/5.73 ( adjust_mod
% 5.46/5.73 = ( ^ [L: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L @ R5 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Divides.adjust_mod_def
% 5.46/5.73 thf(fact_9631_bezw_Oelims,axiom,
% 5.46/5.73 ! [X2: nat,Xa2: nat,Y2: product_prod_int_int] :
% 5.46/5.73 ( ( ( bezw @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.46/5.73 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bezw.elims
% 5.46/5.73 thf(fact_9632_bezw__non__0,axiom,
% 5.46/5.73 ! [Y2: nat,X2: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ Y2 )
% 5.46/5.73 => ( ( bezw @ X2 @ Y2 )
% 5.46/5.73 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bezw_non_0
% 5.46/5.73 thf(fact_9633_bezw_Osimps,axiom,
% 5.46/5.73 ( bezw
% 5.46/5.73 = ( ^ [X: nat,Y: nat] : ( if_Pro3027730157355071871nt_int @ ( Y = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bezw.simps
% 5.46/5.73 thf(fact_9634_Code__Target__Int_Onegative__def,axiom,
% 5.46/5.73 ( code_Target_negative
% 5.46/5.73 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % Code_Target_Int.negative_def
% 5.46/5.73 thf(fact_9635_bezw_Opelims,axiom,
% 5.46/5.73 ! [X2: nat,Xa2: nat,Y2: product_prod_int_int] :
% 5.46/5.73 ( ( ( bezw @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.46/5.73 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.46/5.73 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) )
% 5.46/5.73 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bezw.pelims
% 5.46/5.73 thf(fact_9636_prod__decode__aux_Opelims,axiom,
% 5.46/5.73 ! [X2: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 5.46/5.73 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.46/5.73 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) )
% 5.46/5.73 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % prod_decode_aux.pelims
% 5.46/5.73 thf(fact_9637_normalize__def,axiom,
% 5.46/5.73 ( normalize
% 5.46/5.73 = ( ^ [P5: product_prod_int_int] :
% 5.46/5.73 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 5.46/5.73 @ ( if_Pro3027730157355071871nt_int
% 5.46/5.73 @ ( ( product_snd_int_int @ P5 )
% 5.46/5.73 = zero_zero_int )
% 5.46/5.73 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.46/5.73 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % normalize_def
% 5.46/5.73 thf(fact_9638_gcd__pos__int,axiom,
% 5.46/5.73 ! [M: int,N: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 5.46/5.73 = ( ( M != zero_zero_int )
% 5.46/5.73 | ( N != zero_zero_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_pos_int
% 5.46/5.73 thf(fact_9639_gcd__neg__numeral__2__int,axiom,
% 5.46/5.73 ! [X2: int,N: num] :
% 5.46/5.73 ( ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( gcd_gcd_int @ X2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_neg_numeral_2_int
% 5.46/5.73 thf(fact_9640_gcd__neg__numeral__1__int,axiom,
% 5.46/5.73 ! [N: num,X2: int] :
% 5.46/5.73 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X2 )
% 5.46/5.73 = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_neg_numeral_1_int
% 5.46/5.73 thf(fact_9641_gcd__red__int,axiom,
% 5.46/5.73 ( gcd_gcd_int
% 5.46/5.73 = ( ^ [X: int,Y: int] : ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_red_int
% 5.46/5.73 thf(fact_9642_gcd__le1__int,axiom,
% 5.46/5.73 ! [A: int,B: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.73 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_le1_int
% 5.46/5.73 thf(fact_9643_gcd__le2__int,axiom,
% 5.46/5.73 ! [B: int,A: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.73 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_le2_int
% 5.46/5.73 thf(fact_9644_gcd__non__0__int,axiom,
% 5.46/5.73 ! [Y2: int,X2: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ Y2 )
% 5.46/5.73 => ( ( gcd_gcd_int @ X2 @ Y2 )
% 5.46/5.73 = ( gcd_gcd_int @ Y2 @ ( modulo_modulo_int @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_non_0_int
% 5.46/5.73 thf(fact_9645_gcd__code__int,axiom,
% 5.46/5.73 ( gcd_gcd_int
% 5.46/5.73 = ( ^ [K2: int,L: int] : ( abs_abs_int @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( gcd_gcd_int @ L @ ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_code_int
% 5.46/5.73 thf(fact_9646_nat__descend__induct,axiom,
% 5.46/5.73 ! [N: nat,P: nat > $o,M: nat] :
% 5.46/5.73 ( ! [K3: nat] :
% 5.46/5.73 ( ( ord_less_nat @ N @ K3 )
% 5.46/5.73 => ( P @ K3 ) )
% 5.46/5.73 => ( ! [K3: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ K3 @ N )
% 5.46/5.73 => ( ! [I3: nat] :
% 5.46/5.73 ( ( ord_less_nat @ K3 @ I3 )
% 5.46/5.73 => ( P @ I3 ) )
% 5.46/5.73 => ( P @ K3 ) ) )
% 5.46/5.73 => ( P @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_descend_induct
% 5.46/5.73 thf(fact_9647_card__greaterThanLessThan__int,axiom,
% 5.46/5.73 ! [L2: int,U: int] :
% 5.46/5.73 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 5.46/5.73 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_greaterThanLessThan_int
% 5.46/5.73 thf(fact_9648_xor__minus__numerals_I1_J,axiom,
% 5.46/5.73 ! [N: num,K: int] :
% 5.46/5.73 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_minus_numerals(1)
% 5.46/5.73 thf(fact_9649_gcd__1__nat,axiom,
% 5.46/5.73 ! [M: nat] :
% 5.46/5.73 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_1_nat
% 5.46/5.73 thf(fact_9650_gcd__Suc__0,axiom,
% 5.46/5.73 ! [M: nat] :
% 5.46/5.73 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_Suc_0
% 5.46/5.73 thf(fact_9651_gcd__pos__nat,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.46/5.73 = ( ( M != zero_zero_nat )
% 5.46/5.73 | ( N != zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_pos_nat
% 5.46/5.73 thf(fact_9652_xor__minus__numerals_I2_J,axiom,
% 5.46/5.73 ! [K: int,N: num] :
% 5.46/5.73 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_minus_numerals(2)
% 5.46/5.73 thf(fact_9653_gcd__le1__nat,axiom,
% 5.46/5.73 ! [A: nat,B: nat] :
% 5.46/5.73 ( ( A != zero_zero_nat )
% 5.46/5.73 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_le1_nat
% 5.46/5.73 thf(fact_9654_gcd__le2__nat,axiom,
% 5.46/5.73 ! [B: nat,A: nat] :
% 5.46/5.73 ( ( B != zero_zero_nat )
% 5.46/5.73 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_le2_nat
% 5.46/5.73 thf(fact_9655_gcd__mult__distrib__nat,axiom,
% 5.46/5.73 ! [K: nat,M: nat,N: nat] :
% 5.46/5.73 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.46/5.73 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_mult_distrib_nat
% 5.46/5.73 thf(fact_9656_gcd__red__nat,axiom,
% 5.46/5.73 ( gcd_gcd_nat
% 5.46/5.73 = ( ^ [X: nat,Y: nat] : ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_red_nat
% 5.46/5.73 thf(fact_9657_gcd__diff2__nat,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.73 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.46/5.73 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_diff2_nat
% 5.46/5.73 thf(fact_9658_gcd__diff1__nat,axiom,
% 5.46/5.73 ! [N: nat,M: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.46/5.73 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_diff1_nat
% 5.46/5.73 thf(fact_9659_gcd__non__0__nat,axiom,
% 5.46/5.73 ! [Y2: nat,X2: nat] :
% 5.46/5.73 ( ( Y2 != zero_zero_nat )
% 5.46/5.73 => ( ( gcd_gcd_nat @ X2 @ Y2 )
% 5.46/5.73 = ( gcd_gcd_nat @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_non_0_nat
% 5.46/5.73 thf(fact_9660_gcd__nat_Osimps,axiom,
% 5.46/5.73 ( gcd_gcd_nat
% 5.46/5.73 = ( ^ [X: nat,Y: nat] : ( if_nat @ ( Y = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_nat.simps
% 5.46/5.73 thf(fact_9661_gcd__nat_Oelims,axiom,
% 5.46/5.73 ! [X2: nat,Xa2: nat,Y2: nat] :
% 5.46/5.73 ( ( ( gcd_gcd_nat @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.73 => ( Y2 = X2 ) )
% 5.46/5.73 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_nat.elims
% 5.46/5.73 thf(fact_9662_bezout__nat,axiom,
% 5.46/5.73 ! [A: nat,B: nat] :
% 5.46/5.73 ( ( A != zero_zero_nat )
% 5.46/5.73 => ? [X3: nat,Y3: nat] :
% 5.46/5.73 ( ( times_times_nat @ A @ X3 )
% 5.46/5.73 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bezout_nat
% 5.46/5.73 thf(fact_9663_bezout__gcd__nat_H,axiom,
% 5.46/5.73 ! [B: nat,A: nat] :
% 5.46/5.73 ? [X3: nat,Y3: nat] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 5.46/5.73 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.46/5.73 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.46/5.73 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 5.46/5.73 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.46/5.73 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bezout_gcd_nat'
% 5.46/5.73 thf(fact_9664_gcd__code__integer,axiom,
% 5.46/5.73 ( gcd_gcd_Code_integer
% 5.46/5.73 = ( ^ [K2: code_integer,L: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L = zero_z3403309356797280102nteger ) @ K2 @ ( gcd_gcd_Code_integer @ L @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_code_integer
% 5.46/5.73 thf(fact_9665_gcd__is__Max__divisors__nat,axiom,
% 5.46/5.73 ! [N: nat,M: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( gcd_gcd_nat @ M @ N )
% 5.46/5.73 = ( lattic8265883725875713057ax_nat
% 5.46/5.73 @ ( collect_nat
% 5.46/5.73 @ ^ [D: nat] :
% 5.46/5.73 ( ( dvd_dvd_nat @ D @ M )
% 5.46/5.73 & ( dvd_dvd_nat @ D @ N ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_is_Max_divisors_nat
% 5.46/5.73 thf(fact_9666_sub__BitM__One__eq,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.46/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sub_BitM_One_eq
% 5.46/5.73 thf(fact_9667_gcd__nat_Opelims,axiom,
% 5.46/5.73 ! [X2: nat,Xa2: nat,Y2: nat] :
% 5.46/5.73 ( ( ( gcd_gcd_nat @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.46/5.73 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.46/5.73 => ( Y2 = X2 ) )
% 5.46/5.73 & ( ( Xa2 != zero_zero_nat )
% 5.46/5.73 => ( Y2
% 5.46/5.73 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) ) )
% 5.46/5.73 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % gcd_nat.pelims
% 5.46/5.73 thf(fact_9668_card__greaterThanLessThan,axiom,
% 5.46/5.73 ! [L2: nat,U: nat] :
% 5.46/5.73 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 5.46/5.73 = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_greaterThanLessThan
% 5.46/5.73 thf(fact_9669_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.46/5.73 ! [L2: nat,U: nat] :
% 5.46/5.73 ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 5.46/5.73 = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeastSucLessThan_greaterThanLessThan
% 5.46/5.73 thf(fact_9670_tanh__real__bounds,axiom,
% 5.46/5.73 ! [X2: real] : ( member_real @ ( tanh_real @ X2 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_bounds
% 5.46/5.73 thf(fact_9671_Suc__funpow,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( compow_nat_nat @ N @ suc )
% 5.46/5.73 = ( plus_plus_nat @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_funpow
% 5.46/5.73 thf(fact_9672_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.46/5.73 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.46/5.73 @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 5.46/5.73 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ).
% 5.46/5.73
% 5.46/5.73 % max_nat.semilattice_neutr_order_axioms
% 5.46/5.73 thf(fact_9673_times__int_Oabs__eq,axiom,
% 5.46/5.73 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.46/5.73 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.46/5.73 = ( abs_Integ
% 5.46/5.73 @ ( produc27273713700761075at_nat
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc2626176000494625587at_nat
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) )
% 5.46/5.73 @ Xa2
% 5.46/5.73 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % times_int.abs_eq
% 5.46/5.73 thf(fact_9674_eq__Abs__Integ,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ~ ! [X3: nat,Y3: nat] :
% 5.46/5.73 ( Z
% 5.46/5.73 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % eq_Abs_Integ
% 5.46/5.73 thf(fact_9675_nat_Oabs__eq,axiom,
% 5.46/5.73 ! [X2: product_prod_nat_nat] :
% 5.46/5.73 ( ( nat2 @ ( abs_Integ @ X2 ) )
% 5.46/5.73 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat.abs_eq
% 5.46/5.73 thf(fact_9676_zero__int__def,axiom,
% 5.46/5.73 ( zero_zero_int
% 5.46/5.73 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_int_def
% 5.46/5.73 thf(fact_9677_int__def,axiom,
% 5.46/5.73 ( semiri1314217659103216013at_int
% 5.46/5.73 = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_def
% 5.46/5.73 thf(fact_9678_uminus__int_Oabs__eq,axiom,
% 5.46/5.73 ! [X2: product_prod_nat_nat] :
% 5.46/5.73 ( ( uminus_uminus_int @ ( abs_Integ @ X2 ) )
% 5.46/5.73 = ( abs_Integ
% 5.46/5.73 @ ( produc2626176000494625587at_nat
% 5.46/5.73 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X )
% 5.46/5.73 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % uminus_int.abs_eq
% 5.46/5.73 thf(fact_9679_one__int__def,axiom,
% 5.46/5.73 ( one_one_int
% 5.46/5.73 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_int_def
% 5.46/5.73 thf(fact_9680_less__int_Oabs__eq,axiom,
% 5.46/5.73 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.46/5.73 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.46/5.73 = ( produc8739625826339149834_nat_o
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc6081775807080527818_nat_o
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.46/5.73 @ Xa2
% 5.46/5.73 @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_int.abs_eq
% 5.46/5.73 thf(fact_9681_less__eq__int_Oabs__eq,axiom,
% 5.46/5.73 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.46/5.73 = ( produc8739625826339149834_nat_o
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc6081775807080527818_nat_o
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.46/5.73 @ Xa2
% 5.46/5.73 @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_eq_int.abs_eq
% 5.46/5.73 thf(fact_9682_plus__int_Oabs__eq,axiom,
% 5.46/5.73 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.46/5.73 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.46/5.73 = ( abs_Integ
% 5.46/5.73 @ ( produc27273713700761075at_nat
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc2626176000494625587at_nat
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 5.46/5.73 @ Xa2
% 5.46/5.73 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % plus_int.abs_eq
% 5.46/5.73 thf(fact_9683_minus__int_Oabs__eq,axiom,
% 5.46/5.73 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.46/5.73 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.46/5.73 = ( abs_Integ
% 5.46/5.73 @ ( produc27273713700761075at_nat
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc2626176000494625587at_nat
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) )
% 5.46/5.73 @ Xa2
% 5.46/5.73 @ X2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_int.abs_eq
% 5.46/5.73 thf(fact_9684_Gcd__remove0__nat,axiom,
% 5.46/5.73 ! [M7: set_nat] :
% 5.46/5.73 ( ( finite_finite_nat @ M7 )
% 5.46/5.73 => ( ( gcd_Gcd_nat @ M7 )
% 5.46/5.73 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Gcd_remove0_nat
% 5.46/5.73 thf(fact_9685_Gcd__nat__eq__one,axiom,
% 5.46/5.73 ! [N4: set_nat] :
% 5.46/5.73 ( ( member_nat @ one_one_nat @ N4 )
% 5.46/5.73 => ( ( gcd_Gcd_nat @ N4 )
% 5.46/5.73 = one_one_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % Gcd_nat_eq_one
% 5.46/5.73 thf(fact_9686_less__eq__int_Orep__eq,axiom,
% 5.46/5.73 ( ord_less_eq_int
% 5.46/5.73 = ( ^ [X: int,Xa4: int] :
% 5.46/5.73 ( produc8739625826339149834_nat_o
% 5.46/5.73 @ ^ [Y: nat,Z4: nat] :
% 5.46/5.73 ( produc6081775807080527818_nat_o
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 5.46/5.73 @ ( rep_Integ @ X )
% 5.46/5.73 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_eq_int.rep_eq
% 5.46/5.73 thf(fact_9687_less__int_Orep__eq,axiom,
% 5.46/5.73 ( ord_less_int
% 5.46/5.73 = ( ^ [X: int,Xa4: int] :
% 5.46/5.73 ( produc8739625826339149834_nat_o
% 5.46/5.73 @ ^ [Y: nat,Z4: nat] :
% 5.46/5.73 ( produc6081775807080527818_nat_o
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 5.46/5.73 @ ( rep_Integ @ X )
% 5.46/5.73 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_int.rep_eq
% 5.46/5.73 thf(fact_9688_prod__encode__def,axiom,
% 5.46/5.73 ( nat_prod_encode
% 5.46/5.73 = ( produc6842872674320459806at_nat
% 5.46/5.73 @ ^ [M3: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M3 @ N2 ) ) @ M3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % prod_encode_def
% 5.46/5.73 thf(fact_9689_le__prod__encode__1,axiom,
% 5.46/5.73 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % le_prod_encode_1
% 5.46/5.73 thf(fact_9690_le__prod__encode__2,axiom,
% 5.46/5.73 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % le_prod_encode_2
% 5.46/5.73 thf(fact_9691_nat_Orep__eq,axiom,
% 5.46/5.73 ( nat2
% 5.46/5.73 = ( ^ [X: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat.rep_eq
% 5.46/5.73 thf(fact_9692_prod__encode__prod__decode__aux,axiom,
% 5.46/5.73 ! [K: nat,M: nat] :
% 5.46/5.73 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.46/5.73 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.46/5.73
% 5.46/5.73 % prod_encode_prod_decode_aux
% 5.46/5.73 thf(fact_9693_uminus__int__def,axiom,
% 5.46/5.73 ( uminus_uminus_int
% 5.46/5.73 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.46/5.73 @ ( produc2626176000494625587at_nat
% 5.46/5.73 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % uminus_int_def
% 5.46/5.73 thf(fact_9694_num__of__nat_Osimps_I2_J,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( num_of_nat @ ( suc @ N ) )
% 5.46/5.73 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( num_of_nat @ ( suc @ N ) )
% 5.46/5.73 = one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % num_of_nat.simps(2)
% 5.46/5.73 thf(fact_9695_num__of__nat__numeral__eq,axiom,
% 5.46/5.73 ! [Q2: num] :
% 5.46/5.73 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.46/5.73 = Q2 ) ).
% 5.46/5.73
% 5.46/5.73 % num_of_nat_numeral_eq
% 5.46/5.73 thf(fact_9696_num__of__nat_Osimps_I1_J,axiom,
% 5.46/5.73 ( ( num_of_nat @ zero_zero_nat )
% 5.46/5.73 = one ) ).
% 5.46/5.73
% 5.46/5.73 % num_of_nat.simps(1)
% 5.46/5.73 thf(fact_9697_numeral__num__of__nat,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.46/5.73 = N ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_num_of_nat
% 5.46/5.73 thf(fact_9698_num__of__nat__One,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.46/5.73 => ( ( num_of_nat @ N )
% 5.46/5.73 = one ) ) ).
% 5.46/5.73
% 5.46/5.73 % num_of_nat_One
% 5.46/5.73 thf(fact_9699_num__of__nat__double,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.46/5.73 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % num_of_nat_double
% 5.46/5.73 thf(fact_9700_num__of__nat__plus__distrib,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.73 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % num_of_nat_plus_distrib
% 5.46/5.73 thf(fact_9701_times__int__def,axiom,
% 5.46/5.73 ( times_times_int
% 5.46/5.73 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.46/5.73 @ ( produc27273713700761075at_nat
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc2626176000494625587at_nat
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % times_int_def
% 5.46/5.73 thf(fact_9702_minus__int__def,axiom,
% 5.46/5.73 ( minus_minus_int
% 5.46/5.73 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.46/5.73 @ ( produc27273713700761075at_nat
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc2626176000494625587at_nat
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % minus_int_def
% 5.46/5.73 thf(fact_9703_plus__int__def,axiom,
% 5.46/5.73 ( plus_plus_int
% 5.46/5.73 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.46/5.73 @ ( produc27273713700761075at_nat
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc2626176000494625587at_nat
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % plus_int_def
% 5.46/5.73 thf(fact_9704_pow_Osimps_I3_J,axiom,
% 5.46/5.73 ! [X2: num,Y2: num] :
% 5.46/5.73 ( ( pow @ X2 @ ( bit1 @ Y2 ) )
% 5.46/5.73 = ( times_times_num @ ( sqr @ ( pow @ X2 @ Y2 ) ) @ X2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % pow.simps(3)
% 5.46/5.73 thf(fact_9705_sqr_Osimps_I2_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( sqr @ ( bit0 @ N ) )
% 5.46/5.73 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqr.simps(2)
% 5.46/5.73 thf(fact_9706_sqr_Osimps_I1_J,axiom,
% 5.46/5.73 ( ( sqr @ one )
% 5.46/5.73 = one ) ).
% 5.46/5.73
% 5.46/5.73 % sqr.simps(1)
% 5.46/5.73 thf(fact_9707_sqr__conv__mult,axiom,
% 5.46/5.73 ( sqr
% 5.46/5.73 = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqr_conv_mult
% 5.46/5.73 thf(fact_9708_pow_Osimps_I2_J,axiom,
% 5.46/5.73 ! [X2: num,Y2: num] :
% 5.46/5.73 ( ( pow @ X2 @ ( bit0 @ Y2 ) )
% 5.46/5.73 = ( sqr @ ( pow @ X2 @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % pow.simps(2)
% 5.46/5.73 thf(fact_9709_sqr_Osimps_I3_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( sqr @ ( bit1 @ N ) )
% 5.46/5.73 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqr.simps(3)
% 5.46/5.73 thf(fact_9710_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.46/5.73 ! [N: nat,J: nat,I: nat] :
% 5.46/5.73 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 5.46/5.73 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 5.46/5.73 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nth_sorted_list_of_set_greaterThanLessThan
% 5.46/5.73 thf(fact_9711_rat__floor__lemma,axiom,
% 5.46/5.73 ! [A: int,B: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.46/5.73 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % rat_floor_lemma
% 5.46/5.73 thf(fact_9712_divide__rat,axiom,
% 5.46/5.73 ! [A: int,B: int,C: int,D2: int] :
% 5.46/5.73 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D2 ) )
% 5.46/5.73 = ( fract @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % divide_rat
% 5.46/5.73 thf(fact_9713_floor__Fract,axiom,
% 5.46/5.73 ! [A: int,B: int] :
% 5.46/5.73 ( ( archim3151403230148437115or_rat @ ( fract @ A @ B ) )
% 5.46/5.73 = ( divide_divide_int @ A @ B ) ) ).
% 5.46/5.73
% 5.46/5.73 % floor_Fract
% 5.46/5.73 thf(fact_9714_less__rat,axiom,
% 5.46/5.73 ! [B: int,D2: int,A: int,C: int] :
% 5.46/5.73 ( ( B != zero_zero_int )
% 5.46/5.73 => ( ( D2 != zero_zero_int )
% 5.46/5.73 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D2 ) )
% 5.46/5.73 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ D2 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_rat
% 5.46/5.73 thf(fact_9715_diff__rat,axiom,
% 5.46/5.73 ! [B: int,D2: int,A: int,C: int] :
% 5.46/5.73 ( ( B != zero_zero_int )
% 5.46/5.73 => ( ( D2 != zero_zero_int )
% 5.46/5.73 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D2 ) )
% 5.46/5.73 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_rat
% 5.46/5.73 thf(fact_9716_Rat__induct__pos,axiom,
% 5.46/5.73 ! [P: rat > $o,Q2: rat] :
% 5.46/5.73 ( ! [A5: int,B5: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.46/5.73 => ( P @ ( fract @ A5 @ B5 ) ) )
% 5.46/5.73 => ( P @ Q2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % Rat_induct_pos
% 5.46/5.73 thf(fact_9717_Fract__coprime,axiom,
% 5.46/5.73 ! [A: int,B: int] :
% 5.46/5.73 ( ( fract @ ( divide_divide_int @ A @ ( gcd_gcd_int @ A @ B ) ) @ ( divide_divide_int @ B @ ( gcd_gcd_int @ A @ B ) ) )
% 5.46/5.73 = ( fract @ A @ B ) ) ).
% 5.46/5.73
% 5.46/5.73 % Fract_coprime
% 5.46/5.73 thf(fact_9718_Fract__of__int__quotient,axiom,
% 5.46/5.73 ( fract
% 5.46/5.73 = ( ^ [K2: int,L: int] : ( divide_divide_rat @ ( ring_1_of_int_rat @ K2 ) @ ( ring_1_of_int_rat @ L ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Fract_of_int_quotient
% 5.46/5.73 thf(fact_9719_rat__number__expand_I3_J,axiom,
% 5.46/5.73 ( numeral_numeral_rat
% 5.46/5.73 = ( ^ [K2: num] : ( fract @ ( numeral_numeral_int @ K2 ) @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % rat_number_expand(3)
% 5.46/5.73 thf(fact_9720_rat__number__collapse_I3_J,axiom,
% 5.46/5.73 ! [W: num] :
% 5.46/5.73 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.46/5.73 = ( numeral_numeral_rat @ W ) ) ).
% 5.46/5.73
% 5.46/5.73 % rat_number_collapse(3)
% 5.46/5.73 thf(fact_9721_Fract__less__zero__iff,axiom,
% 5.46/5.73 ! [B: int,A: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.73 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.46/5.73 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Fract_less_zero_iff
% 5.46/5.73 thf(fact_9722_zero__less__Fract__iff,axiom,
% 5.46/5.73 ! [B: int,A: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.73 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.46/5.73 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_less_Fract_iff
% 5.46/5.73 thf(fact_9723_one__less__Fract__iff,axiom,
% 5.46/5.73 ! [B: int,A: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.73 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.46/5.73 = ( ord_less_int @ B @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_less_Fract_iff
% 5.46/5.73 thf(fact_9724_Fract__less__one__iff,axiom,
% 5.46/5.73 ! [B: int,A: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.73 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.46/5.73 = ( ord_less_int @ A @ B ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Fract_less_one_iff
% 5.46/5.73 thf(fact_9725_zero__le__Fract__iff,axiom,
% 5.46/5.73 ! [B: int,A: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_le_Fract_iff
% 5.46/5.73 thf(fact_9726_Fract__le__zero__iff,axiom,
% 5.46/5.73 ! [B: int,A: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.73 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.46/5.73 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Fract_le_zero_iff
% 5.46/5.73 thf(fact_9727_one__le__Fract__iff,axiom,
% 5.46/5.73 ! [B: int,A: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.73 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.46/5.73 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_le_Fract_iff
% 5.46/5.73 thf(fact_9728_Fract__le__one__iff,axiom,
% 5.46/5.73 ! [B: int,A: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.73 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.46/5.73 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Fract_le_one_iff
% 5.46/5.73 thf(fact_9729_rat__number__expand_I5_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.46/5.73 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % rat_number_expand(5)
% 5.46/5.73 thf(fact_9730_rat__number__collapse_I4_J,axiom,
% 5.46/5.73 ! [W: num] :
% 5.46/5.73 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.46/5.73 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % rat_number_collapse(4)
% 5.46/5.73 thf(fact_9731_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.46/5.73 ! [N: nat,J: nat,I: nat] :
% 5.46/5.73 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 5.46/5.73 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 5.46/5.73 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nth_sorted_list_of_set_greaterThanAtMost
% 5.46/5.73 thf(fact_9732_take__bit__numeral__minus__numeral__int,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( case_option_int_num @ zero_zero_int
% 5.46/5.73 @ ^ [Q4: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q4 ) ) )
% 5.46/5.73 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_minus_numeral_int
% 5.46/5.73 thf(fact_9733_of__nat__eq__id,axiom,
% 5.46/5.73 semiri1316708129612266289at_nat = id_nat ).
% 5.46/5.73
% 5.46/5.73 % of_nat_eq_id
% 5.46/5.73 thf(fact_9734_take__bit__num__simps_I1_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.46/5.73 = none_num ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_num_simps(1)
% 5.46/5.73 thf(fact_9735_take__bit__num__simps_I2_J,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.46/5.73 = ( some_num @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_num_simps(2)
% 5.46/5.73 thf(fact_9736_take__bit__num__simps_I5_J,axiom,
% 5.46/5.73 ! [R: num] :
% 5.46/5.73 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ one )
% 5.46/5.73 = ( some_num @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_num_simps(5)
% 5.46/5.73 thf(fact_9737_card__greaterThanAtMost,axiom,
% 5.46/5.73 ! [L2: nat,U: nat] :
% 5.46/5.73 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) )
% 5.46/5.73 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_greaterThanAtMost
% 5.46/5.73 thf(fact_9738_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_take_bit_num @ N @ one )
% 5.46/5.73 = ( case_nat_option_num @ none_num
% 5.46/5.73 @ ^ [N2: nat] : ( some_num @ one )
% 5.46/5.73 @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.46/5.73 thf(fact_9739_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.46/5.73 ! [L2: nat,U: nat] :
% 5.46/5.73 ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 5.46/5.73 = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeastSucAtMost_greaterThanAtMost
% 5.46/5.73 thf(fact_9740_less__int__def,axiom,
% 5.46/5.73 ( ord_less_int
% 5.46/5.73 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.46/5.73 @ ( produc8739625826339149834_nat_o
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc6081775807080527818_nat_o
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_int_def
% 5.46/5.73 thf(fact_9741_less__eq__int__def,axiom,
% 5.46/5.73 ( ord_less_eq_int
% 5.46/5.73 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.46/5.73 @ ( produc8739625826339149834_nat_o
% 5.46/5.73 @ ^ [X: nat,Y: nat] :
% 5.46/5.73 ( produc6081775807080527818_nat_o
% 5.46/5.73 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_eq_int_def
% 5.46/5.73 thf(fact_9742_nat__def,axiom,
% 5.46/5.73 ( nat2
% 5.46/5.73 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_def
% 5.46/5.73 thf(fact_9743_take__bit__num__def,axiom,
% 5.46/5.73 ( bit_take_bit_num
% 5.46/5.73 = ( ^ [N2: nat,M3: num] :
% 5.46/5.73 ( if_option_num
% 5.46/5.73 @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M3 ) )
% 5.46/5.73 = zero_zero_nat )
% 5.46/5.73 @ none_num
% 5.46/5.73 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_num_def
% 5.46/5.73 thf(fact_9744_and__minus__numerals_I3_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_minus_numerals(3)
% 5.46/5.73 thf(fact_9745_and__minus__numerals_I7_J,axiom,
% 5.46/5.73 ! [N: num,M: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.46/5.73 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_minus_numerals(7)
% 5.46/5.73 thf(fact_9746_and__minus__numerals_I4_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_minus_numerals(4)
% 5.46/5.73 thf(fact_9747_card__greaterThanAtMost__int,axiom,
% 5.46/5.73 ! [L2: int,U: int] :
% 5.46/5.73 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L2 @ U ) )
% 5.46/5.73 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_greaterThanAtMost_int
% 5.46/5.73 thf(fact_9748_take__bit__num__simps_I4_J,axiom,
% 5.46/5.73 ! [N: nat,M: num] :
% 5.46/5.73 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.46/5.73 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_num_simps(4)
% 5.46/5.73 thf(fact_9749_take__bit__num__simps_I3_J,axiom,
% 5.46/5.73 ! [N: nat,M: num] :
% 5.46/5.73 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.46/5.73 = ( case_o6005452278849405969um_num @ none_num
% 5.46/5.73 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.46/5.73 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_num_simps(3)
% 5.46/5.73 thf(fact_9750_take__bit__num__simps_I7_J,axiom,
% 5.46/5.73 ! [R: num,M: num] :
% 5.46/5.73 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 5.46/5.73 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_num_simps(7)
% 5.46/5.73 thf(fact_9751_take__bit__num__simps_I6_J,axiom,
% 5.46/5.73 ! [R: num,M: num] :
% 5.46/5.73 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 5.46/5.73 = ( case_o6005452278849405969um_num @ none_num
% 5.46/5.73 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.46/5.73 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_num_simps(6)
% 5.46/5.73 thf(fact_9752_and__minus__numerals_I8_J,axiom,
% 5.46/5.73 ! [N: num,M: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.46/5.73 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_minus_numerals(8)
% 5.46/5.73 thf(fact_9753_and__not__num_Osimps_I8_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.73 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.73 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.46/5.73 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.simps(8)
% 5.46/5.73 thf(fact_9754_and__not__num_Osimps_I1_J,axiom,
% 5.46/5.73 ( ( bit_and_not_num @ one @ one )
% 5.46/5.73 = none_num ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.simps(1)
% 5.46/5.73 thf(fact_9755_and__not__num_Osimps_I4_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.46/5.73 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.simps(4)
% 5.46/5.73 thf(fact_9756_and__not__num_Osimps_I2_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.46/5.73 = ( some_num @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.simps(2)
% 5.46/5.73 thf(fact_9757_and__not__num_Osimps_I3_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.46/5.73 = none_num ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.simps(3)
% 5.46/5.73 thf(fact_9758_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.46/5.73 ! [N: nat,M: num] :
% 5.46/5.73 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.46/5.73 = ( case_nat_option_num @ none_num
% 5.46/5.73 @ ^ [N2: nat] :
% 5.46/5.73 ( case_o6005452278849405969um_num @ none_num
% 5.46/5.73 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.46/5.73 @ ( bit_take_bit_num @ N2 @ M ) )
% 5.46/5.73 @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.46/5.73 thf(fact_9759_and__not__num_Osimps_I7_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.46/5.73 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.simps(7)
% 5.46/5.73 thf(fact_9760_and__not__num__eq__Some__iff,axiom,
% 5.46/5.73 ! [M: num,N: num,Q2: num] :
% 5.46/5.73 ( ( ( bit_and_not_num @ M @ N )
% 5.46/5.73 = ( some_num @ Q2 ) )
% 5.46/5.73 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num_eq_Some_iff
% 5.46/5.73 thf(fact_9761_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.46/5.73 ! [N: nat,M: num] :
% 5.46/5.73 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.46/5.73 = ( case_nat_option_num @ none_num
% 5.46/5.73 @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 5.46/5.73 @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.46/5.73 thf(fact_9762_and__not__num__eq__None__iff,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( ( bit_and_not_num @ M @ N )
% 5.46/5.73 = none_num )
% 5.46/5.73 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num_eq_None_iff
% 5.46/5.73 thf(fact_9763_int__numeral__and__not__num,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_numeral_and_not_num
% 5.46/5.73 thf(fact_9764_int__numeral__not__and__num,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_numeral_not_and_num
% 5.46/5.73 thf(fact_9765_Bit__Operations_Otake__bit__num__code,axiom,
% 5.46/5.73 ( bit_take_bit_num
% 5.46/5.73 = ( ^ [N2: nat,M3: num] :
% 5.46/5.73 ( produc478579273971653890on_num
% 5.46/5.73 @ ^ [A3: nat,X: num] :
% 5.46/5.73 ( case_nat_option_num @ none_num
% 5.46/5.73 @ ^ [O: nat] :
% 5.46/5.73 ( case_num_option_num @ ( some_num @ one )
% 5.46/5.73 @ ^ [P5: num] :
% 5.46/5.73 ( case_o6005452278849405969um_num @ none_num
% 5.46/5.73 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.46/5.73 @ ( bit_take_bit_num @ O @ P5 ) )
% 5.46/5.73 @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 5.46/5.73 @ X )
% 5.46/5.73 @ A3 )
% 5.46/5.73 @ ( product_Pair_nat_num @ N2 @ M3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Bit_Operations.take_bit_num_code
% 5.46/5.73 thf(fact_9766_positive__rat,axiom,
% 5.46/5.73 ! [A: int,B: int] :
% 5.46/5.73 ( ( positive @ ( fract @ A @ B ) )
% 5.46/5.73 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % positive_rat
% 5.46/5.73 thf(fact_9767_less__rat__def,axiom,
% 5.46/5.73 ( ord_less_rat
% 5.46/5.73 = ( ^ [X: rat,Y: rat] : ( positive @ ( minus_minus_rat @ Y @ X ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_rat_def
% 5.46/5.73 thf(fact_9768_Rat_Opositive_Orep__eq,axiom,
% 5.46/5.73 ( positive
% 5.46/5.73 = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Rat.positive.rep_eq
% 5.46/5.73 thf(fact_9769_and__not__num_Oelims,axiom,
% 5.46/5.73 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.46/5.73 ( ( ( bit_and_not_num @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2 != none_num ) ) )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ( ? [N3: num] :
% 5.46/5.73 ( Xa2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ one ) ) ) )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ( ? [N3: num] :
% 5.46/5.73 ( Xa2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( Y2 != none_num ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.73 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.46/5.73 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 5.46/5.73 => ~ ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.elims
% 5.46/5.73 thf(fact_9770_and__not__num_Osimps_I5_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.46/5.73 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.simps(5)
% 5.46/5.73 thf(fact_9771_and__not__num_Osimps_I6_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.simps(6)
% 5.46/5.73 thf(fact_9772_and__not__num_Osimps_I9_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_not_num.simps(9)
% 5.46/5.73 thf(fact_9773_Rat_Opositive__def,axiom,
% 5.46/5.73 ( positive
% 5.46/5.73 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.46/5.73 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Rat.positive_def
% 5.46/5.73 thf(fact_9774_and__num_Oelims,axiom,
% 5.46/5.73 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.46/5.73 ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ one ) ) ) )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ( ? [N3: num] :
% 5.46/5.73 ( Xa2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( Y2 != none_num ) ) )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ( ? [N3: num] :
% 5.46/5.73 ( Xa2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ one ) ) ) )
% 5.46/5.73 => ( ( ? [M4: num] :
% 5.46/5.73 ( X2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2 != none_num ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 5.46/5.73 => ( ( ? [M4: num] :
% 5.46/5.73 ( X2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ one ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 5.46/5.73 => ~ ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.73 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.46/5.73 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.elims
% 5.46/5.73 thf(fact_9775_xor__num_Oelims,axiom,
% 5.46/5.73 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.46/5.73 ( ( ( bit_un2480387367778600638or_num @ X2 @ Xa2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2 != none_num ) ) )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 5.46/5.73 => ( ( ( X2 = one )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit0 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ( ( Xa2 = one )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.46/5.73 => ( ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit0 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 5.46/5.73 => ~ ! [M4: num] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( bit1 @ M4 ) )
% 5.46/5.73 => ! [N3: num] :
% 5.46/5.73 ( ( Xa2
% 5.46/5.73 = ( bit1 @ N3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.elims
% 5.46/5.73 thf(fact_9776_and__num_Osimps_I1_J,axiom,
% 5.46/5.73 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.46/5.73 = ( some_num @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.simps(1)
% 5.46/5.73 thf(fact_9777_xor__num_Osimps_I1_J,axiom,
% 5.46/5.73 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.46/5.73 = none_num ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.simps(1)
% 5.46/5.73 thf(fact_9778_xor__num_Osimps_I5_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.46/5.73 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.simps(5)
% 5.46/5.73 thf(fact_9779_and__num_Osimps_I5_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.46/5.73 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.simps(5)
% 5.46/5.73 thf(fact_9780_and__num_Osimps_I3_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 5.46/5.73 = ( some_num @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.simps(3)
% 5.46/5.73 thf(fact_9781_and__num_Osimps_I7_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.46/5.73 = ( some_num @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.simps(7)
% 5.46/5.73 thf(fact_9782_and__num_Osimps_I2_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 5.46/5.73 = none_num ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.simps(2)
% 5.46/5.73 thf(fact_9783_and__num_Osimps_I4_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.46/5.73 = none_num ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.simps(4)
% 5.46/5.73 thf(fact_9784_and__num_Osimps_I8_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.73 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.simps(8)
% 5.46/5.73 thf(fact_9785_and__num_Osimps_I6_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.simps(6)
% 5.46/5.73 thf(fact_9786_xor__num_Osimps_I9_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.simps(9)
% 5.46/5.73 thf(fact_9787_xor__num_Osimps_I2_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 5.46/5.73 = ( some_num @ ( bit1 @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.simps(2)
% 5.46/5.73 thf(fact_9788_xor__num_Osimps_I3_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 5.46/5.73 = ( some_num @ ( bit0 @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.simps(3)
% 5.46/5.73 thf(fact_9789_xor__num_Osimps_I4_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.46/5.73 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.simps(4)
% 5.46/5.73 thf(fact_9790_xor__num_Osimps_I7_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.46/5.73 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.simps(7)
% 5.46/5.73 thf(fact_9791_and__num_Osimps_I9_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.73 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.46/5.73 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_num.simps(9)
% 5.46/5.73 thf(fact_9792_xor__num_Osimps_I6_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.simps(6)
% 5.46/5.73 thf(fact_9793_xor__num_Osimps_I8_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.73 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % xor_num.simps(8)
% 5.46/5.73 thf(fact_9794_xor__num__dict,axiom,
% 5.46/5.73 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.46/5.73
% 5.46/5.73 % xor_num_dict
% 5.46/5.73 thf(fact_9795_and__num__dict,axiom,
% 5.46/5.73 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.46/5.73
% 5.46/5.73 % and_num_dict
% 5.46/5.73 thf(fact_9796_of__rat__dense,axiom,
% 5.46/5.73 ! [X2: real,Y2: real] :
% 5.46/5.73 ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.73 => ? [Q3: rat] :
% 5.46/5.73 ( ( ord_less_real @ X2 @ ( field_7254667332652039916t_real @ Q3 ) )
% 5.46/5.73 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q3 ) @ Y2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_rat_dense
% 5.46/5.73 thf(fact_9797_min__Suc__Suc,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.46/5.73 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % min_Suc_Suc
% 5.46/5.73 thf(fact_9798_min__0R,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % min_0R
% 5.46/5.73 thf(fact_9799_min__0L,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % min_0L
% 5.46/5.73 thf(fact_9800_min__Suc__numeral,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.73 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % min_Suc_numeral
% 5.46/5.73 thf(fact_9801_min__numeral__Suc,axiom,
% 5.46/5.73 ! [K: num,N: nat] :
% 5.46/5.73 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.73 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % min_numeral_Suc
% 5.46/5.73 thf(fact_9802_nat__mult__min__left,axiom,
% 5.46/5.73 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.73 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 5.46/5.73 = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_mult_min_left
% 5.46/5.73 thf(fact_9803_nat__mult__min__right,axiom,
% 5.46/5.73 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.73 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 5.46/5.73 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_mult_min_right
% 5.46/5.73 thf(fact_9804_min__diff,axiom,
% 5.46/5.73 ! [M: nat,I: nat,N: nat] :
% 5.46/5.73 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 5.46/5.73 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 5.46/5.73
% 5.46/5.73 % min_diff
% 5.46/5.73 thf(fact_9805_concat__bit__assoc__sym,axiom,
% 5.46/5.73 ! [M: nat,N: nat,K: int,L2: int,R: int] :
% 5.46/5.73 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L2 ) @ R )
% 5.46/5.73 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L2 @ R ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_assoc_sym
% 5.46/5.73 thf(fact_9806_take__bit__concat__bit__eq,axiom,
% 5.46/5.73 ! [M: nat,N: nat,K: int,L2: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L2 ) )
% 5.46/5.73 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_concat_bit_eq
% 5.46/5.73 thf(fact_9807_min__Suc2,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 5.46/5.73 = ( case_nat_nat @ zero_zero_nat
% 5.46/5.73 @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ M5 @ N ) )
% 5.46/5.73 @ M ) ) ).
% 5.46/5.73
% 5.46/5.73 % min_Suc2
% 5.46/5.73 thf(fact_9808_min__Suc1,axiom,
% 5.46/5.73 ! [N: nat,M: nat] :
% 5.46/5.73 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 5.46/5.73 = ( case_nat_nat @ zero_zero_nat
% 5.46/5.73 @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ N @ M5 ) )
% 5.46/5.73 @ M ) ) ).
% 5.46/5.73
% 5.46/5.73 % min_Suc1
% 5.46/5.73 thf(fact_9809_min__enat__simps_I2_J,axiom,
% 5.46/5.73 ! [Q2: extended_enat] :
% 5.46/5.73 ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.46/5.73 = zero_z5237406670263579293d_enat ) ).
% 5.46/5.73
% 5.46/5.73 % min_enat_simps(2)
% 5.46/5.73 thf(fact_9810_min__enat__simps_I3_J,axiom,
% 5.46/5.73 ! [Q2: extended_enat] :
% 5.46/5.73 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.46/5.73 = zero_z5237406670263579293d_enat ) ).
% 5.46/5.73
% 5.46/5.73 % min_enat_simps(3)
% 5.46/5.73 thf(fact_9811_Inf__real__def,axiom,
% 5.46/5.73 ( comple4887499456419720421f_real
% 5.46/5.73 = ( ^ [X5: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X5 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Inf_real_def
% 5.46/5.73 thf(fact_9812_range__mod,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( image_nat_nat
% 5.46/5.73 @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N )
% 5.46/5.73 @ top_top_set_nat )
% 5.46/5.73 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % range_mod
% 5.46/5.73 thf(fact_9813_suminf__eq__SUP__real,axiom,
% 5.46/5.73 ! [X7: nat > real] :
% 5.46/5.73 ( ( summable_real @ X7 )
% 5.46/5.73 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X7 @ I2 ) )
% 5.46/5.73 => ( ( suminf_real @ X7 )
% 5.46/5.73 = ( comple1385675409528146559p_real
% 5.46/5.73 @ ( image_nat_real
% 5.46/5.73 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ X7 @ ( set_ord_lessThan_nat @ I4 ) )
% 5.46/5.73 @ top_top_set_nat ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % suminf_eq_SUP_real
% 5.46/5.73 thf(fact_9814_UNIV__nat__eq,axiom,
% 5.46/5.73 ( top_top_set_nat
% 5.46/5.73 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % UNIV_nat_eq
% 5.46/5.73 thf(fact_9815_card__UNIV__unit,axiom,
% 5.46/5.73 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % card_UNIV_unit
% 5.46/5.73 thf(fact_9816_card__UNIV__bool,axiom,
% 5.46/5.73 ( ( finite_card_o @ top_top_set_o )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_UNIV_bool
% 5.46/5.73 thf(fact_9817_range__mult,axiom,
% 5.46/5.73 ! [A: real] :
% 5.46/5.73 ( ( ( A = zero_zero_real )
% 5.46/5.73 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.46/5.73 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.46/5.73 & ( ( A != zero_zero_real )
% 5.46/5.73 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.46/5.73 = top_top_set_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % range_mult
% 5.46/5.73 thf(fact_9818_root__def,axiom,
% 5.46/5.73 ( root
% 5.46/5.73 = ( ^ [N2: nat,X: real] :
% 5.46/5.73 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.46/5.73 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.46/5.73 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) )
% 5.46/5.73 @ X ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % root_def
% 5.46/5.73 thf(fact_9819_inf__nat__def,axiom,
% 5.46/5.73 inf_inf_nat = ord_min_nat ).
% 5.46/5.73
% 5.46/5.73 % inf_nat_def
% 5.46/5.73 thf(fact_9820_inf__enat__def,axiom,
% 5.46/5.73 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.46/5.73
% 5.46/5.73 % inf_enat_def
% 5.46/5.73 thf(fact_9821_card__UNIV__char,axiom,
% 5.46/5.73 ( ( finite_card_char @ top_top_set_char )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % card_UNIV_char
% 5.46/5.73 thf(fact_9822_UNIV__char__of__nat,axiom,
% 5.46/5.73 ( top_top_set_char
% 5.46/5.73 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % UNIV_char_of_nat
% 5.46/5.73 thf(fact_9823_char_Osize_I2_J,axiom,
% 5.46/5.73 ! [X1: $o,X23: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X8: $o] :
% 5.46/5.73 ( ( size_size_char @ ( char2 @ X1 @ X23 @ X33 @ X42 @ X52 @ X62 @ X72 @ X8 ) )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % char.size(2)
% 5.46/5.73 thf(fact_9824_nat__of__char__less__256,axiom,
% 5.46/5.73 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nat_of_char_less_256
% 5.46/5.73 thf(fact_9825_range__nat__of__char,axiom,
% 5.46/5.73 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.46/5.73 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % range_nat_of_char
% 5.46/5.73 thf(fact_9826_integer__of__char__code,axiom,
% 5.46/5.73 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.46/5.73 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.46/5.73 = ( 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 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % integer_of_char_code
% 5.46/5.73 thf(fact_9827_String_Ochar__of__ascii__of,axiom,
% 5.46/5.73 ! [C: char] :
% 5.46/5.73 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.46/5.73 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % String.char_of_ascii_of
% 5.46/5.73 thf(fact_9828_sorted__list__of__set__lessThan__Suc,axiom,
% 5.46/5.73 ! [K: nat] :
% 5.46/5.73 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.46/5.73 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sorted_list_of_set_lessThan_Suc
% 5.46/5.73 thf(fact_9829_sorted__list__of__set__atMost__Suc,axiom,
% 5.46/5.73 ! [K: nat] :
% 5.46/5.73 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.46/5.73 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sorted_list_of_set_atMost_Suc
% 5.46/5.73 thf(fact_9830_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.46/5.73 ! [I: nat,J: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 5.46/5.73 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 5.46/5.73 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sorted_list_of_set_greaterThanAtMost
% 5.46/5.73 thf(fact_9831_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.46/5.73 ! [I: nat,J: nat] :
% 5.46/5.73 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 5.46/5.73 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 5.46/5.73 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sorted_list_of_set_greaterThanLessThan
% 5.46/5.73 thf(fact_9832_list__encode_Oelims,axiom,
% 5.46/5.73 ! [X2: list_nat,Y2: nat] :
% 5.46/5.73 ( ( ( nat_list_encode @ X2 )
% 5.46/5.73 = Y2 )
% 5.46/5.73 => ( ( ( X2 = nil_nat )
% 5.46/5.73 => ( Y2 != zero_zero_nat ) )
% 5.46/5.73 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.46/5.73 ( ( X2
% 5.46/5.73 = ( cons_nat @ X3 @ Xs3 ) )
% 5.46/5.73 => ( Y2
% 5.46/5.73 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % list_encode.elims
% 5.46/5.73 thf(fact_9833_upto__aux__rec,axiom,
% 5.46/5.73 ( upto_aux
% 5.46/5.73 = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_aux_rec
% 5.46/5.73 thf(fact_9834_list__encode_Osimps_I2_J,axiom,
% 5.46/5.73 ! [X2: nat,Xs2: list_nat] :
% 5.46/5.73 ( ( nat_list_encode @ ( cons_nat @ X2 @ Xs2 ) )
% 5.46/5.73 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X2 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % list_encode.simps(2)
% 5.46/5.73 thf(fact_9835_upto__rec__numeral_I2_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = nil_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_rec_numeral(2)
% 5.46/5.73 thf(fact_9836_upto__rec__numeral_I3_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = nil_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_rec_numeral(3)
% 5.46/5.73 thf(fact_9837_upto__Nil,axiom,
% 5.46/5.73 ! [I: int,J: int] :
% 5.46/5.73 ( ( ( upto @ I @ J )
% 5.46/5.73 = nil_int )
% 5.46/5.73 = ( ord_less_int @ J @ I ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_Nil
% 5.46/5.73 thf(fact_9838_upto__Nil2,axiom,
% 5.46/5.73 ! [I: int,J: int] :
% 5.46/5.73 ( ( nil_int
% 5.46/5.73 = ( upto @ I @ J ) )
% 5.46/5.73 = ( ord_less_int @ J @ I ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_Nil2
% 5.46/5.73 thf(fact_9839_upto__empty,axiom,
% 5.46/5.73 ! [J: int,I: int] :
% 5.46/5.73 ( ( ord_less_int @ J @ I )
% 5.46/5.73 => ( ( upto @ I @ J )
% 5.46/5.73 = nil_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_empty
% 5.46/5.73 thf(fact_9840_length__upto,axiom,
% 5.46/5.73 ! [I: int,J: int] :
% 5.46/5.73 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 5.46/5.73 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % length_upto
% 5.46/5.73 thf(fact_9841_upto__rec__numeral_I1_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = nil_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_rec_numeral(1)
% 5.46/5.73 thf(fact_9842_upto__rec__numeral_I4_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = nil_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_rec_numeral(4)
% 5.46/5.73 thf(fact_9843_upto__split1,axiom,
% 5.46/5.73 ! [I: int,J: int,K: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ I @ J )
% 5.46/5.73 => ( ( ord_less_eq_int @ J @ K )
% 5.46/5.73 => ( ( upto @ I @ K )
% 5.46/5.73 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_split1
% 5.46/5.73 thf(fact_9844_atLeastLessThan__upto,axiom,
% 5.46/5.73 ( set_or4662586982721622107an_int
% 5.46/5.73 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeastLessThan_upto
% 5.46/5.73 thf(fact_9845_upto__rec2,axiom,
% 5.46/5.73 ! [I: int,J: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ I @ J )
% 5.46/5.73 => ( ( upto @ I @ J )
% 5.46/5.73 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_rec2
% 5.46/5.73 thf(fact_9846_greaterThanLessThan__upto,axiom,
% 5.46/5.73 ( set_or5832277885323065728an_int
% 5.46/5.73 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % greaterThanLessThan_upto
% 5.46/5.73 thf(fact_9847_upto__split3,axiom,
% 5.46/5.73 ! [I: int,J: int,K: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ I @ J )
% 5.46/5.73 => ( ( ord_less_eq_int @ J @ K )
% 5.46/5.73 => ( ( upto @ I @ K )
% 5.46/5.73 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % upto_split3
% 5.46/5.73 thf(fact_9848_DERIV__even__real__root,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_even_real_root
% 5.46/5.73 thf(fact_9849_DERIV__real__root__generic,axiom,
% 5.46/5.73 ! [N: nat,X2: real,D4: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( X2 != zero_zero_real )
% 5.46/5.73 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( D4
% 5.46/5.73 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.46/5.73 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.73 => ( D4
% 5.46/5.73 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.46/5.73 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( D4
% 5.46/5.73 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_real_root_generic
% 5.46/5.73 thf(fact_9850_DERIV__ln,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_ln
% 5.46/5.73 thf(fact_9851_has__real__derivative__neg__dec__right,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real,S2: set_real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ S2 ) )
% 5.46/5.73 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.73 => ? [D3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.73 & ! [H4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.73 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S2 )
% 5.46/5.73 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.73 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % has_real_derivative_neg_dec_right
% 5.46/5.73 thf(fact_9852_has__real__derivative__pos__inc__right,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real,S2: set_real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ S2 ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.73 => ? [D3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.73 & ! [H4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.73 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S2 )
% 5.46/5.73 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.73 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % has_real_derivative_pos_inc_right
% 5.46/5.73 thf(fact_9853_has__real__derivative__pos__inc__left,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real,S2: set_real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ S2 ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.73 => ? [D3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.73 & ! [H4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.73 => ( ( member_real @ ( minus_minus_real @ X2 @ H4 ) @ S2 )
% 5.46/5.73 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.73 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % has_real_derivative_pos_inc_left
% 5.46/5.73 thf(fact_9854_has__real__derivative__neg__dec__left,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real,S2: set_real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ S2 ) )
% 5.46/5.73 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.73 => ? [D3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.73 & ! [H4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.73 => ( ( member_real @ ( minus_minus_real @ X2 @ H4 ) @ S2 )
% 5.46/5.73 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.73 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % has_real_derivative_neg_dec_left
% 5.46/5.73 thf(fact_9855_DERIV__isconst3,axiom,
% 5.46/5.73 ! [A: real,B: real,X2: real,Y2: real,F: real > real] :
% 5.46/5.73 ( ( ord_less_real @ A @ B )
% 5.46/5.73 => ( ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.46/5.73 => ( ( member_real @ Y2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.73 => ( ( F @ X2 )
% 5.46/5.73 = ( F @ Y2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_isconst3
% 5.46/5.73 thf(fact_9856_DERIV__const__ratio__const,axiom,
% 5.46/5.73 ! [A: real,B: real,F: real > real,K: real] :
% 5.46/5.73 ( ( A != B )
% 5.46/5.73 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.46/5.73 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_const_ratio_const
% 5.46/5.73 thf(fact_9857_DERIV__pos__inc__right,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.73 => ? [D3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.73 & ! [H4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.73 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.73 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_pos_inc_right
% 5.46/5.73 thf(fact_9858_DERIV__neg__dec__right,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.73 => ? [D3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.73 & ! [H4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.73 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.73 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_neg_dec_right
% 5.46/5.73 thf(fact_9859_DERIV__pos__inc__left,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.73 => ? [D3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.73 & ! [H4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.73 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.73 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_pos_inc_left
% 5.46/5.73 thf(fact_9860_DERIV__neg__dec__left,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.73 => ? [D3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.73 & ! [H4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.73 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.73 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_neg_dec_left
% 5.46/5.73 thf(fact_9861_DERIV__const__ratio__const2,axiom,
% 5.46/5.73 ! [A: real,B: real,F: real > real,K: real] :
% 5.46/5.73 ( ( A != B )
% 5.46/5.73 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 5.46/5.73 = K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_const_ratio_const2
% 5.46/5.73 thf(fact_9862_DERIV__neg__imp__decreasing,axiom,
% 5.46/5.73 ! [A: real,B: real,F: real > real] :
% 5.46/5.73 ( ( ord_less_real @ A @ B )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X3 @ B )
% 5.46/5.73 => ? [Y4: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.46/5.73 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_neg_imp_decreasing
% 5.46/5.73 thf(fact_9863_DERIV__pos__imp__increasing,axiom,
% 5.46/5.73 ! [A: real,B: real,F: real > real] :
% 5.46/5.73 ( ( ord_less_real @ A @ B )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X3 @ B )
% 5.46/5.73 => ? [Y4: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.46/5.73 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_pos_imp_increasing
% 5.46/5.73 thf(fact_9864_deriv__nonneg__imp__mono,axiom,
% 5.46/5.73 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.46/5.73 ( ! [X3: real] :
% 5.46/5.73 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.46/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 5.46/5.73 => ( ( ord_less_eq_real @ A @ B )
% 5.46/5.73 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % deriv_nonneg_imp_mono
% 5.46/5.73 thf(fact_9865_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.46/5.73 ! [A: real,B: real,F: real > real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X3 @ B )
% 5.46/5.73 => ? [Y4: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 5.46/5.73 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_nonpos_imp_nonincreasing
% 5.46/5.73 thf(fact_9866_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.46/5.73 ! [A: real,B: real,F: real > real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X3 @ B )
% 5.46/5.73 => ? [Y4: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 5.46/5.73 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_nonneg_imp_nondecreasing
% 5.46/5.73 thf(fact_9867_DERIV__local__const,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real,D2: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.46/5.73 => ( ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D2 )
% 5.46/5.73 => ( ( F @ X2 )
% 5.46/5.73 = ( F @ Y3 ) ) )
% 5.46/5.73 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_local_const
% 5.46/5.73 thf(fact_9868_MVT2,axiom,
% 5.46/5.73 ! [A: real,B: real,F: real > real,F3: real > real] :
% 5.46/5.73 ( ( ord_less_real @ A @ B )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X3 @ B )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ F @ ( F3 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.73 => ? [Z3: real] :
% 5.46/5.73 ( ( ord_less_real @ A @ Z3 )
% 5.46/5.73 & ( ord_less_real @ Z3 @ B )
% 5.46/5.73 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.46/5.73 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F3 @ Z3 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % MVT2
% 5.46/5.73 thf(fact_9869_DERIV__const__average,axiom,
% 5.46/5.73 ! [A: real,B: real,V: real > real,K: real] :
% 5.46/5.73 ( ( A != B )
% 5.46/5.73 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_const_average
% 5.46/5.73 thf(fact_9870_DERIV__local__min,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real,D2: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.46/5.73 => ( ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D2 )
% 5.46/5.73 => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 5.46/5.73 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_local_min
% 5.46/5.73 thf(fact_9871_DERIV__local__max,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,X2: real,D2: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.46/5.73 => ( ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D2 )
% 5.46/5.73 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 5.46/5.73 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_local_max
% 5.46/5.73 thf(fact_9872_DERIV__ln__divide,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_ln_divide
% 5.46/5.73 thf(fact_9873_DERIV__pow,axiom,
% 5.46/5.73 ! [N: nat,X2: real,S: set_real] :
% 5.46/5.73 ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [X: real] : ( power_power_real @ X @ N )
% 5.46/5.73 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ S ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_pow
% 5.46/5.73 thf(fact_9874_DERIV__fun__pow,axiom,
% 5.46/5.73 ! [G: real > real,M: real,X2: real,N: nat] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N )
% 5.46/5.73 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X2 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_fun_pow
% 5.46/5.73 thf(fact_9875_has__real__derivative__powr,axiom,
% 5.46/5.73 ! [Z: real,R: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.46/5.73 => ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [Z4: real] : ( powr_real @ Z4 @ R )
% 5.46/5.73 @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % has_real_derivative_powr
% 5.46/5.73 thf(fact_9876_DERIV__log,axiom,
% 5.46/5.73 ! [X2: real,B: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X2 ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_log
% 5.46/5.73 thf(fact_9877_DERIV__fun__powr,axiom,
% 5.46/5.73 ! [G: real > real,M: real,X2: real,R: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R )
% 5.46/5.73 @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X2 ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_fun_powr
% 5.46/5.73 thf(fact_9878_DERIV__powr,axiom,
% 5.46/5.73 ! [G: real > real,M: real,X2: real,F: real > real,R: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.46/5.73 => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 5.46/5.73 @ ( times_times_real @ ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X2 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X2 ) ) @ ( G @ X2 ) ) ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_powr
% 5.46/5.73 thf(fact_9879_DERIV__real__sqrt,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_real_sqrt
% 5.46/5.73 thf(fact_9880_DERIV__series_H,axiom,
% 5.46/5.73 ! [F: real > nat > real,F3: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.46/5.73 ( ! [N3: nat] :
% 5.46/5.73 ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [X: real] : ( F @ X @ N3 )
% 5.46/5.73 @ ( F3 @ X0 @ N3 )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.46/5.73 => ( summable_real @ ( F @ X3 ) ) )
% 5.46/5.73 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.46/5.73 => ( ( summable_real @ ( F3 @ X0 ) )
% 5.46/5.73 => ( ( summable_real @ L5 )
% 5.46/5.73 => ( ! [N3: nat,X3: real,Y3: real] :
% 5.46/5.73 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.46/5.73 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.46/5.73 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N3 ) @ ( F @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 5.46/5.73 @ ( suminf_real @ ( F3 @ X0 ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_series'
% 5.46/5.73 thf(fact_9881_DERIV__arctan,axiom,
% 5.46/5.73 ! [X2: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_arctan
% 5.46/5.73 thf(fact_9882_arsinh__real__has__field__derivative,axiom,
% 5.46/5.73 ! [X2: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % arsinh_real_has_field_derivative
% 5.46/5.73 thf(fact_9883_DERIV__real__sqrt__generic,axiom,
% 5.46/5.73 ! [X2: real,D4: real] :
% 5.46/5.73 ( ( X2 != zero_zero_real )
% 5.46/5.73 => ( ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( D4
% 5.46/5.73 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.73 => ( ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.46/5.73 => ( D4
% 5.46/5.73 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_real_sqrt_generic
% 5.46/5.73 thf(fact_9884_arcosh__real__has__field__derivative,axiom,
% 5.46/5.73 ! [X2: real,A2: set_real] :
% 5.46/5.73 ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % arcosh_real_has_field_derivative
% 5.46/5.73 thf(fact_9885_artanh__real__has__field__derivative,axiom,
% 5.46/5.73 ! [X2: real,A2: set_real] :
% 5.46/5.73 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % artanh_real_has_field_derivative
% 5.46/5.73 thf(fact_9886_DERIV__power__series_H,axiom,
% 5.46/5.73 ! [R2: real,F: nat > real,X0: real] :
% 5.46/5.73 ( ! [X3: real] :
% 5.46/5.73 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.46/5.73 => ( summable_real
% 5.46/5.73 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 5.46/5.73 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.46/5.73 => ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( suminf_real
% 5.46/5.73 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) )
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_power_series'
% 5.46/5.73 thf(fact_9887_DERIV__real__root,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_real_root
% 5.46/5.73 thf(fact_9888_DERIV__arccos,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_arccos
% 5.46/5.73 thf(fact_9889_DERIV__arcsin,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_arcsin
% 5.46/5.73 thf(fact_9890_Maclaurin__all__le__objl,axiom,
% 5.46/5.73 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.46/5.73 ( ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 & ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X2 ) )
% 5.46/5.73 & ( ( F @ X2 )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Maclaurin_all_le_objl
% 5.46/5.73 thf(fact_9891_Maclaurin__all__le,axiom,
% 5.46/5.73 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.46/5.73 ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X2 ) )
% 5.46/5.73 & ( ( F @ X2 )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Maclaurin_all_le
% 5.46/5.73 thf(fact_9892_DERIV__odd__real__root,axiom,
% 5.46/5.73 ! [N: nat,X2: real] :
% 5.46/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( ( X2 != zero_zero_real )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_odd_real_root
% 5.46/5.73 thf(fact_9893_Maclaurin__minus,axiom,
% 5.46/5.73 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.46/5.73 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.46/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 => ( ! [M4: nat,T5: real] :
% 5.46/5.73 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.73 & ( ord_less_eq_real @ H2 @ T5 )
% 5.46/5.73 & ( ord_less_eq_real @ T5 @ zero_zero_real ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ord_less_real @ H2 @ T5 )
% 5.46/5.73 & ( ord_less_real @ T5 @ zero_zero_real )
% 5.46/5.73 & ( ( F @ H2 )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Maclaurin_minus
% 5.46/5.73 thf(fact_9894_Maclaurin2,axiom,
% 5.46/5.73 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.46/5.73 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 => ( ! [M4: nat,T5: real] :
% 5.46/5.73 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.73 & ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.46/5.73 & ( ord_less_eq_real @ T5 @ H2 ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.46/5.73 & ( ord_less_eq_real @ T5 @ H2 )
% 5.46/5.73 & ( ( F @ H2 )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Maclaurin2
% 5.46/5.73 thf(fact_9895_Maclaurin,axiom,
% 5.46/5.73 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.46/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 => ( ! [M4: nat,T5: real] :
% 5.46/5.73 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.73 & ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.46/5.73 & ( ord_less_eq_real @ T5 @ H2 ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.46/5.73 & ( ord_less_real @ T5 @ H2 )
% 5.46/5.73 & ( ( F @ H2 )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Maclaurin
% 5.46/5.73 thf(fact_9896_Maclaurin__all__lt,axiom,
% 5.46/5.73 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.46/5.73 ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( X2 != zero_zero_real )
% 5.46/5.73 => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T5 ) )
% 5.46/5.73 & ( ord_less_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X2 ) )
% 5.46/5.73 & ( ( F @ X2 )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Maclaurin_all_lt
% 5.46/5.73 thf(fact_9897_Maclaurin__bi__le,axiom,
% 5.46/5.73 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.46/5.73 ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 => ( ! [M4: nat,T5: real] :
% 5.46/5.73 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.73 & ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X2 ) ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X2 ) )
% 5.46/5.73 & ( ( F @ X2 )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Maclaurin_bi_le
% 5.46/5.73 thf(fact_9898_Taylor__down,axiom,
% 5.46/5.73 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 => ( ! [M4: nat,T5: real] :
% 5.46/5.73 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.73 & ( ord_less_eq_real @ A @ T5 )
% 5.46/5.73 & ( ord_less_eq_real @ T5 @ B ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.46/5.73 => ( ( ord_less_real @ A @ C )
% 5.46/5.73 => ( ( ord_less_eq_real @ C @ B )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ord_less_real @ A @ T5 )
% 5.46/5.73 & ( ord_less_real @ T5 @ C )
% 5.46/5.73 & ( ( F @ A )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Taylor_down
% 5.46/5.73 thf(fact_9899_Taylor__up,axiom,
% 5.46/5.73 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 => ( ! [M4: nat,T5: real] :
% 5.46/5.73 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.73 & ( ord_less_eq_real @ A @ T5 )
% 5.46/5.73 & ( ord_less_eq_real @ T5 @ B ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.46/5.73 => ( ( ord_less_eq_real @ A @ C )
% 5.46/5.73 => ( ( ord_less_real @ C @ B )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ord_less_real @ C @ T5 )
% 5.46/5.73 & ( ord_less_real @ T5 @ B )
% 5.46/5.73 & ( ( F @ B )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Taylor_up
% 5.46/5.73 thf(fact_9900_Taylor,axiom,
% 5.46/5.73 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X2: real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.73 = F )
% 5.46/5.73 => ( ! [M4: nat,T5: real] :
% 5.46/5.73 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.73 & ( ord_less_eq_real @ A @ T5 )
% 5.46/5.73 & ( ord_less_eq_real @ T5 @ B ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.46/5.73 => ( ( ord_less_eq_real @ A @ C )
% 5.46/5.73 => ( ( ord_less_eq_real @ C @ B )
% 5.46/5.73 => ( ( ord_less_eq_real @ A @ X2 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X2 @ B )
% 5.46/5.73 => ( ( X2 != C )
% 5.46/5.73 => ? [T5: real] :
% 5.46/5.73 ( ( ( ord_less_real @ X2 @ C )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ T5 )
% 5.46/5.73 & ( ord_less_real @ T5 @ C ) ) )
% 5.46/5.73 & ( ~ ( ord_less_real @ X2 @ C )
% 5.46/5.73 => ( ( ord_less_real @ C @ T5 )
% 5.46/5.73 & ( ord_less_real @ T5 @ X2 ) ) )
% 5.46/5.73 & ( ( F @ X2 )
% 5.46/5.73 = ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ M3 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.73 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T5 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Taylor
% 5.46/5.73 thf(fact_9901_Maclaurin__lemma2,axiom,
% 5.46/5.73 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B3: real] :
% 5.46/5.73 ( ! [M4: nat,T5: real] :
% 5.46/5.73 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.73 & ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.46/5.73 & ( ord_less_eq_real @ T5 @ H2 ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.46/5.73 => ( ( N
% 5.46/5.73 = ( suc @ K ) )
% 5.46/5.73 => ! [M2: nat,T7: real] :
% 5.46/5.73 ( ( ( ord_less_nat @ M2 @ N )
% 5.46/5.73 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.46/5.73 & ( ord_less_eq_real @ T7 @ H2 ) )
% 5.46/5.73 => ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [U2: real] :
% 5.46/5.73 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 5.46/5.73 @ ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 5.46/5.73 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 5.46/5.73 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T7 )
% 5.46/5.73 @ ( plus_plus_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T7 @ P5 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 5.46/5.73 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Maclaurin_lemma2
% 5.46/5.73 thf(fact_9902_DERIV__arctan__series,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.73 => ( has_fi5821293074295781190e_real
% 5.46/5.73 @ ^ [X9: real] :
% 5.46/5.73 ( suminf_real
% 5.46/5.73 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X2 @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_arctan_series
% 5.46/5.73 thf(fact_9903_isCont__Lb__Ub,axiom,
% 5.46/5.73 ! [A: real,B: real,F: real > real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.73 & ( ord_less_eq_real @ X3 @ B ) )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.46/5.73 => ? [L6: real,M9: real] :
% 5.46/5.73 ( ! [X4: real] :
% 5.46/5.73 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.46/5.73 & ( ord_less_eq_real @ X4 @ B ) )
% 5.46/5.73 => ( ( ord_less_eq_real @ L6 @ ( F @ X4 ) )
% 5.46/5.73 & ( ord_less_eq_real @ ( F @ X4 ) @ M9 ) ) )
% 5.46/5.73 & ! [Y4: real] :
% 5.46/5.73 ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 5.46/5.73 & ( ord_less_eq_real @ Y4 @ M9 ) )
% 5.46/5.73 => ? [X3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.73 & ( ord_less_eq_real @ X3 @ B )
% 5.46/5.73 & ( ( F @ X3 )
% 5.46/5.73 = Y4 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % isCont_Lb_Ub
% 5.46/5.73 thf(fact_9904_LIM__fun__less__zero,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,C: real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.73 => ? [R3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.73 & ! [X4: real] :
% 5.46/5.73 ( ( ( X4 != C )
% 5.46/5.73 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R3 ) )
% 5.46/5.73 => ( ord_less_real @ ( F @ X4 ) @ zero_zero_real ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIM_fun_less_zero
% 5.46/5.73 thf(fact_9905_LIM__fun__not__zero,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,C: real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.46/5.73 => ( ( L2 != zero_zero_real )
% 5.46/5.73 => ? [R3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.73 & ! [X4: real] :
% 5.46/5.73 ( ( ( X4 != C )
% 5.46/5.73 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R3 ) )
% 5.46/5.73 => ( ( F @ X4 )
% 5.46/5.73 != zero_zero_real ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIM_fun_not_zero
% 5.46/5.73 thf(fact_9906_LIM__fun__gt__zero,axiom,
% 5.46/5.73 ! [F: real > real,L2: real,C: real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.73 => ? [R3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.73 & ! [X4: real] :
% 5.46/5.73 ( ( ( X4 != C )
% 5.46/5.73 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R3 ) )
% 5.46/5.73 => ( ord_less_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIM_fun_gt_zero
% 5.46/5.73 thf(fact_9907_isCont__real__sqrt,axiom,
% 5.46/5.73 ! [X2: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ sqrt ) ).
% 5.46/5.73
% 5.46/5.73 % isCont_real_sqrt
% 5.46/5.73 thf(fact_9908_isCont__real__root,axiom,
% 5.46/5.73 ! [X2: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ ( root @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % isCont_real_root
% 5.46/5.73 thf(fact_9909_isCont__inverse__function2,axiom,
% 5.46/5.73 ! [A: real,X2: real,B: real,G: real > real,F: real > real] :
% 5.46/5.73 ( ( ord_less_real @ A @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ B )
% 5.46/5.73 => ( ! [Z3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ Z3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.46/5.73 => ( ( G @ ( F @ Z3 ) )
% 5.46/5.73 = Z3 ) ) )
% 5.46/5.73 => ( ! [Z3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ Z3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % isCont_inverse_function2
% 5.46/5.73 thf(fact_9910_isCont__arcosh,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % isCont_arcosh
% 5.46/5.73 thf(fact_9911_LIM__cos__div__sin,axiom,
% 5.46/5.73 ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIM_cos_div_sin
% 5.46/5.73 thf(fact_9912_DERIV__inverse__function,axiom,
% 5.46/5.73 ! [F: real > real,D4: real,G: real > real,X2: real,A: real,B: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X2 ) @ top_top_set_real ) )
% 5.46/5.73 => ( ( D4 != zero_zero_real )
% 5.46/5.73 => ( ( ord_less_real @ A @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ B )
% 5.46/5.73 => ( ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ A @ Y3 )
% 5.46/5.73 => ( ( ord_less_real @ Y3 @ B )
% 5.46/5.73 => ( ( F @ ( G @ Y3 ) )
% 5.46/5.73 = Y3 ) ) )
% 5.46/5.73 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ G )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_inverse_function
% 5.46/5.73 thf(fact_9913_isCont__arccos,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % isCont_arccos
% 5.46/5.73 thf(fact_9914_isCont__arcsin,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % isCont_arcsin
% 5.46/5.73 thf(fact_9915_LIM__less__bound,axiom,
% 5.46/5.73 ! [B: real,X2: real,F: real > real] :
% 5.46/5.73 ( ( ord_less_real @ B @ X2 )
% 5.46/5.73 => ( ! [X3: real] :
% 5.46/5.73 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B @ X2 ) )
% 5.46/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.73 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ F )
% 5.46/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIM_less_bound
% 5.46/5.73 thf(fact_9916_isCont__artanh,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % isCont_artanh
% 5.46/5.73 thf(fact_9917_isCont__inverse__function,axiom,
% 5.46/5.73 ! [D2: real,X2: real,G: real > real,F: real > real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.46/5.73 => ( ! [Z3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X2 ) ) @ D2 )
% 5.46/5.73 => ( ( G @ ( F @ Z3 ) )
% 5.46/5.73 = Z3 ) )
% 5.46/5.73 => ( ! [Z3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X2 ) ) @ D2 )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % isCont_inverse_function
% 5.46/5.73 thf(fact_9918_GMVT_H,axiom,
% 5.46/5.73 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F3: real > real] :
% 5.46/5.73 ( ( ord_less_real @ A @ B )
% 5.46/5.73 => ( ! [Z3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ Z3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 5.46/5.73 => ( ! [Z3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ A @ Z3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.46/5.73 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 5.46/5.73 => ( ! [Z3: real] :
% 5.46/5.73 ( ( ord_less_real @ A @ Z3 )
% 5.46/5.73 => ( ( ord_less_real @ Z3 @ B )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.46/5.73 => ( ! [Z3: real] :
% 5.46/5.73 ( ( ord_less_real @ A @ Z3 )
% 5.46/5.73 => ( ( ord_less_real @ Z3 @ B )
% 5.46/5.73 => ( has_fi5821293074295781190e_real @ F @ ( F3 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.46/5.73 => ? [C2: real] :
% 5.46/5.73 ( ( ord_less_real @ A @ C2 )
% 5.46/5.73 & ( ord_less_real @ C2 @ B )
% 5.46/5.73 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 5.46/5.73 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F3 @ C2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % GMVT'
% 5.46/5.73 thf(fact_9919_summable__Leibniz_I3_J,axiom,
% 5.46/5.73 ! [A: nat > real] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.73 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.46/5.73 => ! [N7: nat] :
% 5.46/5.73 ( member_real
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.46/5.73 @ ( set_or1222579329274155063t_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) )
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable_Leibniz(3)
% 5.46/5.73 thf(fact_9920_summable__Leibniz_I2_J,axiom,
% 5.46/5.73 ! [A: nat > real] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.46/5.73 => ! [N7: nat] :
% 5.46/5.73 ( member_real
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.46/5.73 @ ( set_or1222579329274155063t_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable_Leibniz(2)
% 5.46/5.73 thf(fact_9921_mult__nat__right__at__top,axiom,
% 5.46/5.73 ! [C: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.73 => ( filterlim_nat_nat
% 5.46/5.73 @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 5.46/5.73 @ at_top_nat
% 5.46/5.73 @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % mult_nat_right_at_top
% 5.46/5.73 thf(fact_9922_mult__nat__left__at__top,axiom,
% 5.46/5.73 ! [C: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.73 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % mult_nat_left_at_top
% 5.46/5.73 thf(fact_9923_monoseq__convergent,axiom,
% 5.46/5.73 ! [X7: nat > real,B3: real] :
% 5.46/5.73 ( ( topolo6980174941875973593q_real @ X7 )
% 5.46/5.73 => ( ! [I2: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X7 @ I2 ) ) @ B3 )
% 5.46/5.73 => ~ ! [L6: real] :
% 5.46/5.73 ~ ( filterlim_nat_real @ X7 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % monoseq_convergent
% 5.46/5.73 thf(fact_9924_LIMSEQ__root,axiom,
% 5.46/5.73 ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.46/5.73 @ at_top_nat ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_root
% 5.46/5.73 thf(fact_9925_nested__sequence__unique,axiom,
% 5.46/5.73 ! [F: nat > real,G: nat > real] :
% 5.46/5.73 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.46/5.73 => ( ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_nat )
% 5.46/5.73 => ? [L4: real] :
% 5.46/5.73 ( ! [N7: nat] : ( ord_less_eq_real @ ( F @ N7 ) @ L4 )
% 5.46/5.73 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.46/5.73 & ! [N7: nat] : ( ord_less_eq_real @ L4 @ ( G @ N7 ) )
% 5.46/5.73 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % nested_sequence_unique
% 5.46/5.73 thf(fact_9926_LIMSEQ__inverse__zero,axiom,
% 5.46/5.73 ! [X7: nat > real] :
% 5.46/5.73 ( ! [R3: real] :
% 5.46/5.73 ? [N8: nat] :
% 5.46/5.73 ! [N3: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.46/5.73 => ( ord_less_real @ R3 @ ( X7 @ N3 ) ) )
% 5.46/5.73 => ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( inverse_inverse_real @ ( X7 @ N2 ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_inverse_zero
% 5.46/5.73 thf(fact_9927_lim__inverse__n_H,axiom,
% 5.46/5.73 ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_nat ) ).
% 5.46/5.73
% 5.46/5.73 % lim_inverse_n'
% 5.46/5.73 thf(fact_9928_LIMSEQ__root__const,axiom,
% 5.46/5.73 ! [C: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.73 => ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( root @ N2 @ C )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.46/5.73 @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_root_const
% 5.46/5.73 thf(fact_9929_LIMSEQ__inverse__real__of__nat,axiom,
% 5.46/5.73 ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_nat ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_inverse_real_of_nat
% 5.46/5.73 thf(fact_9930_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.46/5.73 ! [R: real] :
% 5.46/5.73 ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ R )
% 5.46/5.73 @ at_top_nat ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_inverse_real_of_nat_add
% 5.46/5.73 thf(fact_9931_increasing__LIMSEQ,axiom,
% 5.46/5.73 ! [F: nat > real,L2: real] :
% 5.46/5.73 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 5.46/5.73 => ( ! [E2: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.46/5.73 => ? [N7: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N7 ) @ E2 ) ) )
% 5.46/5.73 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % increasing_LIMSEQ
% 5.46/5.73 thf(fact_9932_LIMSEQ__realpow__zero,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.73 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.46/5.73 => ( filterlim_nat_real @ ( power_power_real @ X2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_realpow_zero
% 5.46/5.73 thf(fact_9933_LIMSEQ__divide__realpow__zero,axiom,
% 5.46/5.73 ! [X2: real,A: real] :
% 5.46/5.73 ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.73 => ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X2 @ N2 ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_divide_realpow_zero
% 5.46/5.73 thf(fact_9934_LIMSEQ__abs__realpow__zero,axiom,
% 5.46/5.73 ! [C: real] :
% 5.46/5.73 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.46/5.73 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_abs_realpow_zero
% 5.46/5.73 thf(fact_9935_LIMSEQ__abs__realpow__zero2,axiom,
% 5.46/5.73 ! [C: real] :
% 5.46/5.73 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.46/5.73 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_abs_realpow_zero2
% 5.46/5.73 thf(fact_9936_LIMSEQ__inverse__realpow__zero,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_real @ one_one_real @ X2 )
% 5.46/5.73 => ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X2 @ N2 ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_inverse_realpow_zero
% 5.46/5.73 thf(fact_9937_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.46/5.73 ! [R: real] :
% 5.46/5.73 ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ R )
% 5.46/5.73 @ at_top_nat ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.46/5.73 thf(fact_9938_tendsto__exp__limit__sequentially,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.46/5.73 @ at_top_nat ) ).
% 5.46/5.73
% 5.46/5.73 % tendsto_exp_limit_sequentially
% 5.46/5.73 thf(fact_9939_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.46/5.73 ! [R: real] :
% 5.46/5.73 ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ R )
% 5.46/5.73 @ at_top_nat ) ).
% 5.46/5.73
% 5.46/5.73 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.46/5.73 thf(fact_9940_summable__Leibniz_I1_J,axiom,
% 5.46/5.73 ! [A: nat > real] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.73 => ( summable_real
% 5.46/5.73 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable_Leibniz(1)
% 5.46/5.73 thf(fact_9941_summable,axiom,
% 5.46/5.73 ! [A: nat > real] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.46/5.73 => ( summable_real
% 5.46/5.73 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable
% 5.46/5.73 thf(fact_9942_cos__diff__limit__1,axiom,
% 5.46/5.73 ! [Theta: nat > real,Theta2: real] :
% 5.46/5.73 ( ( filterlim_nat_real
% 5.46/5.73 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.46/5.73 @ at_top_nat )
% 5.46/5.73 => ~ ! [K3: nat > int] :
% 5.46/5.73 ~ ( filterlim_nat_real
% 5.46/5.73 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.46/5.73 @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % cos_diff_limit_1
% 5.46/5.73 thf(fact_9943_cos__limit__1,axiom,
% 5.46/5.73 ! [Theta: nat > real] :
% 5.46/5.73 ( ( filterlim_nat_real
% 5.46/5.73 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.46/5.73 @ at_top_nat )
% 5.46/5.73 => ? [K3: nat > int] :
% 5.46/5.73 ( filterlim_nat_real
% 5.46/5.73 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % cos_limit_1
% 5.46/5.73 thf(fact_9944_summable__Leibniz_I4_J,axiom,
% 5.46/5.73 ! [A: nat > real] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.73 => ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] :
% 5.46/5.73 ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.46/5.73 @ at_top_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable_Leibniz(4)
% 5.46/5.73 thf(fact_9945_zeroseq__arctan__series,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.46/5.73 => ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % zeroseq_arctan_series
% 5.46/5.73 thf(fact_9946_summable__Leibniz_H_I2_J,axiom,
% 5.46/5.73 ! [A: nat > real,N: nat] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.46/5.73 => ( ord_less_eq_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable_Leibniz'(2)
% 5.46/5.73 thf(fact_9947_summable__Leibniz_H_I3_J,axiom,
% 5.46/5.73 ! [A: nat > real] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.46/5.73 => ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] :
% 5.46/5.73 ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.46/5.73 @ at_top_nat ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable_Leibniz'(3)
% 5.46/5.73 thf(fact_9948_sums__alternating__upper__lower,axiom,
% 5.46/5.73 ! [A: nat > real] :
% 5.46/5.73 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.46/5.73 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ? [L4: real] :
% 5.46/5.73 ( ! [N7: nat] :
% 5.46/5.73 ( ord_less_eq_real
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.46/5.73 @ L4 )
% 5.46/5.73 & ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] :
% 5.46/5.73 ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ L4 )
% 5.46/5.73 @ at_top_nat )
% 5.46/5.73 & ! [N7: nat] :
% 5.46/5.73 ( ord_less_eq_real @ L4
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) )
% 5.46/5.73 & ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] :
% 5.46/5.73 ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ L4 )
% 5.46/5.73 @ at_top_nat ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sums_alternating_upper_lower
% 5.46/5.73 thf(fact_9949_summable__Leibniz_I5_J,axiom,
% 5.46/5.73 ! [A: nat > real] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.73 => ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] :
% 5.46/5.73 ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.46/5.73 @ at_top_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable_Leibniz(5)
% 5.46/5.73 thf(fact_9950_summable__Leibniz_H_I4_J,axiom,
% 5.46/5.73 ! [A: nat > real,N: nat] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.46/5.73 => ( ord_less_eq_real
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.46/5.73 @ ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable_Leibniz'(4)
% 5.46/5.73 thf(fact_9951_summable__Leibniz_H_I5_J,axiom,
% 5.46/5.73 ! [A: nat > real] :
% 5.46/5.73 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.46/5.73 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.46/5.73 => ( filterlim_nat_real
% 5.46/5.73 @ ^ [N2: nat] :
% 5.46/5.73 ( groups6591440286371151544t_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.46/5.73 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real
% 5.46/5.73 @ ( suminf_real
% 5.46/5.73 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.46/5.73 @ at_top_nat ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % summable_Leibniz'(5)
% 5.46/5.73 thf(fact_9952_real__bounded__linear,axiom,
% 5.46/5.73 ( real_V5970128139526366754l_real
% 5.46/5.73 = ( ^ [F4: real > real] :
% 5.46/5.73 ? [C3: real] :
% 5.46/5.73 ( F4
% 5.46/5.73 = ( ^ [X: real] : ( times_times_real @ X @ C3 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_bounded_linear
% 5.46/5.73 thf(fact_9953_filterlim__Suc,axiom,
% 5.46/5.73 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.46/5.73
% 5.46/5.73 % filterlim_Suc
% 5.46/5.73 thf(fact_9954_tendsto__exp__limit__at__right,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( filterlim_real_real
% 5.46/5.73 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X2 @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % tendsto_exp_limit_at_right
% 5.46/5.73 thf(fact_9955_dist__complex__def,axiom,
% 5.46/5.73 ( real_V3694042436643373181omplex
% 5.46/5.73 = ( ^ [X: complex,Y: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dist_complex_def
% 5.46/5.73 thf(fact_9956_dist__real__def,axiom,
% 5.46/5.73 ( real_V975177566351809787t_real
% 5.46/5.73 = ( ^ [X: real,Y: real] : ( abs_abs_real @ ( minus_minus_real @ X @ Y ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dist_real_def
% 5.46/5.73 thf(fact_9957_tendsto__arcosh__at__left__1,axiom,
% 5.46/5.73 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % tendsto_arcosh_at_left_1
% 5.46/5.73 thf(fact_9958_filterlim__tan__at__right,axiom,
% 5.46/5.73 filterlim_real_real @ tan_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % filterlim_tan_at_right
% 5.46/5.73 thf(fact_9959_greaterThan__0,axiom,
% 5.46/5.73 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.46/5.73 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % greaterThan_0
% 5.46/5.73 thf(fact_9960_greaterThan__Suc,axiom,
% 5.46/5.73 ! [K: nat] :
% 5.46/5.73 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.46/5.73 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % greaterThan_Suc
% 5.46/5.73 thf(fact_9961_tanh__real__at__bot,axiom,
% 5.46/5.73 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_at_bot
% 5.46/5.73 thf(fact_9962_artanh__real__at__right__1,axiom,
% 5.46/5.73 filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % artanh_real_at_right_1
% 5.46/5.73 thf(fact_9963_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.46/5.73 ! [B: real,F: real > real,Flim: real] :
% 5.46/5.73 ( ! [X3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ X3 @ B )
% 5.46/5.73 => ? [Y4: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 5.46/5.73 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.46/5.73 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_pos_imp_increasing_at_bot
% 5.46/5.73 thf(fact_9964_filterlim__pow__at__bot__odd,axiom,
% 5.46/5.73 ! [N: nat,F: real > real,F5: filter_real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.46/5.73 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.46/5.73 @ at_bot_real
% 5.46/5.73 @ F5 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % filterlim_pow_at_bot_odd
% 5.46/5.73 thf(fact_9965_tendsto__arctan__at__bot,axiom,
% 5.46/5.73 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.46/5.73
% 5.46/5.73 % tendsto_arctan_at_bot
% 5.46/5.73 thf(fact_9966_filterlim__pow__at__bot__even,axiom,
% 5.46/5.73 ! [N: nat,F: real > real,F5: filter_real] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.46/5.73 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.46/5.73 @ at_top_real
% 5.46/5.73 @ F5 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % filterlim_pow_at_bot_even
% 5.46/5.73 thf(fact_9967_atLeast__Suc__greaterThan,axiom,
% 5.46/5.73 ! [K: nat] :
% 5.46/5.73 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.46/5.73 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeast_Suc_greaterThan
% 5.46/5.73 thf(fact_9968_sqrt__at__top,axiom,
% 5.46/5.73 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.46/5.73
% 5.46/5.73 % sqrt_at_top
% 5.46/5.73 thf(fact_9969_tanh__real__at__top,axiom,
% 5.46/5.73 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_at_top
% 5.46/5.73 thf(fact_9970_artanh__real__at__left__1,axiom,
% 5.46/5.73 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % artanh_real_at_left_1
% 5.46/5.73 thf(fact_9971_atLeast__Suc,axiom,
% 5.46/5.73 ! [K: nat] :
% 5.46/5.73 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.46/5.73 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % atLeast_Suc
% 5.46/5.73 thf(fact_9972_ln__x__over__x__tendsto__0,axiom,
% 5.46/5.73 ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ X ) @ X )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_real ) ).
% 5.46/5.73
% 5.46/5.73 % ln_x_over_x_tendsto_0
% 5.46/5.73 thf(fact_9973_tendsto__power__div__exp__0,axiom,
% 5.46/5.73 ! [K: nat] :
% 5.46/5.73 ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( power_power_real @ X @ K ) @ ( exp_real @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.73 @ at_top_real ) ).
% 5.46/5.73
% 5.46/5.73 % tendsto_power_div_exp_0
% 5.46/5.73 thf(fact_9974_tendsto__exp__limit__at__top,axiom,
% 5.46/5.73 ! [X2: real] :
% 5.46/5.73 ( filterlim_real_real
% 5.46/5.73 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ Y ) ) @ Y )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.46/5.73 @ at_top_real ) ).
% 5.46/5.73
% 5.46/5.73 % tendsto_exp_limit_at_top
% 5.46/5.73 thf(fact_9975_filterlim__tan__at__left,axiom,
% 5.46/5.73 filterlim_real_real @ tan_real @ at_top_real @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( set_or5984915006950818249n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % filterlim_tan_at_left
% 5.46/5.73 thf(fact_9976_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.46/5.73 ! [B: real,F: real > real,Flim: real] :
% 5.46/5.73 ( ! [X3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ B @ X3 )
% 5.46/5.73 => ? [Y4: real] :
% 5.46/5.73 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.73 & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 5.46/5.73 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.46/5.73 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % DERIV_neg_imp_decreasing_at_top
% 5.46/5.73 thf(fact_9977_tendsto__arctan__at__top,axiom,
% 5.46/5.73 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.46/5.73
% 5.46/5.73 % tendsto_arctan_at_top
% 5.46/5.73 thf(fact_9978_lhopital__right__at__top,axiom,
% 5.46/5.73 ! [G: real > real,X2: real,G2: real > real,F: real > real,F3: real > real,Y2: real] :
% 5.46/5.73 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( ( G2 @ X )
% 5.46/5.73 != zero_zero_real )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ Y2 )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ Y2 )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_right_at_top
% 5.46/5.73 thf(fact_9979_lhopital__right__0__at__top,axiom,
% 5.46/5.73 ! [G: real > real,G2: real > real,F: real > real,F3: real > real,X2: real] :
% 5.46/5.73 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( ( G2 @ X )
% 5.46/5.73 != zero_zero_real )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ X2 )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ X2 )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_right_0_at_top
% 5.46/5.73 thf(fact_9980_eventually__at__left__real,axiom,
% 5.46/5.73 ! [B: real,A: real] :
% 5.46/5.73 ( ( ord_less_real @ B @ A )
% 5.46/5.73 => ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B @ A ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % eventually_at_left_real
% 5.46/5.73 thf(fact_9981_eventually__at__right__to__0,axiom,
% 5.46/5.73 ! [P: real > $o,A: real] :
% 5.46/5.73 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.73 = ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( P @ ( plus_plus_real @ X @ A ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % eventually_at_right_to_0
% 5.46/5.73 thf(fact_9982_eventually__at__right__real,axiom,
% 5.46/5.73 ! [A: real,B: real] :
% 5.46/5.73 ( ( ord_less_real @ A @ B )
% 5.46/5.73 => ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % eventually_at_right_real
% 5.46/5.73 thf(fact_9983_lhopital__at__top__at__top,axiom,
% 5.46/5.73 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ at_top_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ at_top_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_at_top_at_top
% 5.46/5.73 thf(fact_9984_lhopital__left__at__top__at__top,axiom,
% 5.46/5.73 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ at_top_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ at_top_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_left_at_top_at_top
% 5.46/5.73 thf(fact_9985_lhopital,axiom,
% 5.46/5.73 ! [F: real > real,X2: real,G: real > real,G2: real > real,F3: real > real,F5: filter_real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( ( G @ X )
% 5.46/5.73 != zero_zero_real )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( ( G2 @ X )
% 5.46/5.73 != zero_zero_real )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ F5
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ F5
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital
% 5.46/5.73 thf(fact_9986_lhopital__left,axiom,
% 5.46/5.73 ! [F: real > real,X2: real,G: real > real,G2: real > real,F3: real > real,F5: filter_real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( ( G @ X )
% 5.46/5.73 != zero_zero_real )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( ( G2 @ X )
% 5.46/5.73 != zero_zero_real )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ F5
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ F5
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_left
% 5.46/5.73 thf(fact_9987_lhopital__right__at__top__at__top,axiom,
% 5.46/5.73 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.73 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ at_top_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ at_top_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_right_at_top_at_top
% 5.46/5.73 thf(fact_9988_lhopital__at__top__at__bot,axiom,
% 5.46/5.73 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ at_bot_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ at_bot_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_at_top_at_bot
% 5.46/5.73 thf(fact_9989_lhopital__left__at__top__at__bot,axiom,
% 5.46/5.73 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.46/5.73 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ at_bot_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ at_bot_real
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_left_at_top_at_bot
% 5.46/5.73 thf(fact_9990_lhopital__at__top,axiom,
% 5.46/5.73 ! [G: real > real,X2: real,G2: real > real,F: real > real,F3: real > real,Y2: real] :
% 5.46/5.73 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( ( G2 @ X )
% 5.46/5.73 != zero_zero_real )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ Y2 )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ Y2 )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_at_top
% 5.46/5.73 thf(fact_9991_lhospital__at__top__at__top,axiom,
% 5.46/5.73 ! [G: real > real,G2: real > real,F: real > real,F3: real > real,X2: real] :
% 5.46/5.73 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( ( G2 @ X )
% 5.46/5.73 != zero_zero_real )
% 5.46/5.73 @ at_top_real )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ at_top_real )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ at_top_real )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ X2 )
% 5.46/5.73 @ at_top_real )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ X2 )
% 5.46/5.73 @ at_top_real ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhospital_at_top_at_top
% 5.46/5.73 thf(fact_9992_lhopital__left__at__top,axiom,
% 5.46/5.73 ! [G: real > real,X2: real,G2: real > real,F: real > real,F3: real > real,Y2: real] :
% 5.46/5.73 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] :
% 5.46/5.73 ( ( G2 @ X )
% 5.46/5.73 != zero_zero_real )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( eventually_real
% 5.46/5.73 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ Y2 )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.46/5.73 => ( filterlim_real_real
% 5.46/5.73 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.73 @ ( topolo2815343760600316023s_real @ Y2 )
% 5.46/5.73 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lhopital_left_at_top
% 5.46/5.73 thf(fact_9993_lhopital__right__0,axiom,
% 5.46/5.73 ! [F0: real > real,G0: real > real,G2: real > real,F3: real > real,F5: filter_real] :
% 5.46/5.73 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.74 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] :
% 5.46/5.74 ( ( G0 @ X )
% 5.46/5.74 != zero_zero_real )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] :
% 5.46/5.74 ( ( G2 @ X )
% 5.46/5.74 != zero_zero_real )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.74 => ( ( filterlim_real_real
% 5.46/5.74 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.74 @ F5
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.74 => ( filterlim_real_real
% 5.46/5.74 @ ^ [X: real] : ( divide_divide_real @ ( F0 @ X ) @ ( G0 @ X ) )
% 5.46/5.74 @ F5
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % lhopital_right_0
% 5.46/5.74 thf(fact_9994_lhopital__right,axiom,
% 5.46/5.74 ! [F: real > real,X2: real,G: real > real,G2: real > real,F3: real > real,F5: filter_real] :
% 5.46/5.74 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.74 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] :
% 5.46/5.74 ( ( G @ X )
% 5.46/5.74 != zero_zero_real )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] :
% 5.46/5.74 ( ( G2 @ X )
% 5.46/5.74 != zero_zero_real )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.74 => ( ( filterlim_real_real
% 5.46/5.74 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.74 @ F5
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.46/5.74 => ( filterlim_real_real
% 5.46/5.74 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.74 @ F5
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % lhopital_right
% 5.46/5.74 thf(fact_9995_lhopital__right__at__top__at__bot,axiom,
% 5.46/5.74 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.46/5.74 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.74 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.74 => ( ( eventually_real
% 5.46/5.74 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.74 => ( ( filterlim_real_real
% 5.46/5.74 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.46/5.74 @ at_bot_real
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.74 => ( filterlim_real_real
% 5.46/5.74 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.74 @ at_bot_real
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % lhopital_right_at_top_at_bot
% 5.46/5.74 thf(fact_9996_eventually__sequentially__Suc,axiom,
% 5.46/5.74 ! [P: nat > $o] :
% 5.46/5.74 ( ( eventually_nat
% 5.46/5.74 @ ^ [I4: nat] : ( P @ ( suc @ I4 ) )
% 5.46/5.74 @ at_top_nat )
% 5.46/5.74 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % eventually_sequentially_Suc
% 5.46/5.74 thf(fact_9997_eventually__sequentially__seg,axiom,
% 5.46/5.74 ! [P: nat > $o,K: nat] :
% 5.46/5.74 ( ( eventually_nat
% 5.46/5.74 @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 5.46/5.74 @ at_top_nat )
% 5.46/5.74 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % eventually_sequentially_seg
% 5.46/5.74 thf(fact_9998_le__sequentially,axiom,
% 5.46/5.74 ! [F5: filter_nat] :
% 5.46/5.74 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.46/5.74 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F5 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % le_sequentially
% 5.46/5.74 thf(fact_9999_eventually__sequentially,axiom,
% 5.46/5.74 ! [P: nat > $o] :
% 5.46/5.74 ( ( eventually_nat @ P @ at_top_nat )
% 5.46/5.74 = ( ? [N6: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N6 @ N2 )
% 5.46/5.74 => ( P @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % eventually_sequentially
% 5.46/5.74 thf(fact_10000_eventually__sequentiallyI,axiom,
% 5.46/5.74 ! [C: nat,P: nat > $o] :
% 5.46/5.74 ( ! [X3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ C @ X3 )
% 5.46/5.74 => ( P @ X3 ) )
% 5.46/5.74 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % eventually_sequentiallyI
% 5.46/5.74 thf(fact_10001_sequentially__offset,axiom,
% 5.46/5.74 ! [P: nat > $o,K: nat] :
% 5.46/5.74 ( ( eventually_nat @ P @ at_top_nat )
% 5.46/5.74 => ( eventually_nat
% 5.46/5.74 @ ^ [I4: nat] : ( P @ ( plus_plus_nat @ I4 @ K ) )
% 5.46/5.74 @ at_top_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % sequentially_offset
% 5.46/5.74 thf(fact_10002_Bseq__realpow,axiom,
% 5.46/5.74 ! [X2: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.74 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.46/5.74 => ( bfun_nat_real @ ( power_power_real @ X2 ) @ at_top_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Bseq_realpow
% 5.46/5.74 thf(fact_10003_GreatestI__ex__nat,axiom,
% 5.46/5.74 ! [P: nat > $o,B: nat] :
% 5.46/5.74 ( ? [X_12: nat] : ( P @ X_12 )
% 5.46/5.74 => ( ! [Y3: nat] :
% 5.46/5.74 ( ( P @ Y3 )
% 5.46/5.74 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.46/5.74 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % GreatestI_ex_nat
% 5.46/5.74 thf(fact_10004_Greatest__le__nat,axiom,
% 5.46/5.74 ! [P: nat > $o,K: nat,B: nat] :
% 5.46/5.74 ( ( P @ K )
% 5.46/5.74 => ( ! [Y3: nat] :
% 5.46/5.74 ( ( P @ Y3 )
% 5.46/5.74 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.46/5.74 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Greatest_le_nat
% 5.46/5.74 thf(fact_10005_GreatestI__nat,axiom,
% 5.46/5.74 ! [P: nat > $o,K: nat,B: nat] :
% 5.46/5.74 ( ( P @ K )
% 5.46/5.74 => ( ! [Y3: nat] :
% 5.46/5.74 ( ( P @ Y3 )
% 5.46/5.74 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.46/5.74 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % GreatestI_nat
% 5.46/5.74 thf(fact_10006_decseq__bounded,axiom,
% 5.46/5.74 ! [X7: nat > real,B3: real] :
% 5.46/5.74 ( ( order_9091379641038594480t_real @ X7 )
% 5.46/5.74 => ( ! [I2: nat] : ( ord_less_eq_real @ B3 @ ( X7 @ I2 ) )
% 5.46/5.74 => ( bfun_nat_real @ X7 @ at_top_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % decseq_bounded
% 5.46/5.74 thf(fact_10007_decseq__convergent,axiom,
% 5.46/5.74 ! [X7: nat > real,B3: real] :
% 5.46/5.74 ( ( order_9091379641038594480t_real @ X7 )
% 5.46/5.74 => ( ! [I2: nat] : ( ord_less_eq_real @ B3 @ ( X7 @ I2 ) )
% 5.46/5.74 => ~ ! [L6: real] :
% 5.46/5.74 ( ( filterlim_nat_real @ X7 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.46/5.74 => ~ ! [I3: nat] : ( ord_less_eq_real @ L6 @ ( X7 @ I3 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % decseq_convergent
% 5.46/5.74 thf(fact_10008_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.46/5.74 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.74 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.46/5.74 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.46/5.74 ( X2
% 5.46/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.74 => ( Xa2 = one_one_nat ) )
% 5.46/5.74 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.74 => ( ( Deg2 = Xa2 )
% 5.46/5.74 & ! [X3: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 & ( case_o184042715313410164at_nat
% 5.46/5.74 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.74 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 & ! [I4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.46/5.74 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.46/5.74 & ( ( Mi3 = Ma3 )
% 5.46/5.74 => ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 & ( ( Mi3 != Ma3 )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.46/5.74 & ! [X: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.46/5.74 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.74 @ Mima ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % VEBT_internal.valid'.elims(3)
% 5.46/5.74 thf(fact_10009_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.46/5.74 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.74 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.46/5.74 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.46/5.74 ( X2
% 5.46/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.74 => ( Xa2 != one_one_nat ) )
% 5.46/5.74 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.74 => ~ ( ( Deg2 = Xa2 )
% 5.46/5.74 & ! [X4: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 & ( case_o184042715313410164at_nat
% 5.46/5.74 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.74 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 & ! [I4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.46/5.74 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.46/5.74 & ( ( Mi3 = Ma3 )
% 5.46/5.74 => ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 & ( ( Mi3 != Ma3 )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.46/5.74 & ! [X: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.46/5.74 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.74 @ Mima ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % VEBT_internal.valid'.elims(2)
% 5.46/5.74 thf(fact_10010_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.46/5.74 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.46/5.74 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 5.46/5.74 = ( ( Deg = Deg4 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.74 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 & ( case_o184042715313410164at_nat
% 5.46/5.74 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X5 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.74 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.46/5.74 & ! [I4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X5 ) )
% 5.46/5.74 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.46/5.74 & ( ( Mi3 = Ma3 )
% 5.46/5.74 => ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 & ( ( Mi3 != Ma3 )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.46/5.74 & ! [X: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.46/5.74 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.74 @ Mima2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % VEBT_internal.valid'.simps(2)
% 5.46/5.74 thf(fact_10011_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.46/5.74 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.46/5.74 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.46/5.74 = Y2 )
% 5.46/5.74 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.46/5.74 ( X2
% 5.46/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.74 => ( Y2
% 5.46/5.74 = ( Xa2 != one_one_nat ) ) )
% 5.46/5.74 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.74 => ( Y2
% 5.46/5.74 = ( ~ ( ( Deg2 = Xa2 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 & ( case_o184042715313410164at_nat
% 5.46/5.74 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.74 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 & ! [I4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.46/5.74 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.46/5.74 & ( ( Mi3 = Ma3 )
% 5.46/5.74 => ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 & ( ( Mi3 != Ma3 )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.46/5.74 & ! [X: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.46/5.74 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.74 @ Mima ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % VEBT_internal.valid'.elims(1)
% 5.46/5.74 thf(fact_10012_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.46/5.74 ! [X2: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.46/5.74 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.46/5.74 = Y2 )
% 5.46/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.74 => ( ! [Uu2: $o,Uv2: $o] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( Xa2 = one_one_nat ) )
% 5.46/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.46/5.74 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( ( Deg2 = Xa2 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 & ( case_o184042715313410164at_nat
% 5.46/5.74 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.74 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 & ! [I4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.46/5.74 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.46/5.74 & ( ( Mi3 = Ma3 )
% 5.46/5.74 => ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 & ( ( Mi3 != Ma3 )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.46/5.74 & ! [X: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.46/5.74 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.74 @ Mima ) ) )
% 5.46/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % VEBT_internal.valid'.pelims(1)
% 5.46/5.74 thf(fact_10013_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.46/5.74 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.74 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.46/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.74 => ( ! [Uu2: $o,Uv2: $o] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.46/5.74 => ( Xa2 != one_one_nat ) ) )
% 5.46/5.74 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.46/5.74 => ~ ( ( Deg2 = Xa2 )
% 5.46/5.74 & ! [X4: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 & ( case_o184042715313410164at_nat
% 5.46/5.74 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.74 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 & ! [I4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.46/5.74 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.46/5.74 & ( ( Mi3 = Ma3 )
% 5.46/5.74 => ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 & ( ( Mi3 != Ma3 )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.46/5.74 & ! [X: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.46/5.74 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.74 @ Mima ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % VEBT_internal.valid'.pelims(2)
% 5.46/5.74 thf(fact_10014_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.46/5.74 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.46/5.74 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.46/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.46/5.74 => ( ! [Uu2: $o,Uv2: $o] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.46/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.46/5.74 => ( Xa2 = one_one_nat ) ) )
% 5.46/5.74 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.46/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.46/5.74 => ( ( Deg2 = Xa2 )
% 5.46/5.74 & ! [X3: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 & ( case_o184042715313410164at_nat
% 5.46/5.74 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.46/5.74 & ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.74 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 & ! [I4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.74 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.46/5.74 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.46/5.74 & ( ( Mi3 = Ma3 )
% 5.46/5.74 => ! [X: vEBT_VEBT] :
% 5.46/5.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.74 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.46/5.74 & ( ( Mi3 != Ma3 )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.46/5.74 & ! [X: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.74 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.46/5.74 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.74 @ Mima ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % VEBT_internal.valid'.pelims(3)
% 5.46/5.74 thf(fact_10015_GMVT,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.46/5.74 ( ( ord_less_real @ A @ B )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.74 & ( ord_less_eq_real @ X3 @ B ) )
% 5.46/5.74 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 & ( ord_less_real @ X3 @ B ) )
% 5.46/5.74 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.74 & ( ord_less_eq_real @ X3 @ B ) )
% 5.46/5.74 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 & ( ord_less_real @ X3 @ B ) )
% 5.46/5.74 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.74 => ? [G_c: real,F_c: real,C2: real] :
% 5.46/5.74 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.46/5.74 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.46/5.74 & ( ord_less_real @ A @ C2 )
% 5.46/5.74 & ( ord_less_real @ C2 @ B )
% 5.46/5.74 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.46/5.74 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % GMVT
% 5.46/5.74 thf(fact_10016_MVT,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real] :
% 5.46/5.74 ( ( ord_less_real @ A @ B )
% 5.46/5.74 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 => ( ( ord_less_real @ X3 @ B )
% 5.46/5.74 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.74 => ? [L4: real,Z3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ Z3 )
% 5.46/5.74 & ( ord_less_real @ Z3 @ B )
% 5.46/5.74 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 5.46/5.74 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.46/5.74 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % MVT
% 5.46/5.74 thf(fact_10017_continuous__on__arcosh,axiom,
% 5.46/5.74 ! [A2: set_real] :
% 5.46/5.74 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.46/5.74 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % continuous_on_arcosh
% 5.46/5.74 thf(fact_10018_continuous__on__arcosh_H,axiom,
% 5.46/5.74 ! [A2: set_real,F: real > real] :
% 5.46/5.74 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( member_real @ X3 @ A2 )
% 5.46/5.74 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.46/5.74 => ( topolo5044208981011980120l_real @ A2
% 5.46/5.74 @ ^ [X: real] : ( arcosh_real @ ( F @ X ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % continuous_on_arcosh'
% 5.46/5.74 thf(fact_10019_continuous__image__closed__interval,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real] :
% 5.46/5.74 ( ( ord_less_eq_real @ A @ B )
% 5.46/5.74 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.46/5.74 => ? [C2: real,D3: real] :
% 5.46/5.74 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.46/5.74 = ( set_or1222579329274155063t_real @ C2 @ D3 ) )
% 5.46/5.74 & ( ord_less_eq_real @ C2 @ D3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % continuous_image_closed_interval
% 5.46/5.74 thf(fact_10020_continuous__on__arccos_H,axiom,
% 5.46/5.74 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.46/5.74
% 5.46/5.74 % continuous_on_arccos'
% 5.46/5.74 thf(fact_10021_continuous__on__arcsin_H,axiom,
% 5.46/5.74 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.46/5.74
% 5.46/5.74 % continuous_on_arcsin'
% 5.46/5.74 thf(fact_10022_continuous__on__artanh,axiom,
% 5.46/5.74 ! [A2: set_real] :
% 5.46/5.74 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.46/5.74 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % continuous_on_artanh
% 5.46/5.74 thf(fact_10023_continuous__on__artanh_H,axiom,
% 5.46/5.74 ! [A2: set_real,F: real > real] :
% 5.46/5.74 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( member_real @ X3 @ A2 )
% 5.46/5.74 => ( member_real @ ( F @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.46/5.74 => ( topolo5044208981011980120l_real @ A2
% 5.46/5.74 @ ^ [X: real] : ( artanh_real @ ( F @ X ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % continuous_on_artanh'
% 5.46/5.74 thf(fact_10024_Rolle__deriv,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real,F3: real > real > real] :
% 5.46/5.74 ( ( ord_less_real @ A @ B )
% 5.46/5.74 => ( ( ( F @ A )
% 5.46/5.74 = ( F @ B ) )
% 5.46/5.74 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 => ( ( ord_less_real @ X3 @ B )
% 5.46/5.74 => ( has_de1759254742604945161l_real @ F @ ( F3 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.74 => ? [Z3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ Z3 )
% 5.46/5.74 & ( ord_less_real @ Z3 @ B )
% 5.46/5.74 & ( ( F3 @ Z3 )
% 5.46/5.74 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rolle_deriv
% 5.46/5.74 thf(fact_10025_mvt,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real,F3: real > real > real] :
% 5.46/5.74 ( ( ord_less_real @ A @ B )
% 5.46/5.74 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 => ( ( ord_less_real @ X3 @ B )
% 5.46/5.74 => ( has_de1759254742604945161l_real @ F @ ( F3 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.74 => ~ ! [Xi: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ Xi )
% 5.46/5.74 => ( ( ord_less_real @ Xi @ B )
% 5.46/5.74 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.46/5.74 != ( F3 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mvt
% 5.46/5.74 thf(fact_10026_DERIV__isconst__end,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real] :
% 5.46/5.74 ( ( ord_less_real @ A @ B )
% 5.46/5.74 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 => ( ( ord_less_real @ X3 @ B )
% 5.46/5.74 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.74 => ( ( F @ B )
% 5.46/5.74 = ( F @ A ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % DERIV_isconst_end
% 5.46/5.74 thf(fact_10027_DERIV__neg__imp__decreasing__open,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real] :
% 5.46/5.74 ( ( ord_less_real @ A @ B )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 => ( ( ord_less_real @ X3 @ B )
% 5.46/5.74 => ? [Y4: real] :
% 5.46/5.74 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.74 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.46/5.74 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.46/5.74 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % DERIV_neg_imp_decreasing_open
% 5.46/5.74 thf(fact_10028_DERIV__pos__imp__increasing__open,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real] :
% 5.46/5.74 ( ( ord_less_real @ A @ B )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 => ( ( ord_less_real @ X3 @ B )
% 5.46/5.74 => ? [Y4: real] :
% 5.46/5.74 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.74 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.46/5.74 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.46/5.74 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % DERIV_pos_imp_increasing_open
% 5.46/5.74 thf(fact_10029_DERIV__isconst2,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real,X2: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ B )
% 5.46/5.74 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 => ( ( ord_less_real @ X3 @ B )
% 5.46/5.74 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.74 => ( ( ord_less_eq_real @ A @ X2 )
% 5.46/5.74 => ( ( ord_less_eq_real @ X2 @ B )
% 5.46/5.74 => ( ( F @ X2 )
% 5.46/5.74 = ( F @ A ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % DERIV_isconst2
% 5.46/5.74 thf(fact_10030_Rolle,axiom,
% 5.46/5.74 ! [A: real,B: real,F: real > real] :
% 5.46/5.74 ( ( ord_less_real @ A @ B )
% 5.46/5.74 => ( ( ( F @ A )
% 5.46/5.74 = ( F @ B ) )
% 5.46/5.74 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.46/5.74 => ( ! [X3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X3 )
% 5.46/5.74 => ( ( ord_less_real @ X3 @ B )
% 5.46/5.74 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.74 => ? [Z3: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ Z3 )
% 5.46/5.74 & ( ord_less_real @ Z3 @ B )
% 5.46/5.74 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rolle
% 5.46/5.74 thf(fact_10031_uniformity__real__def,axiom,
% 5.46/5.74 ( topolo1511823702728130853y_real
% 5.46/5.74 = ( comple2936214249959783750l_real
% 5.46/5.74 @ ( image_2178119161166701260l_real
% 5.46/5.74 @ ^ [E3: real] :
% 5.46/5.74 ( princi6114159922880469582l_real
% 5.46/5.74 @ ( collec3799799289383736868l_real
% 5.46/5.74 @ ( produc5414030515140494994real_o
% 5.46/5.74 @ ^ [X: real,Y: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X @ Y ) @ E3 ) ) ) )
% 5.46/5.74 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % uniformity_real_def
% 5.46/5.74 thf(fact_10032_uniformity__complex__def,axiom,
% 5.46/5.74 ( topolo896644834953643431omplex
% 5.46/5.74 = ( comple8358262395181532106omplex
% 5.46/5.74 @ ( image_5971271580939081552omplex
% 5.46/5.74 @ ^ [E3: real] :
% 5.46/5.74 ( princi3496590319149328850omplex
% 5.46/5.74 @ ( collec8663557070575231912omplex
% 5.46/5.74 @ ( produc6771430404735790350plex_o
% 5.46/5.74 @ ^ [X: complex,Y: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X @ Y ) @ E3 ) ) ) )
% 5.46/5.74 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % uniformity_complex_def
% 5.46/5.74 thf(fact_10033_mono__times__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.74 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mono_times_nat
% 5.46/5.74 thf(fact_10034_mono__Suc,axiom,
% 5.46/5.74 order_mono_nat_nat @ suc ).
% 5.46/5.74
% 5.46/5.74 % mono_Suc
% 5.46/5.74 thf(fact_10035_incseq__bounded,axiom,
% 5.46/5.74 ! [X7: nat > real,B3: real] :
% 5.46/5.74 ( ( order_mono_nat_real @ X7 )
% 5.46/5.74 => ( ! [I2: nat] : ( ord_less_eq_real @ ( X7 @ I2 ) @ B3 )
% 5.46/5.74 => ( bfun_nat_real @ X7 @ at_top_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % incseq_bounded
% 5.46/5.74 thf(fact_10036_incseq__convergent,axiom,
% 5.46/5.74 ! [X7: nat > real,B3: real] :
% 5.46/5.74 ( ( order_mono_nat_real @ X7 )
% 5.46/5.74 => ( ! [I2: nat] : ( ord_less_eq_real @ ( X7 @ I2 ) @ B3 )
% 5.46/5.74 => ~ ! [L6: real] :
% 5.46/5.74 ( ( filterlim_nat_real @ X7 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.46/5.74 => ~ ! [I3: nat] : ( ord_less_eq_real @ ( X7 @ I3 ) @ L6 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % incseq_convergent
% 5.46/5.74 thf(fact_10037_mono__ge2__power__minus__self,axiom,
% 5.46/5.74 ! [K: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.46/5.74 => ( order_mono_nat_nat
% 5.46/5.74 @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mono_ge2_power_minus_self
% 5.46/5.74 thf(fact_10038_eventually__prod__sequentially,axiom,
% 5.46/5.74 ! [P: product_prod_nat_nat > $o] :
% 5.46/5.74 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.46/5.74 = ( ? [N6: nat] :
% 5.46/5.74 ! [M3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N6 @ M3 )
% 5.46/5.74 => ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N6 @ N2 )
% 5.46/5.74 => ( P @ ( product_Pair_nat_nat @ N2 @ M3 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % eventually_prod_sequentially
% 5.46/5.74 thf(fact_10039_nonneg__incseq__Bseq__subseq__iff,axiom,
% 5.46/5.74 ! [F: nat > real,G: nat > nat] :
% 5.46/5.74 ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.74 => ( ( order_mono_nat_real @ F )
% 5.46/5.74 => ( ( order_5726023648592871131at_nat @ G )
% 5.46/5.74 => ( ( bfun_nat_real
% 5.46/5.74 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 5.46/5.74 @ at_top_nat )
% 5.46/5.74 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % nonneg_incseq_Bseq_subseq_iff
% 5.46/5.74 thf(fact_10040_strict__mono__imp__increasing,axiom,
% 5.46/5.74 ! [F: nat > nat,N: nat] :
% 5.46/5.74 ( ( order_5726023648592871131at_nat @ F )
% 5.46/5.74 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % strict_mono_imp_increasing
% 5.46/5.74 thf(fact_10041_filtermap__at__right__shift,axiom,
% 5.46/5.74 ! [D2: real,A: real] :
% 5.46/5.74 ( ( filtermap_real_real
% 5.46/5.74 @ ^ [X: real] : ( minus_minus_real @ X @ D2 )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.74 = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D2 ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % filtermap_at_right_shift
% 5.46/5.74 thf(fact_10042_at__right__to__0,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.46/5.74 = ( filtermap_real_real
% 5.46/5.74 @ ^ [X: real] : ( plus_plus_real @ X @ A )
% 5.46/5.74 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % at_right_to_0
% 5.46/5.74 thf(fact_10043_inj__sgn__power,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.74 => ( inj_on_real_real
% 5.46/5.74 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.46/5.74 @ top_top_set_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % inj_sgn_power
% 5.46/5.74 thf(fact_10044_log__inj,axiom,
% 5.46/5.74 ! [B: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ B )
% 5.46/5.74 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_inj
% 5.46/5.74 thf(fact_10045_pos__deriv__imp__strict__mono,axiom,
% 5.46/5.74 ! [F: real > real,F3: real > real] :
% 5.46/5.74 ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.74 => ( ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( F3 @ X3 ) )
% 5.46/5.74 => ( order_7092887310737990675l_real @ F ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % pos_deriv_imp_strict_mono
% 5.46/5.74 thf(fact_10046_inj__on__diff__nat,axiom,
% 5.46/5.74 ! [N4: set_nat,K: nat] :
% 5.46/5.74 ( ! [N3: nat] :
% 5.46/5.74 ( ( member_nat @ N3 @ N4 )
% 5.46/5.74 => ( ord_less_eq_nat @ K @ N3 ) )
% 5.46/5.74 => ( inj_on_nat_nat
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 5.46/5.74 @ N4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % inj_on_diff_nat
% 5.46/5.74 thf(fact_10047_inj__Suc,axiom,
% 5.46/5.74 ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 5.46/5.74
% 5.46/5.74 % inj_Suc
% 5.46/5.74 thf(fact_10048_summable__reindex,axiom,
% 5.46/5.74 ! [F: nat > real,G: nat > nat] :
% 5.46/5.74 ( ( summable_real @ F )
% 5.46/5.74 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.46/5.74 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.74 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % summable_reindex
% 5.46/5.74 thf(fact_10049_suminf__reindex__mono,axiom,
% 5.46/5.74 ! [F: nat > real,G: nat > nat] :
% 5.46/5.74 ( ( summable_real @ F )
% 5.46/5.74 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.46/5.74 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.74 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % suminf_reindex_mono
% 5.46/5.74 thf(fact_10050_inj__on__char__of__nat,axiom,
% 5.46/5.74 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % inj_on_char_of_nat
% 5.46/5.74 thf(fact_10051_suminf__reindex,axiom,
% 5.46/5.74 ! [F: nat > real,G: nat > nat] :
% 5.46/5.74 ( ( summable_real @ F )
% 5.46/5.74 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.46/5.74 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.74 => ( ! [X3: nat] :
% 5.46/5.74 ( ~ ( member_nat @ X3 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 5.46/5.74 => ( ( F @ X3 )
% 5.46/5.74 = zero_zero_real ) )
% 5.46/5.74 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 5.46/5.74 = ( suminf_real @ F ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % suminf_reindex
% 5.46/5.74 thf(fact_10052_powr__real__of__int_H,axiom,
% 5.46/5.74 ! [X2: real,N: int] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.46/5.74 => ( ( ( X2 != zero_zero_real )
% 5.46/5.74 | ( ord_less_int @ zero_zero_int @ N ) )
% 5.46/5.74 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.46/5.74 = ( power_int_real @ X2 @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % powr_real_of_int'
% 5.46/5.74 thf(fact_10053_pred__nat__def,axiom,
% 5.46/5.74 ( pred_nat
% 5.46/5.74 = ( collec3392354462482085612at_nat
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [M3: nat,N2: nat] :
% 5.46/5.74 ( N2
% 5.46/5.74 = ( suc @ M3 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % pred_nat_def
% 5.46/5.74 thf(fact_10054_atLeastLessThan__add__Un,axiom,
% 5.46/5.74 ! [I: nat,J: nat,K: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.74 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 5.46/5.74 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % atLeastLessThan_add_Un
% 5.46/5.74 thf(fact_10055_sup__nat__def,axiom,
% 5.46/5.74 sup_sup_nat = ord_max_nat ).
% 5.46/5.74
% 5.46/5.74 % sup_nat_def
% 5.46/5.74 thf(fact_10056_sup__enat__def,axiom,
% 5.46/5.74 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.46/5.74
% 5.46/5.74 % sup_enat_def
% 5.46/5.74 thf(fact_10057_Rats__eq__int__div__nat,axiom,
% 5.46/5.74 ( field_5140801741446780682s_real
% 5.46/5.74 = ( collect_real
% 5.46/5.74 @ ^ [Uu3: real] :
% 5.46/5.74 ? [I4: int,N2: nat] :
% 5.46/5.74 ( ( Uu3
% 5.46/5.74 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.46/5.74 & ( N2 != zero_zero_nat ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rats_eq_int_div_nat
% 5.46/5.74 thf(fact_10058_Rats__abs__iff,axiom,
% 5.46/5.74 ! [X2: real] :
% 5.46/5.74 ( ( member_real @ ( abs_abs_real @ X2 ) @ field_5140801741446780682s_real )
% 5.46/5.74 = ( member_real @ X2 @ field_5140801741446780682s_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rats_abs_iff
% 5.46/5.74 thf(fact_10059_Rats__no__top__le,axiom,
% 5.46/5.74 ! [X2: real] :
% 5.46/5.74 ? [X3: real] :
% 5.46/5.74 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.46/5.74 & ( ord_less_eq_real @ X2 @ X3 ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rats_no_top_le
% 5.46/5.74 thf(fact_10060_Rats__no__bot__less,axiom,
% 5.46/5.74 ! [X2: real] :
% 5.46/5.74 ? [X3: real] :
% 5.46/5.74 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.46/5.74 & ( ord_less_real @ X3 @ X2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rats_no_bot_less
% 5.46/5.74 thf(fact_10061_Rats__dense__in__real,axiom,
% 5.46/5.74 ! [X2: real,Y2: real] :
% 5.46/5.74 ( ( ord_less_real @ X2 @ Y2 )
% 5.46/5.74 => ? [X3: real] :
% 5.46/5.74 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.46/5.74 & ( ord_less_real @ X2 @ X3 )
% 5.46/5.74 & ( ord_less_real @ X3 @ Y2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rats_dense_in_real
% 5.46/5.74 thf(fact_10062_Rats__eq__int__div__int,axiom,
% 5.46/5.74 ( field_5140801741446780682s_real
% 5.46/5.74 = ( collect_real
% 5.46/5.74 @ ^ [Uu3: real] :
% 5.46/5.74 ? [I4: int,J3: int] :
% 5.46/5.74 ( ( Uu3
% 5.46/5.74 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.46/5.74 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rats_eq_int_div_int
% 5.46/5.74 thf(fact_10063_less__eq,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.46/5.74 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % less_eq
% 5.46/5.74 thf(fact_10064_pred__nat__trancl__eq__le,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.46/5.74 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % pred_nat_trancl_eq_le
% 5.46/5.74 thf(fact_10065_tl__upt,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( tl_nat @ ( upt @ M @ N ) )
% 5.46/5.74 = ( upt @ ( suc @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % tl_upt
% 5.46/5.74 thf(fact_10066_hd__upt,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I @ J )
% 5.46/5.74 => ( ( hd_nat @ ( upt @ I @ J ) )
% 5.46/5.74 = I ) ) ).
% 5.46/5.74
% 5.46/5.74 % hd_upt
% 5.46/5.74 thf(fact_10067_drop__upt,axiom,
% 5.46/5.74 ! [M: nat,I: nat,J: nat] :
% 5.46/5.74 ( ( drop_nat @ M @ ( upt @ I @ J ) )
% 5.46/5.74 = ( upt @ ( plus_plus_nat @ I @ M ) @ J ) ) ).
% 5.46/5.74
% 5.46/5.74 % drop_upt
% 5.46/5.74 thf(fact_10068_length__upt,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 5.46/5.74 = ( minus_minus_nat @ J @ I ) ) ).
% 5.46/5.74
% 5.46/5.74 % length_upt
% 5.46/5.74 thf(fact_10069_take__upt,axiom,
% 5.46/5.74 ! [I: nat,M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 5.46/5.74 => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 5.46/5.74 = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % take_upt
% 5.46/5.74 thf(fact_10070_upt__conv__Nil,axiom,
% 5.46/5.74 ! [J: nat,I: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ J @ I )
% 5.46/5.74 => ( ( upt @ I @ J )
% 5.46/5.74 = nil_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_conv_Nil
% 5.46/5.74 thf(fact_10071_upt__eq__Nil__conv,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( ( upt @ I @ J )
% 5.46/5.74 = nil_nat )
% 5.46/5.74 = ( ( J = zero_zero_nat )
% 5.46/5.74 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_eq_Nil_conv
% 5.46/5.74 thf(fact_10072_nth__upt,axiom,
% 5.46/5.74 ! [I: nat,K: nat,J: nat] :
% 5.46/5.74 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 5.46/5.74 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 5.46/5.74 = ( plus_plus_nat @ I @ K ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % nth_upt
% 5.46/5.74 thf(fact_10073_upt__rec__numeral,axiom,
% 5.46/5.74 ! [M: num,N: num] :
% 5.46/5.74 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.46/5.74 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = nil_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_rec_numeral
% 5.46/5.74 thf(fact_10074_map__Suc__upt,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 5.46/5.74 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % map_Suc_upt
% 5.46/5.74 thf(fact_10075_map__add__upt,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( map_nat_nat
% 5.46/5.74 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 5.46/5.74 @ ( upt @ zero_zero_nat @ M ) )
% 5.46/5.74 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % map_add_upt
% 5.46/5.74 thf(fact_10076_atMost__upto,axiom,
% 5.46/5.74 ( set_ord_atMost_nat
% 5.46/5.74 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % atMost_upto
% 5.46/5.74 thf(fact_10077_upt__conv__Cons__Cons,axiom,
% 5.46/5.74 ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 5.46/5.74 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 5.46/5.74 = ( upt @ M @ Q2 ) )
% 5.46/5.74 = ( ( cons_nat @ N @ Ns )
% 5.46/5.74 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_conv_Cons_Cons
% 5.46/5.74 thf(fact_10078_greaterThanAtMost__upt,axiom,
% 5.46/5.74 ( set_or6659071591806873216st_nat
% 5.46/5.74 = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M3 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % greaterThanAtMost_upt
% 5.46/5.74 thf(fact_10079_greaterThanLessThan__upt,axiom,
% 5.46/5.74 ( set_or5834768355832116004an_nat
% 5.46/5.74 = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % greaterThanLessThan_upt
% 5.46/5.74 thf(fact_10080_atLeastAtMost__upt,axiom,
% 5.46/5.74 ( set_or1269000886237332187st_nat
% 5.46/5.74 = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M3 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % atLeastAtMost_upt
% 5.46/5.74 thf(fact_10081_upt__conv__Cons,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I @ J )
% 5.46/5.74 => ( ( upt @ I @ J )
% 5.46/5.74 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_conv_Cons
% 5.46/5.74 thf(fact_10082_map__decr__upt,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( map_nat_nat
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.46/5.74 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.46/5.74 = ( upt @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % map_decr_upt
% 5.46/5.74 thf(fact_10083_upt__add__eq__append,axiom,
% 5.46/5.74 ! [I: nat,J: nat,K: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.74 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 5.46/5.74 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_add_eq_append
% 5.46/5.74 thf(fact_10084_upt__eq__Cons__conv,axiom,
% 5.46/5.74 ! [I: nat,J: nat,X2: nat,Xs2: list_nat] :
% 5.46/5.74 ( ( ( upt @ I @ J )
% 5.46/5.74 = ( cons_nat @ X2 @ Xs2 ) )
% 5.46/5.74 = ( ( ord_less_nat @ I @ J )
% 5.46/5.74 & ( I = X2 )
% 5.46/5.74 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 5.46/5.74 = Xs2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_eq_Cons_conv
% 5.46/5.74 thf(fact_10085_upt__rec,axiom,
% 5.46/5.74 ( upt
% 5.46/5.74 = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_rec
% 5.46/5.74 thf(fact_10086_upt__Suc__append,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.74 => ( ( upt @ I @ ( suc @ J ) )
% 5.46/5.74 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_Suc_append
% 5.46/5.74 thf(fact_10087_upt__Suc,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.74 => ( ( upt @ I @ ( suc @ J ) )
% 5.46/5.74 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.46/5.74 & ( ~ ( ord_less_eq_nat @ I @ J )
% 5.46/5.74 => ( ( upt @ I @ ( suc @ J ) )
% 5.46/5.74 = nil_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % upt_Suc
% 5.46/5.74 thf(fact_10088_sum__list__upt,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.74 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.46/5.74 = ( groups3542108847815614940at_nat
% 5.46/5.74 @ ^ [X: nat] : X
% 5.46/5.74 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % sum_list_upt
% 5.46/5.74 thf(fact_10089_card__length__sum__list__rec,axiom,
% 5.46/5.74 ! [M: nat,N4: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.46/5.74 => ( ( finite_card_list_nat
% 5.46/5.74 @ ( collect_list_nat
% 5.46/5.74 @ ^ [L: list_nat] :
% 5.46/5.74 ( ( ( size_size_list_nat @ L )
% 5.46/5.74 = M )
% 5.46/5.74 & ( ( groups4561878855575611511st_nat @ L )
% 5.46/5.74 = N4 ) ) ) )
% 5.46/5.74 = ( plus_plus_nat
% 5.46/5.74 @ ( finite_card_list_nat
% 5.46/5.74 @ ( collect_list_nat
% 5.46/5.74 @ ^ [L: list_nat] :
% 5.46/5.74 ( ( ( size_size_list_nat @ L )
% 5.46/5.74 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.46/5.74 & ( ( groups4561878855575611511st_nat @ L )
% 5.46/5.74 = N4 ) ) ) )
% 5.46/5.74 @ ( finite_card_list_nat
% 5.46/5.74 @ ( collect_list_nat
% 5.46/5.74 @ ^ [L: list_nat] :
% 5.46/5.74 ( ( ( size_size_list_nat @ L )
% 5.46/5.74 = M )
% 5.46/5.74 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L ) @ one_one_nat )
% 5.46/5.74 = N4 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % card_length_sum_list_rec
% 5.46/5.74 thf(fact_10090_card__length__sum__list,axiom,
% 5.46/5.74 ! [M: nat,N4: nat] :
% 5.46/5.74 ( ( finite_card_list_nat
% 5.46/5.74 @ ( collect_list_nat
% 5.46/5.74 @ ^ [L: list_nat] :
% 5.46/5.74 ( ( ( size_size_list_nat @ L )
% 5.46/5.74 = M )
% 5.46/5.74 & ( ( groups4561878855575611511st_nat @ L )
% 5.46/5.74 = N4 ) ) ) )
% 5.46/5.74 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % card_length_sum_list
% 5.46/5.74 thf(fact_10091_sorted__upt,axiom,
% 5.46/5.74 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % sorted_upt
% 5.46/5.74 thf(fact_10092_sorted__wrt__upt,axiom,
% 5.46/5.74 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % sorted_wrt_upt
% 5.46/5.74 thf(fact_10093_sorted__wrt__less__idx,axiom,
% 5.46/5.74 ! [Ns: list_nat,I: nat] :
% 5.46/5.74 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.46/5.74 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 5.46/5.74 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % sorted_wrt_less_idx
% 5.46/5.74 thf(fact_10094_sorted__wrt__upto,axiom,
% 5.46/5.74 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 5.46/5.74
% 5.46/5.74 % sorted_wrt_upto
% 5.46/5.74 thf(fact_10095_list__encode_Opelims,axiom,
% 5.46/5.74 ! [X2: list_nat,Y2: nat] :
% 5.46/5.74 ( ( ( nat_list_encode @ X2 )
% 5.46/5.74 = Y2 )
% 5.46/5.74 => ( ( accp_list_nat @ nat_list_encode_rel @ X2 )
% 5.46/5.74 => ( ( ( X2 = nil_nat )
% 5.46/5.74 => ( ( Y2 = zero_zero_nat )
% 5.46/5.74 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.46/5.74 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( cons_nat @ X3 @ Xs3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.46/5.74 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % list_encode.pelims
% 5.46/5.74 thf(fact_10096_quotient__of__def,axiom,
% 5.46/5.74 ( quotient_of
% 5.46/5.74 = ( ^ [X: rat] :
% 5.46/5.74 ( the_Pr4378521158711661632nt_int
% 5.46/5.74 @ ^ [Pair: product_prod_int_int] :
% 5.46/5.74 ( ( X
% 5.46/5.74 = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 5.46/5.74 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 5.46/5.74 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % quotient_of_def
% 5.46/5.74 thf(fact_10097_coprime__abs__right__iff,axiom,
% 5.46/5.74 ! [K: int,L2: int] :
% 5.46/5.74 ( ( algebr932160517623751201me_int @ K @ ( abs_abs_int @ L2 ) )
% 5.46/5.74 = ( algebr932160517623751201me_int @ K @ L2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_abs_right_iff
% 5.46/5.74 thf(fact_10098_coprime__abs__left__iff,axiom,
% 5.46/5.74 ! [K: int,L2: int] :
% 5.46/5.74 ( ( algebr932160517623751201me_int @ ( abs_abs_int @ K ) @ L2 )
% 5.46/5.74 = ( algebr932160517623751201me_int @ K @ L2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_abs_left_iff
% 5.46/5.74 thf(fact_10099_normalize__stable,axiom,
% 5.46/5.74 ! [Q2: int,P2: int] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ Q2 )
% 5.46/5.74 => ( ( algebr932160517623751201me_int @ P2 @ Q2 )
% 5.46/5.74 => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.46/5.74 = ( product_Pair_int_int @ P2 @ Q2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % normalize_stable
% 5.46/5.74 thf(fact_10100_coprime__common__divisor__int,axiom,
% 5.46/5.74 ! [A: int,B: int,X2: int] :
% 5.46/5.74 ( ( algebr932160517623751201me_int @ A @ B )
% 5.46/5.74 => ( ( dvd_dvd_int @ X2 @ A )
% 5.46/5.74 => ( ( dvd_dvd_int @ X2 @ B )
% 5.46/5.74 => ( ( abs_abs_int @ X2 )
% 5.46/5.74 = one_one_int ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_common_divisor_int
% 5.46/5.74 thf(fact_10101_Rat__cases,axiom,
% 5.46/5.74 ! [Q2: rat] :
% 5.46/5.74 ~ ! [A5: int,B5: int] :
% 5.46/5.74 ( ( Q2
% 5.46/5.74 = ( fract @ A5 @ B5 ) )
% 5.46/5.74 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.46/5.74 => ~ ( algebr932160517623751201me_int @ A5 @ B5 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rat_cases
% 5.46/5.74 thf(fact_10102_Rat__induct,axiom,
% 5.46/5.74 ! [P: rat > $o,Q2: rat] :
% 5.46/5.74 ( ! [A5: int,B5: int] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.46/5.74 => ( ( algebr932160517623751201me_int @ A5 @ B5 )
% 5.46/5.74 => ( P @ ( fract @ A5 @ B5 ) ) ) )
% 5.46/5.74 => ( P @ Q2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rat_induct
% 5.46/5.74 thf(fact_10103_Rat__cases__nonzero,axiom,
% 5.46/5.74 ! [Q2: rat] :
% 5.46/5.74 ( ! [A5: int,B5: int] :
% 5.46/5.74 ( ( Q2
% 5.46/5.74 = ( fract @ A5 @ B5 ) )
% 5.46/5.74 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.46/5.74 => ( ( A5 != zero_zero_int )
% 5.46/5.74 => ~ ( algebr932160517623751201me_int @ A5 @ B5 ) ) ) )
% 5.46/5.74 => ( Q2 = zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rat_cases_nonzero
% 5.46/5.74 thf(fact_10104_quotient__of__unique,axiom,
% 5.46/5.74 ! [R: rat] :
% 5.46/5.74 ? [X3: product_prod_int_int] :
% 5.46/5.74 ( ( R
% 5.46/5.74 = ( fract @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 5.46/5.74 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X3 ) )
% 5.46/5.74 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) )
% 5.46/5.74 & ! [Y4: product_prod_int_int] :
% 5.46/5.74 ( ( ( R
% 5.46/5.74 = ( fract @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 5.46/5.74 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y4 ) )
% 5.46/5.74 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 5.46/5.74 => ( Y4 = X3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % quotient_of_unique
% 5.46/5.74 thf(fact_10105_coprime__int__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( algebr934650988132801477me_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_int_iff
% 5.46/5.74 thf(fact_10106_coprime__nat__abs__right__iff,axiom,
% 5.46/5.74 ! [N: nat,K: int] :
% 5.46/5.74 ( ( algebr934650988132801477me_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.46/5.74 = ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_nat_abs_right_iff
% 5.46/5.74 thf(fact_10107_coprime__nat__abs__left__iff,axiom,
% 5.46/5.74 ! [K: int,N: nat] :
% 5.46/5.74 ( ( algebr934650988132801477me_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.46/5.74 = ( algebr932160517623751201me_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_nat_abs_left_iff
% 5.46/5.74 thf(fact_10108_coprime__crossproduct__nat,axiom,
% 5.46/5.74 ! [A: nat,D2: nat,B: nat,C: nat] :
% 5.46/5.74 ( ( algebr934650988132801477me_nat @ A @ D2 )
% 5.46/5.74 => ( ( algebr934650988132801477me_nat @ B @ C )
% 5.46/5.74 => ( ( ( times_times_nat @ A @ C )
% 5.46/5.74 = ( times_times_nat @ B @ D2 ) )
% 5.46/5.74 = ( ( A = B )
% 5.46/5.74 & ( C = D2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_crossproduct_nat
% 5.46/5.74 thf(fact_10109_coprime__Suc__0__left,axiom,
% 5.46/5.74 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_Suc_0_left
% 5.46/5.74 thf(fact_10110_coprime__Suc__0__right,axiom,
% 5.46/5.74 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_Suc_0_right
% 5.46/5.74 thf(fact_10111_coprime__Suc__right__nat,axiom,
% 5.46/5.74 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_Suc_right_nat
% 5.46/5.74 thf(fact_10112_coprime__Suc__left__nat,axiom,
% 5.46/5.74 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_Suc_left_nat
% 5.46/5.74 thf(fact_10113_coprime__common__divisor__nat,axiom,
% 5.46/5.74 ! [A: nat,B: nat,X2: nat] :
% 5.46/5.74 ( ( algebr934650988132801477me_nat @ A @ B )
% 5.46/5.74 => ( ( dvd_dvd_nat @ X2 @ A )
% 5.46/5.74 => ( ( dvd_dvd_nat @ X2 @ B )
% 5.46/5.74 => ( X2 = one_one_nat ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_common_divisor_nat
% 5.46/5.74 thf(fact_10114_coprime__diff__one__left__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.74 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_diff_one_left_nat
% 5.46/5.74 thf(fact_10115_coprime__diff__one__right__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.74 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % coprime_diff_one_right_nat
% 5.46/5.74 thf(fact_10116_Rats__abs__nat__div__natE,axiom,
% 5.46/5.74 ! [X2: real] :
% 5.46/5.74 ( ( member_real @ X2 @ field_5140801741446780682s_real )
% 5.46/5.74 => ~ ! [M4: nat,N3: nat] :
% 5.46/5.74 ( ( N3 != zero_zero_nat )
% 5.46/5.74 => ( ( ( abs_abs_real @ X2 )
% 5.46/5.74 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 5.46/5.74 => ~ ( algebr934650988132801477me_nat @ M4 @ N3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Rats_abs_nat_div_natE
% 5.46/5.74 thf(fact_10117_vanishes__mult__bounded,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ? [A8: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ A8 )
% 5.46/5.74 & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N3 ) ) @ A8 ) )
% 5.46/5.74 => ( ( vanishes @ Y6 )
% 5.46/5.74 => ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : ( times_times_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % vanishes_mult_bounded
% 5.46/5.74 thf(fact_10118_vanishes__const,axiom,
% 5.46/5.74 ! [C: rat] :
% 5.46/5.74 ( ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : C )
% 5.46/5.74 = ( C = zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % vanishes_const
% 5.46/5.74 thf(fact_10119_vanishes__diff,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( vanishes @ X7 )
% 5.46/5.74 => ( ( vanishes @ Y6 )
% 5.46/5.74 => ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % vanishes_diff
% 5.46/5.74 thf(fact_10120_vanishes__minus,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( vanishes @ X7 )
% 5.46/5.74 => ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X7 @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % vanishes_minus
% 5.46/5.74 thf(fact_10121_vanishes__add,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( vanishes @ X7 )
% 5.46/5.74 => ( ( vanishes @ Y6 )
% 5.46/5.74 => ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : ( plus_plus_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % vanishes_add
% 5.46/5.74 thf(fact_10122_vanishesD,axiom,
% 5.46/5.74 ! [X7: nat > rat,R: rat] :
% 5.46/5.74 ( ( vanishes @ X7 )
% 5.46/5.74 => ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.46/5.74 => ? [K3: nat] :
% 5.46/5.74 ! [N7: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.46/5.74 => ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N7 ) ) @ R ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % vanishesD
% 5.46/5.74 thf(fact_10123_vanishesI,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ! [R3: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.46/5.74 => ? [K4: nat] :
% 5.46/5.74 ! [N3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.46/5.74 => ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N3 ) ) @ R3 ) ) )
% 5.46/5.74 => ( vanishes @ X7 ) ) ).
% 5.46/5.74
% 5.46/5.74 % vanishesI
% 5.46/5.74 thf(fact_10124_vanishes__def,axiom,
% 5.46/5.74 ( vanishes
% 5.46/5.74 = ( ^ [X5: nat > rat] :
% 5.46/5.74 ! [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 => ? [K2: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_rat @ ( abs_abs_rat @ ( X5 @ N2 ) ) @ R5 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % vanishes_def
% 5.46/5.74 thf(fact_10125_and__not__num_Opelims,axiom,
% 5.46/5.74 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.46/5.74 ( ( ( bit_and_not_num @ X2 @ Xa2 )
% 5.46/5.74 = Y2 )
% 5.46/5.74 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2 = none_num )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ one ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Y2 = none_num )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.74 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.46/5.74 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ~ ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % and_not_num.pelims
% 5.46/5.74 thf(fact_10126_rcis__inverse,axiom,
% 5.46/5.74 ! [R: real,A: real] :
% 5.46/5.74 ( ( invers8013647133539491842omplex @ ( rcis @ R @ A ) )
% 5.46/5.74 = ( rcis @ ( divide_divide_real @ one_one_real @ R ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % rcis_inverse
% 5.46/5.74 thf(fact_10127_Re__rcis,axiom,
% 5.46/5.74 ! [R: real,A: real] :
% 5.46/5.74 ( ( re @ ( rcis @ R @ A ) )
% 5.46/5.74 = ( times_times_real @ R @ ( cos_real @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Re_rcis
% 5.46/5.74 thf(fact_10128_Im__rcis,axiom,
% 5.46/5.74 ! [R: real,A: real] :
% 5.46/5.74 ( ( im @ ( rcis @ R @ A ) )
% 5.46/5.74 = ( times_times_real @ R @ ( sin_real @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Im_rcis
% 5.46/5.74 thf(fact_10129_cis__rcis__eq,axiom,
% 5.46/5.74 ( cis
% 5.46/5.74 = ( rcis @ one_one_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % cis_rcis_eq
% 5.46/5.74 thf(fact_10130_rcis__mult,axiom,
% 5.46/5.74 ! [R1: real,A: real,R22: real,B: real] :
% 5.46/5.74 ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 5.46/5.74 = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % rcis_mult
% 5.46/5.74 thf(fact_10131_rcis__divide,axiom,
% 5.46/5.74 ! [R1: real,A: real,R22: real,B: real] :
% 5.46/5.74 ( ( divide1717551699836669952omplex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 5.46/5.74 = ( rcis @ ( divide_divide_real @ R1 @ R22 ) @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % rcis_divide
% 5.46/5.74 thf(fact_10132_DeMoivre2,axiom,
% 5.46/5.74 ! [R: real,A: real,N: nat] :
% 5.46/5.74 ( ( power_power_complex @ ( rcis @ R @ A ) @ N )
% 5.46/5.74 = ( rcis @ ( power_power_real @ R @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % DeMoivre2
% 5.46/5.74 thf(fact_10133_and__num_Opelims,axiom,
% 5.46/5.74 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.46/5.74 ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa2 )
% 5.46/5.74 = Y2 )
% 5.46/5.74 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ one ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Y2 = none_num )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ one ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2 = none_num )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ one ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ~ ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.74 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.46/5.74 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % and_num.pelims
% 5.46/5.74 thf(fact_10134_xor__num_Opelims,axiom,
% 5.46/5.74 ! [X2: num,Xa2: num,Y2: option_num] :
% 5.46/5.74 ( ( ( bit_un2480387367778600638or_num @ X2 @ Xa2 )
% 5.46/5.74 = Y2 )
% 5.46/5.74 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2 = none_num )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ ( bit1 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ ( bit0 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ ( bit1 @ M4 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.46/5.74 => ( ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.46/5.74 => ~ ! [M4: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ! [N3: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % xor_num.pelims
% 5.46/5.74 thf(fact_10135_or__not__num__neg_Opelims,axiom,
% 5.46/5.74 ! [X2: num,Xa2: num,Y2: num] :
% 5.46/5.74 ( ( ( bit_or_not_num_neg @ X2 @ Xa2 )
% 5.46/5.74 = Y2 )
% 5.46/5.74 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2 = one )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ! [M4: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 5.46/5.74 => ( ( ( X2 = one )
% 5.46/5.74 => ! [M4: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 5.46/5.74 => ( ! [N3: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( bit0 @ one ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.46/5.74 => ( ! [N3: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ! [M4: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.46/5.74 => ( ! [N3: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit0 @ N3 ) )
% 5.46/5.74 => ! [M4: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 5.46/5.74 => ( ! [N3: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ( ( Xa2 = one )
% 5.46/5.74 => ( ( Y2 = one )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.46/5.74 => ( ! [N3: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ! [M4: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit0 @ M4 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.46/5.74 => ~ ! [N3: num] :
% 5.46/5.74 ( ( X2
% 5.46/5.74 = ( bit1 @ N3 ) )
% 5.46/5.74 => ! [M4: num] :
% 5.46/5.74 ( ( Xa2
% 5.46/5.74 = ( bit1 @ M4 ) )
% 5.46/5.74 => ( ( Y2
% 5.46/5.74 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.46/5.74 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % or_not_num_neg.pelims
% 5.46/5.74 thf(fact_10136_and__num__rel__dict,axiom,
% 5.46/5.74 bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 5.46/5.74
% 5.46/5.74 % and_num_rel_dict
% 5.46/5.74 thf(fact_10137_xor__num__rel__dict,axiom,
% 5.46/5.74 bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 5.46/5.74
% 5.46/5.74 % xor_num_rel_dict
% 5.46/5.74 thf(fact_10138_Field__natLeq__on,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( field_nat
% 5.46/5.74 @ ( collec3392354462482085612at_nat
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [X: nat,Y: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ N )
% 5.46/5.74 & ( ord_less_nat @ Y @ N )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Y ) ) ) ) )
% 5.46/5.74 = ( collect_nat
% 5.46/5.74 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Field_natLeq_on
% 5.46/5.74 thf(fact_10139_natLess__def,axiom,
% 5.46/5.74 ( bNF_Ca8459412986667044542atLess
% 5.46/5.74 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % natLess_def
% 5.46/5.74 thf(fact_10140_wf__less,axiom,
% 5.46/5.74 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % wf_less
% 5.46/5.74 thf(fact_10141_product__atMost__eq__Un,axiom,
% 5.46/5.74 ! [A2: set_nat,M: nat] :
% 5.46/5.74 ( ( produc457027306803732586at_nat @ A2
% 5.46/5.74 @ ^ [Uu3: nat] : ( set_ord_atMost_nat @ M ) )
% 5.46/5.74 = ( sup_su6327502436637775413at_nat
% 5.46/5.74 @ ( produc457027306803732586at_nat @ A2
% 5.46/5.74 @ ^ [I4: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ I4 ) ) )
% 5.46/5.74 @ ( produc457027306803732586at_nat @ A2
% 5.46/5.74 @ ^ [I4: nat] : ( set_or6659071591806873216st_nat @ ( minus_minus_nat @ M @ I4 ) @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % product_atMost_eq_Un
% 5.46/5.74 thf(fact_10142_pairs__le__eq__Sigma,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( collec3392354462482085612at_nat
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ M ) ) )
% 5.46/5.74 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.46/5.74 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % pairs_le_eq_Sigma
% 5.46/5.74 thf(fact_10143_finite__vimage__Suc__iff,axiom,
% 5.46/5.74 ! [F5: set_nat] :
% 5.46/5.74 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F5 ) )
% 5.46/5.74 = ( finite_finite_nat @ F5 ) ) ).
% 5.46/5.74
% 5.46/5.74 % finite_vimage_Suc_iff
% 5.46/5.74 thf(fact_10144_vimage__Suc__insert__Suc,axiom,
% 5.46/5.74 ! [N: nat,A2: set_nat] :
% 5.46/5.74 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A2 ) )
% 5.46/5.74 = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % vimage_Suc_insert_Suc
% 5.46/5.74 thf(fact_10145_vimage__Suc__insert__0,axiom,
% 5.46/5.74 ! [A2: set_nat] :
% 5.46/5.74 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 5.46/5.74 = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % vimage_Suc_insert_0
% 5.46/5.74 thf(fact_10146_set__decode__div__2,axiom,
% 5.46/5.74 ! [X2: nat] :
% 5.46/5.74 ( ( nat_set_decode @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % set_decode_div_2
% 5.46/5.74 thf(fact_10147_set__encode__vimage__Suc,axiom,
% 5.46/5.74 ! [A2: set_nat] :
% 5.46/5.74 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A2 ) )
% 5.46/5.74 = ( divide_divide_nat @ ( nat_set_encode @ A2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % set_encode_vimage_Suc
% 5.46/5.74 thf(fact_10148_Restr__natLeq,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.46/5.74 @ ( produc457027306803732586at_nat
% 5.46/5.74 @ ( collect_nat
% 5.46/5.74 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) )
% 5.46/5.74 @ ^ [Uu3: nat] :
% 5.46/5.74 ( collect_nat
% 5.46/5.74 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) )
% 5.46/5.74 = ( collec3392354462482085612at_nat
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [X: nat,Y: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ N )
% 5.46/5.74 & ( ord_less_nat @ Y @ N )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Restr_natLeq
% 5.46/5.74 thf(fact_10149_cauchyD,axiom,
% 5.46/5.74 ! [X7: nat > rat,R: rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.46/5.74 => ? [K3: nat] :
% 5.46/5.74 ! [M2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K3 @ M2 )
% 5.46/5.74 => ! [N7: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.46/5.74 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X7 @ M2 ) @ ( X7 @ N7 ) ) ) @ R ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchyD
% 5.46/5.74 thf(fact_10150_natLeq__def,axiom,
% 5.46/5.74 ( bNF_Ca8665028551170535155natLeq
% 5.46/5.74 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % natLeq_def
% 5.46/5.74 thf(fact_10151_natLeq__natLess__Id,axiom,
% 5.46/5.74 ( bNF_Ca8459412986667044542atLess
% 5.46/5.74 = ( minus_1356011639430497352at_nat @ bNF_Ca8665028551170535155natLeq @ id_nat2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % natLeq_natLess_Id
% 5.46/5.74 thf(fact_10152_cauchy__inverse,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ~ ( vanishes @ X7 )
% 5.46/5.74 => ( cauchy
% 5.46/5.74 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X7 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_inverse
% 5.46/5.74 thf(fact_10153_cauchy__const,axiom,
% 5.46/5.74 ! [X2: rat] :
% 5.46/5.74 ( cauchy
% 5.46/5.74 @ ^ [N2: nat] : X2 ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_const
% 5.46/5.74 thf(fact_10154_cauchy__add,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( cauchy
% 5.46/5.74 @ ^ [N2: nat] : ( plus_plus_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_add
% 5.46/5.74 thf(fact_10155_cauchy__minus,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( cauchy
% 5.46/5.74 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X7 @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_minus
% 5.46/5.74 thf(fact_10156_cauchy__mult,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( cauchy
% 5.46/5.74 @ ^ [N2: nat] : ( times_times_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_mult
% 5.46/5.74 thf(fact_10157_cauchy__diff,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( cauchy
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_diff
% 5.46/5.74 thf(fact_10158_cauchy__imp__bounded,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ? [B5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ B5 )
% 5.46/5.74 & ! [N7: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N7 ) ) @ B5 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_imp_bounded
% 5.46/5.74 thf(fact_10159_vanishes__diff__inverse,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ~ ( vanishes @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( ~ ( vanishes @ Y6 )
% 5.46/5.74 => ( ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) )
% 5.46/5.74 => ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_rat @ ( inverse_inverse_rat @ ( X7 @ N2 ) ) @ ( inverse_inverse_rat @ ( Y6 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % vanishes_diff_inverse
% 5.46/5.74 thf(fact_10160_cauchy__not__vanishes__cases,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ~ ( vanishes @ X7 )
% 5.46/5.74 => ? [B5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ B5 )
% 5.46/5.74 & ? [K3: nat] :
% 5.46/5.74 ( ! [N7: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.46/5.74 => ( ord_less_rat @ B5 @ ( uminus_uminus_rat @ ( X7 @ N7 ) ) ) )
% 5.46/5.74 | ! [N7: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.46/5.74 => ( ord_less_rat @ B5 @ ( X7 @ N7 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_not_vanishes_cases
% 5.46/5.74 thf(fact_10161_cauchy__not__vanishes,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ~ ( vanishes @ X7 )
% 5.46/5.74 => ? [B5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ B5 )
% 5.46/5.74 & ? [K3: nat] :
% 5.46/5.74 ! [N7: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.46/5.74 => ( ord_less_rat @ B5 @ ( abs_abs_rat @ ( X7 @ N7 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_not_vanishes
% 5.46/5.74 thf(fact_10162_cauchy__def,axiom,
% 5.46/5.74 ( cauchy
% 5.46/5.74 = ( ^ [X5: nat > rat] :
% 5.46/5.74 ! [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 => ? [K2: nat] :
% 5.46/5.74 ! [M3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ M3 )
% 5.46/5.74 => ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X5 @ M3 ) @ ( X5 @ N2 ) ) ) @ R5 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchy_def
% 5.46/5.74 thf(fact_10163_cauchyI,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ! [R3: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.46/5.74 => ? [K4: nat] :
% 5.46/5.74 ! [M4: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K4 @ M4 )
% 5.46/5.74 => ! [N3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.46/5.74 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) ) @ R3 ) ) ) )
% 5.46/5.74 => ( cauchy @ X7 ) ) ).
% 5.46/5.74
% 5.46/5.74 % cauchyI
% 5.46/5.74 thf(fact_10164_Restr__natLeq2,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.46/5.74 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.46/5.74 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 5.46/5.74 = ( collec3392354462482085612at_nat
% 5.46/5.74 @ ( produc6081775807080527818_nat_o
% 5.46/5.74 @ ^ [X: nat,Y: nat] :
% 5.46/5.74 ( ( ord_less_nat @ X @ N )
% 5.46/5.74 & ( ord_less_nat @ Y @ N )
% 5.46/5.74 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Restr_natLeq2
% 5.46/5.74 thf(fact_10165_le__Real,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( real2 @ X7 ) @ ( real2 @ Y6 ) )
% 5.46/5.74 = ( ! [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 => ? [K2: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_eq_rat @ ( X7 @ N2 ) @ ( plus_plus_rat @ ( Y6 @ N2 ) @ R5 ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % le_Real
% 5.46/5.74 thf(fact_10166_Real__induct,axiom,
% 5.46/5.74 ! [P: real > $o,X2: real] :
% 5.46/5.74 ( ! [X10: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X10 )
% 5.46/5.74 => ( P @ ( real2 @ X10 ) ) )
% 5.46/5.74 => ( P @ X2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % Real_induct
% 5.46/5.74 thf(fact_10167_natLeq__underS__less,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.46/5.74 = ( collect_nat
% 5.46/5.74 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % natLeq_underS_less
% 5.46/5.74 thf(fact_10168_one__real__def,axiom,
% 5.46/5.74 ( one_one_real
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : one_one_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % one_real_def
% 5.46/5.74 thf(fact_10169_zero__real__def,axiom,
% 5.46/5.74 ( zero_zero_real
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_real_def
% 5.46/5.74 thf(fact_10170_of__rat__Real,axiom,
% 5.46/5.74 ( field_7254667332652039916t_real
% 5.46/5.74 = ( ^ [X: rat] :
% 5.46/5.74 ( real2
% 5.46/5.74 @ ^ [N2: nat] : X ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_rat_Real
% 5.46/5.74 thf(fact_10171_of__nat__Real,axiom,
% 5.46/5.74 ( semiri5074537144036343181t_real
% 5.46/5.74 = ( ^ [X: nat] :
% 5.46/5.74 ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( semiri681578069525770553at_rat @ X ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_Real
% 5.46/5.74 thf(fact_10172_of__int__Real,axiom,
% 5.46/5.74 ( ring_1_of_int_real
% 5.46/5.74 = ( ^ [X: int] :
% 5.46/5.74 ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( ring_1_of_int_rat @ X ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_Real
% 5.46/5.74 thf(fact_10173_less__RealD,axiom,
% 5.46/5.74 ! [Y6: nat > rat,X2: real] :
% 5.46/5.74 ( ( cauchy @ Y6 )
% 5.46/5.74 => ( ( ord_less_real @ X2 @ ( real2 @ Y6 ) )
% 5.46/5.74 => ? [N3: nat] : ( ord_less_real @ X2 @ ( field_7254667332652039916t_real @ ( Y6 @ N3 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % less_RealD
% 5.46/5.74 thf(fact_10174_le__RealI,axiom,
% 5.46/5.74 ! [Y6: nat > rat,X2: real] :
% 5.46/5.74 ( ( cauchy @ Y6 )
% 5.46/5.74 => ( ! [N3: nat] : ( ord_less_eq_real @ X2 @ ( field_7254667332652039916t_real @ ( Y6 @ N3 ) ) )
% 5.46/5.74 => ( ord_less_eq_real @ X2 @ ( real2 @ Y6 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % le_RealI
% 5.46/5.74 thf(fact_10175_Real__leI,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y2: real] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ! [N3: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X7 @ N3 ) ) @ Y2 )
% 5.46/5.74 => ( ord_less_eq_real @ ( real2 @ X7 ) @ Y2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Real_leI
% 5.46/5.74 thf(fact_10176_minus__Real,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( uminus_uminus_real @ ( real2 @ X7 ) )
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X7 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % minus_Real
% 5.46/5.74 thf(fact_10177_add__Real,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( ( plus_plus_real @ ( real2 @ X7 ) @ ( real2 @ Y6 ) )
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( plus_plus_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % add_Real
% 5.46/5.74 thf(fact_10178_mult__Real,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( ( times_times_real @ ( real2 @ X7 ) @ ( real2 @ Y6 ) )
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( times_times_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mult_Real
% 5.46/5.74 thf(fact_10179_diff__Real,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( ( minus_minus_real @ ( real2 @ X7 ) @ ( real2 @ Y6 ) )
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % diff_Real
% 5.46/5.74 thf(fact_10180_eq__Real,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( ( ( real2 @ X7 )
% 5.46/5.74 = ( real2 @ Y6 ) )
% 5.46/5.74 = ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % eq_Real
% 5.46/5.74 thf(fact_10181_inverse__Real,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( ( vanishes @ X7 )
% 5.46/5.74 => ( ( inverse_inverse_real @ ( real2 @ X7 ) )
% 5.46/5.74 = zero_zero_real ) )
% 5.46/5.74 & ( ~ ( vanishes @ X7 )
% 5.46/5.74 => ( ( inverse_inverse_real @ ( real2 @ X7 ) )
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X7 @ N2 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % inverse_Real
% 5.46/5.74 thf(fact_10182_not__positive__Real,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( ~ ( positive2 @ ( real2 @ X7 ) ) )
% 5.46/5.74 = ( ! [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 => ? [K2: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_eq_rat @ ( X7 @ N2 ) @ R5 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % not_positive_Real
% 5.46/5.74 thf(fact_10183_positive__Real,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( positive2 @ ( real2 @ X7 ) )
% 5.46/5.74 = ( ? [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 & ? [K2: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_rat @ R5 @ ( X7 @ N2 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % positive_Real
% 5.46/5.74 thf(fact_10184_less__real__def,axiom,
% 5.46/5.74 ( ord_less_real
% 5.46/5.74 = ( ^ [X: real,Y: real] : ( positive2 @ ( minus_minus_real @ Y @ X ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % less_real_def
% 5.46/5.74 thf(fact_10185_Real_Opositive__minus,axiom,
% 5.46/5.74 ! [X2: real] :
% 5.46/5.74 ( ~ ( positive2 @ X2 )
% 5.46/5.74 => ( ( X2 != zero_zero_real )
% 5.46/5.74 => ( positive2 @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Real.positive_minus
% 5.46/5.74 thf(fact_10186_Real_Opositive__zero,axiom,
% 5.46/5.74 ~ ( positive2 @ zero_zero_real ) ).
% 5.46/5.74
% 5.46/5.74 % Real.positive_zero
% 5.46/5.74 thf(fact_10187_Real_Opositive__add,axiom,
% 5.46/5.74 ! [X2: real,Y2: real] :
% 5.46/5.74 ( ( positive2 @ X2 )
% 5.46/5.74 => ( ( positive2 @ Y2 )
% 5.46/5.74 => ( positive2 @ ( plus_plus_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Real.positive_add
% 5.46/5.74 thf(fact_10188_Real_Opositive__mult,axiom,
% 5.46/5.74 ! [X2: real,Y2: real] :
% 5.46/5.74 ( ( positive2 @ X2 )
% 5.46/5.74 => ( ( positive2 @ Y2 )
% 5.46/5.74 => ( positive2 @ ( times_times_real @ X2 @ Y2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Real.positive_mult
% 5.46/5.74 thf(fact_10189_Real_Opositive_Orep__eq,axiom,
% 5.46/5.74 ( positive2
% 5.46/5.74 = ( ^ [X: real] :
% 5.46/5.74 ? [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 & ? [K2: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_rat @ R5 @ ( rep_real @ X @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Real.positive.rep_eq
% 5.46/5.74 thf(fact_10190_Real_Opositive__def,axiom,
% 5.46/5.74 ( positive2
% 5.46/5.74 = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 5.46/5.74 @ ^ [X5: nat > rat] :
% 5.46/5.74 ? [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 & ? [K2: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_rat @ R5 @ ( X5 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Real.positive_def
% 5.46/5.74 thf(fact_10191_inverse__real__def,axiom,
% 5.46/5.74 ( inverse_inverse_real
% 5.46/5.74 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.46/5.74 @ ^ [X5: nat > rat] :
% 5.46/5.74 ( if_nat_rat @ ( vanishes @ X5 )
% 5.46/5.74 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.74 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X5 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % inverse_real_def
% 5.46/5.74 thf(fact_10192_uminus__real__def,axiom,
% 5.46/5.74 ( uminus_uminus_real
% 5.46/5.74 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.46/5.74 @ ^ [X5: nat > rat,N2: nat] : ( uminus_uminus_rat @ ( X5 @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % uminus_real_def
% 5.46/5.74 thf(fact_10193_times__real__def,axiom,
% 5.46/5.74 ( times_times_real
% 5.46/5.74 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.46/5.74 @ ^ [X5: nat > rat,Y7: nat > rat,N2: nat] : ( times_times_rat @ ( X5 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % times_real_def
% 5.46/5.74 thf(fact_10194_plus__real__def,axiom,
% 5.46/5.74 ( plus_plus_real
% 5.46/5.74 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.46/5.74 @ ^ [X5: nat > rat,Y7: nat > rat,N2: nat] : ( plus_plus_rat @ ( X5 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % plus_real_def
% 5.46/5.74 thf(fact_10195_inverse__real_Oabs__eq,axiom,
% 5.46/5.74 ! [X2: nat > rat] :
% 5.46/5.74 ( ( realrel @ X2 @ X2 )
% 5.46/5.74 => ( ( inverse_inverse_real @ ( real2 @ X2 ) )
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ( if_nat_rat @ ( vanishes @ X2 )
% 5.46/5.74 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.74 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X2 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % inverse_real.abs_eq
% 5.46/5.74 thf(fact_10196_real_Oabs__induct,axiom,
% 5.46/5.74 ! [P: real > $o,X2: real] :
% 5.46/5.74 ( ! [Y3: nat > rat] :
% 5.46/5.74 ( ( realrel @ Y3 @ Y3 )
% 5.46/5.74 => ( P @ ( real2 @ Y3 ) ) )
% 5.46/5.74 => ( P @ X2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % real.abs_induct
% 5.46/5.74 thf(fact_10197_one__real_Orsp,axiom,
% 5.46/5.74 ( realrel
% 5.46/5.74 @ ^ [N2: nat] : one_one_rat
% 5.46/5.74 @ ^ [N2: nat] : one_one_rat ) ).
% 5.46/5.74
% 5.46/5.74 % one_real.rsp
% 5.46/5.74 thf(fact_10198_zero__real_Orsp,axiom,
% 5.46/5.74 ( realrel
% 5.46/5.74 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.74 @ ^ [N2: nat] : zero_zero_rat ) ).
% 5.46/5.74
% 5.46/5.74 % zero_real.rsp
% 5.46/5.74 thf(fact_10199_le__enumerate,axiom,
% 5.46/5.74 ! [S2: set_nat,N: nat] :
% 5.46/5.74 ( ~ ( finite_finite_nat @ S2 )
% 5.46/5.74 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % le_enumerate
% 5.46/5.74 thf(fact_10200_realrel__refl,axiom,
% 5.46/5.74 ! [X7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( realrel @ X7 @ X7 ) ) ).
% 5.46/5.74
% 5.46/5.74 % realrel_refl
% 5.46/5.74 thf(fact_10201_uminus__real_Oabs__eq,axiom,
% 5.46/5.74 ! [X2: nat > rat] :
% 5.46/5.74 ( ( realrel @ X2 @ X2 )
% 5.46/5.74 => ( ( uminus_uminus_real @ ( real2 @ X2 ) )
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X2 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % uminus_real.abs_eq
% 5.46/5.74 thf(fact_10202_plus__real_Oabs__eq,axiom,
% 5.46/5.74 ! [Xa2: nat > rat,X2: nat > rat] :
% 5.46/5.74 ( ( realrel @ Xa2 @ Xa2 )
% 5.46/5.74 => ( ( realrel @ X2 @ X2 )
% 5.46/5.74 => ( ( plus_plus_real @ ( real2 @ Xa2 ) @ ( real2 @ X2 ) )
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( plus_plus_rat @ ( Xa2 @ N2 ) @ ( X2 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % plus_real.abs_eq
% 5.46/5.74 thf(fact_10203_times__real_Oabs__eq,axiom,
% 5.46/5.74 ! [Xa2: nat > rat,X2: nat > rat] :
% 5.46/5.74 ( ( realrel @ Xa2 @ Xa2 )
% 5.46/5.74 => ( ( realrel @ X2 @ X2 )
% 5.46/5.74 => ( ( times_times_real @ ( real2 @ Xa2 ) @ ( real2 @ X2 ) )
% 5.46/5.74 = ( real2
% 5.46/5.74 @ ^ [N2: nat] : ( times_times_rat @ ( Xa2 @ N2 ) @ ( X2 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % times_real.abs_eq
% 5.46/5.74 thf(fact_10204_realrelI,axiom,
% 5.46/5.74 ! [X7: nat > rat,Y6: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X7 )
% 5.46/5.74 => ( ( cauchy @ Y6 )
% 5.46/5.74 => ( ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_rat @ ( X7 @ N2 ) @ ( Y6 @ N2 ) ) )
% 5.46/5.74 => ( realrel @ X7 @ Y6 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % realrelI
% 5.46/5.74 thf(fact_10205_realrel__def,axiom,
% 5.46/5.74 ( realrel
% 5.46/5.74 = ( ^ [X5: nat > rat,Y7: nat > rat] :
% 5.46/5.74 ( ( cauchy @ X5 )
% 5.46/5.74 & ( cauchy @ Y7 )
% 5.46/5.74 & ( vanishes
% 5.46/5.74 @ ^ [N2: nat] : ( minus_minus_rat @ ( X5 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % realrel_def
% 5.46/5.74 thf(fact_10206_finite__le__enumerate,axiom,
% 5.46/5.74 ! [S2: set_nat,N: nat] :
% 5.46/5.74 ( ( finite_finite_nat @ S2 )
% 5.46/5.74 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 5.46/5.74 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % finite_le_enumerate
% 5.46/5.74 thf(fact_10207_Real_Opositive_Oabs__eq,axiom,
% 5.46/5.74 ! [X2: nat > rat] :
% 5.46/5.74 ( ( realrel @ X2 @ X2 )
% 5.46/5.74 => ( ( positive2 @ ( real2 @ X2 ) )
% 5.46/5.74 = ( ? [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 & ? [K2: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_rat @ R5 @ ( X2 @ N2 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Real.positive.abs_eq
% 5.46/5.74 thf(fact_10208_Real_Opositive_Orsp,axiom,
% 5.46/5.74 ( bNF_re728719798268516973at_o_o @ realrel
% 5.46/5.74 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 )
% 5.46/5.74 @ ^ [X5: nat > rat] :
% 5.46/5.74 ? [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 & ? [K2: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_rat @ R5 @ ( X5 @ N2 ) ) ) )
% 5.46/5.74 @ ^ [X5: nat > rat] :
% 5.46/5.74 ? [R5: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.74 & ? [K2: nat] :
% 5.46/5.74 ! [N2: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.46/5.74 => ( ord_less_rat @ R5 @ ( X5 @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Real.positive.rsp
% 5.46/5.74 thf(fact_10209_Least__eq__0,axiom,
% 5.46/5.74 ! [P: nat > $o] :
% 5.46/5.74 ( ( P @ zero_zero_nat )
% 5.46/5.74 => ( ( ord_Least_nat @ P )
% 5.46/5.74 = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % Least_eq_0
% 5.46/5.74 thf(fact_10210_Least__Suc2,axiom,
% 5.46/5.74 ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 5.46/5.74 ( ( P @ N )
% 5.46/5.74 => ( ( Q @ M )
% 5.46/5.74 => ( ~ ( P @ zero_zero_nat )
% 5.46/5.74 => ( ! [K3: nat] :
% 5.46/5.74 ( ( P @ ( suc @ K3 ) )
% 5.46/5.74 = ( Q @ K3 ) )
% 5.46/5.74 => ( ( ord_Least_nat @ P )
% 5.46/5.74 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Least_Suc2
% 5.46/5.74 thf(fact_10211_Least__Suc,axiom,
% 5.46/5.74 ! [P: nat > $o,N: nat] :
% 5.46/5.74 ( ( P @ N )
% 5.46/5.74 => ( ~ ( P @ zero_zero_nat )
% 5.46/5.74 => ( ( ord_Least_nat @ P )
% 5.46/5.74 = ( suc
% 5.46/5.74 @ ( ord_Least_nat
% 5.46/5.74 @ ^ [M3: nat] : ( P @ ( suc @ M3 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Least_Suc
% 5.46/5.74
% 5.46/5.74 % Helper facts (44)
% 5.46/5.74 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.46/5.74 ! [X2: int,Y2: int] :
% 5.46/5.74 ( ( if_int @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.46/5.74 ! [X2: int,Y2: int] :
% 5.46/5.74 ( ( if_int @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.46/5.74 ! [X2: nat,Y2: nat] :
% 5.46/5.74 ( ( if_nat @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.46/5.74 ! [X2: nat,Y2: nat] :
% 5.46/5.74 ( ( if_nat @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.46/5.74 ! [X2: num,Y2: num] :
% 5.46/5.74 ( ( if_num @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.46/5.74 ! [X2: num,Y2: num] :
% 5.46/5.74 ( ( if_num @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.46/5.74 ! [X2: rat,Y2: rat] :
% 5.46/5.74 ( ( if_rat @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.46/5.74 ! [X2: rat,Y2: rat] :
% 5.46/5.74 ( ( if_rat @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.46/5.74 ! [X2: real,Y2: real] :
% 5.46/5.74 ( ( if_real @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.46/5.74 ! [X2: real,Y2: real] :
% 5.46/5.74 ( ( if_real @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.46/5.74 ! [P: real > $o] :
% 5.46/5.74 ( ( P @ ( fChoice_real @ P ) )
% 5.46/5.74 = ( ? [X5: real] : ( P @ X5 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.46/5.74 ! [X2: complex,Y2: complex] :
% 5.46/5.74 ( ( if_complex @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.46/5.74 ! [X2: complex,Y2: complex] :
% 5.46/5.74 ( ( if_complex @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.46/5.74 ! [X2: extended_enat,Y2: extended_enat] :
% 5.46/5.74 ( ( if_Extended_enat @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.46/5.74 ! [X2: extended_enat,Y2: extended_enat] :
% 5.46/5.74 ( ( if_Extended_enat @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.46/5.74 ! [X2: code_integer,Y2: code_integer] :
% 5.46/5.74 ( ( if_Code_integer @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.46/5.74 ! [X2: code_integer,Y2: code_integer] :
% 5.46/5.74 ( ( if_Code_integer @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.46/5.74 ! [X2: set_int,Y2: set_int] :
% 5.46/5.74 ( ( if_set_int @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.46/5.74 ! [X2: set_int,Y2: set_int] :
% 5.46/5.74 ( ( if_set_int @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.46/5.74 ! [X2: set_nat,Y2: set_nat] :
% 5.46/5.74 ( ( if_set_nat @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.46/5.74 ! [X2: set_nat,Y2: set_nat] :
% 5.46/5.74 ( ( if_set_nat @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.46/5.74 ! [X2: vEBT_VEBT,Y2: vEBT_VEBT] :
% 5.46/5.74 ( ( if_VEBT_VEBT @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.46/5.74 ! [X2: vEBT_VEBT,Y2: vEBT_VEBT] :
% 5.46/5.74 ( ( if_VEBT_VEBT @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.46/5.74 ! [X2: list_int,Y2: list_int] :
% 5.46/5.74 ( ( if_list_int @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.46/5.74 ! [X2: list_int,Y2: list_int] :
% 5.46/5.74 ( ( if_list_int @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.46/5.74 ! [X2: list_nat,Y2: list_nat] :
% 5.46/5.74 ( ( if_list_nat @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.46/5.74 ! [X2: list_nat,Y2: list_nat] :
% 5.46/5.74 ( ( if_list_nat @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.46/5.74 ! [X2: int > int,Y2: int > int] :
% 5.46/5.74 ( ( if_int_int @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.46/5.74 ! [X2: int > int,Y2: int > int] :
% 5.46/5.74 ( ( if_int_int @ $true @ X2 @ Y2 )
% 5.46/5.74 = X2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_2_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.46/5.74 ! [X2: nat > rat,Y2: nat > rat] :
% 5.46/5.74 ( ( if_nat_rat @ $false @ X2 @ Y2 )
% 5.46/5.74 = Y2 ) ).
% 5.46/5.74
% 5.46/5.74 thf(help_If_1_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.46/5.74 ! [X2: nat > rat,Y2: nat > rat] :
% 6.79/7.00 ( ( if_nat_rat @ $true @ X2 @ Y2 )
% 6.79/7.00 = X2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 6.79/7.00 ! [X2: option_nat,Y2: option_nat] :
% 6.79/7.00 ( ( if_option_nat @ $false @ X2 @ Y2 )
% 6.79/7.00 = Y2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 6.79/7.00 ! [X2: option_nat,Y2: option_nat] :
% 6.79/7.00 ( ( if_option_nat @ $true @ X2 @ Y2 )
% 6.79/7.00 = X2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 6.79/7.00 ! [X2: option_num,Y2: option_num] :
% 6.79/7.00 ( ( if_option_num @ $false @ X2 @ Y2 )
% 6.79/7.00 = Y2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 6.79/7.00 ! [X2: option_num,Y2: option_num] :
% 6.79/7.00 ( ( if_option_num @ $true @ X2 @ Y2 )
% 6.79/7.00 = X2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.79/7.00 ! [X2: product_prod_int_int,Y2: product_prod_int_int] :
% 6.79/7.00 ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y2 )
% 6.79/7.00 = Y2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.79/7.00 ! [X2: product_prod_int_int,Y2: product_prod_int_int] :
% 6.79/7.00 ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y2 )
% 6.79/7.00 = X2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.79/7.00 ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 6.79/7.00 ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y2 )
% 6.79/7.00 = Y2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.79/7.00 ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 6.79/7.00 ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y2 )
% 6.79/7.00 = X2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.79/7.00 ! [X2: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 6.79/7.00 ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y2 )
% 6.79/7.00 = Y2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.79/7.00 ! [X2: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 6.79/7.00 ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y2 )
% 6.79/7.00 = X2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.79/7.00 ! [P: $o] :
% 6.79/7.00 ( ( P = $true )
% 6.79/7.00 | ( P = $false ) ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.79/7.00 ! [X2: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 6.79/7.00 ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y2 )
% 6.79/7.00 = Y2 ) ).
% 6.79/7.00
% 6.79/7.00 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.79/7.00 ! [X2: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 6.79/7.00 ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y2 )
% 6.79/7.00 = X2 ) ).
% 6.79/7.00
% 6.79/7.00 % Conjectures (1)
% 6.79/7.00 thf(conj_0,conjecture,
% 6.79/7.00 ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( plus_plus_nat @ ( vEBT_VEBT_height @ summary ) @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.79/7.00
% 6.79/7.00 %------------------------------------------------------------------------------
% 6.79/7.00 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.BhkA9x8WNj/cvc5---1.0.5_13404.p...
% 6.79/7.00 (declare-sort $$unsorted 0)
% 6.79/7.00 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 6.79/7.00 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 6.79/7.00 (declare-sort tptp.produc1193250871479095198on_num 0)
% 6.79/7.00 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 6.79/7.00 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 6.79/7.00 (declare-sort tptp.produc3368934014287244435at_num 0)
% 6.79/7.00 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.79/7.00 (declare-sort tptp.produc7036089656553540234on_num 0)
% 6.79/7.00 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 6.79/7.00 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 6.79/7.00 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.79/7.00 (declare-sort tptp.produc3447558737645232053on_num 0)
% 6.79/7.00 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 6.79/7.00 (declare-sort tptp.produc2963631642982155120at_num 0)
% 6.79/7.00 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.79/7.00 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 6.79/7.00 (declare-sort tptp.filter6041513312241820739omplex 0)
% 6.79/7.00 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.79/7.00 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.79/7.00 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.79/7.00 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.79/7.00 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.79/7.00 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.79/7.00 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.79/7.00 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.79/7.00 (declare-sort tptp.filter2146258269922977983l_real 0)
% 6.79/7.00 (declare-sort tptp.list_P8526636022914148096eger_o 0)
% 6.79/7.00 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.79/7.00 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.79/7.00 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.79/7.00 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.79/7.00 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.79/7.00 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.79/7.00 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.79/7.00 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.79/7.00 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.79/7.00 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.79/7.00 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.79/7.00 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.79/7.00 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.79/7.00 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.79/7.00 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.79/7.00 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.79/7.00 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.79/7.00 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.79/7.00 (declare-sort tptp.product_prod_num_num 0)
% 6.79/7.00 (declare-sort tptp.product_prod_nat_num 0)
% 6.79/7.00 (declare-sort tptp.product_prod_nat_nat 0)
% 6.79/7.00 (declare-sort tptp.product_prod_int_int 0)
% 6.79/7.00 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.79/7.00 (declare-sort tptp.set_list_complex 0)
% 6.79/7.00 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.79/7.00 (declare-sort tptp.set_list_nat 0)
% 6.79/7.00 (declare-sort tptp.set_list_int 0)
% 6.79/7.00 (declare-sort tptp.product_prod_o_nat 0)
% 6.79/7.00 (declare-sort tptp.product_prod_o_int 0)
% 6.79/7.00 (declare-sort tptp.list_Code_integer 0)
% 6.79/7.00 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.79/7.00 (declare-sort tptp.set_set_nat 0)
% 6.79/7.00 (declare-sort tptp.set_Code_integer 0)
% 6.79/7.00 (declare-sort tptp.set_Product_unit 0)
% 6.79/7.00 (declare-sort tptp.list_complex 0)
% 6.79/7.00 (declare-sort tptp.set_list_o 0)
% 6.79/7.00 (declare-sort tptp.product_prod_o_o 0)
% 6.79/7.00 (declare-sort tptp.set_complex 0)
% 6.79/7.00 (declare-sort tptp.filter_real 0)
% 6.79/7.00 (declare-sort tptp.option_num 0)
% 6.79/7.00 (declare-sort tptp.option_nat 0)
% 6.79/7.00 (declare-sort tptp.filter_nat 0)
% 6.79/7.00 (declare-sort tptp.set_char 0)
% 6.79/7.00 (declare-sort tptp.list_real 0)
% 6.79/7.00 (declare-sort tptp.set_real 0)
% 6.79/7.00 (declare-sort tptp.list_num 0)
% 6.79/7.00 (declare-sort tptp.list_nat 0)
% 6.79/7.00 (declare-sort tptp.list_int 0)
% 6.79/7.00 (declare-sort tptp.vEBT_VEBT 0)
% 6.79/7.00 (declare-sort tptp.set_rat 0)
% 6.79/7.00 (declare-sort tptp.set_num 0)
% 6.79/7.00 (declare-sort tptp.set_nat 0)
% 6.79/7.00 (declare-sort tptp.set_int 0)
% 6.79/7.00 (declare-sort tptp.code_integer 0)
% 6.79/7.00 (declare-sort tptp.extended_enat 0)
% 6.79/7.00 (declare-sort tptp.list_o 0)
% 6.79/7.00 (declare-sort tptp.complex 0)
% 6.79/7.00 (declare-sort tptp.set_o 0)
% 6.79/7.00 (declare-sort tptp.char 0)
% 6.79/7.00 (declare-sort tptp.real 0)
% 6.79/7.00 (declare-sort tptp.rat 0)
% 6.79/7.00 (declare-sort tptp.num 0)
% 6.79/7.00 (declare-sort tptp.nat 0)
% 6.79/7.00 (declare-sort tptp.int 0)
% 6.79/7.00 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 6.79/7.00 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.79/7.00 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.79/7.00 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.79/7.00 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.79/7.00 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.79/7.00 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.00 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.00 (declare-fun tptp.bNF_re728719798268516973at_o_o ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> Bool Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) Bool)) Bool)
% 6.79/7.00 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.79/7.00 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.79/7.00 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.79/7.00 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.79/7.00 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.79/7.00 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.79/7.00 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.79/7.00 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.79/7.00 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.79/7.00 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.79/7.00 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.79/7.00 (declare-fun tptp.bit_un5425074673868309765um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.79/7.00 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.79/7.00 (declare-fun tptp.bit_un3595099601533988841um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.79/7.00 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.79/7.00 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.79/7.00 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.79/7.00 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.79/7.00 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.79/7.00 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.79/7.00 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.79/7.00 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.79/7.00 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.79/7.00 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.79/7.00 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.79/7.00 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 6.79/7.00 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 6.79/7.00 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 6.79/7.00 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.79/7.00 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.79/7.00 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.79/7.00 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.79/7.00 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.79/7.00 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.79/7.00 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.79/7.00 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.79/7.00 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 6.79/7.00 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.79/7.00 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.79/7.00 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.79/7.00 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.79/7.00 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.79/7.00 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.79/7.00 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.79/7.00 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.79/7.00 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.79/7.00 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.79/7.00 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.79/7.00 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.79/7.00 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.79/7.00 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.79/7.00 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.79/7.00 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.79/7.00 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.79/7.00 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.79/7.00 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.79/7.00 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.79/7.00 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.79/7.00 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.79/7.00 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.79/7.00 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.79/7.00 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.79/7.00 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.79/7.00 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.79/7.00 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.79/7.00 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.79/7.00 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 6.79/7.00 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 6.79/7.00 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.79/7.00 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.79/7.00 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.79/7.00 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.79/7.00 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.79/7.00 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.79/7.00 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.79/7.00 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.79/7.00 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.79/7.00 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.79/7.00 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 6.79/7.00 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 6.79/7.00 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.79/7.00 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 6.79/7.00 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.79/7.00 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.79/7.00 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.79/7.00 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 6.79/7.00 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 6.79/7.00 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.79/7.00 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 6.79/7.00 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.79/7.00 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.79/7.00 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.79/7.00 (declare-fun tptp.comp_C8797469213163452608nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.79/7.00 (declare-fun tptp.comp_C1593894019821074884nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.79/7.00 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.79/7.00 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 6.79/7.00 (declare-fun tptp.id_o (Bool) Bool)
% 6.79/7.00 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.79/7.00 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.79/7.00 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.79/7.00 (declare-fun tptp.map_fu434086159418415080_int_o ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat Bool) tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.int tptp.int) Bool)
% 6.79/7.00 (declare-fun tptp.map_fu4960017516451851995nt_int ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.map_fu4826362097070443709at_o_o ((-> tptp.int tptp.product_prod_nat_nat) (-> Bool Bool) (-> tptp.product_prod_nat_nat Bool) tptp.int) Bool)
% 6.79/7.00 (declare-fun tptp.map_fu2345160673673942751at_nat ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat) tptp.int) tptp.nat)
% 6.79/7.00 (declare-fun tptp.map_fu3667384564859982768at_int ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.map_fu898904425404107465nt_o_o ((-> tptp.rat tptp.product_prod_int_int) (-> Bool Bool) (-> tptp.product_prod_int_int Bool) tptp.rat) Bool)
% 6.79/7.00 (declare-fun tptp.map_fu1532550112467129777l_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.map_fu7146612038024189824t_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.real) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.map_fu1856342031159181835at_o_o ((-> tptp.real tptp.nat tptp.rat) (-> Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) tptp.real) Bool)
% 6.79/7.00 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.79/7.00 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.79/7.00 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.79/7.00 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.79/7.00 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.minus_8727706125548526216plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool) tptp.complex) Bool)
% 6.79/7.00 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 6.79/7.00 (declare-fun tptp.minus_1139252259498527702_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.79/7.00 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 6.79/7.00 (declare-fun tptp.minus_2270307095948843157_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.79/7.00 (declare-fun tptp.minus_minus_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 6.79/7.00 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.79/7.00 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.79/7.00 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.79/7.00 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 6.79/7.00 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.79/7.00 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.00 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.79/7.00 (declare-fun tptp.minus_5127226145743854075T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.79/7.00 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.79/7.00 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.79/7.00 (declare-fun tptp.one_one_int () tptp.int)
% 6.79/7.00 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.79/7.00 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.79/7.00 (declare-fun tptp.one_one_real () tptp.real)
% 6.79/7.00 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.79/7.00 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.79/7.00 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.79/7.00 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.79/7.00 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.79/7.00 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.79/7.00 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.00 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.79/7.00 (declare-fun tptp.uminus8041839845116263051T_VEBT (tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.79/7.00 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.79/7.00 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.79/7.00 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.79/7.00 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.79/7.00 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.79/7.00 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.79/7.00 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.79/7.00 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.79/7.00 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.79/7.00 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.79/7.00 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups6381953495645901045omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.79/7.00 (declare-fun tptp.groups975429370522433651at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.groups342789780944988191at_rat ((-> tptp.product_prod_nat_nat tptp.rat) tptp.set_Pr1261947904930325089at_nat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.79/7.00 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.79/7.00 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups769130701875090982BT_int ((-> tptp.vEBT_VEBT tptp.int) tptp.set_VEBT_VEBT) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups771621172384141258BT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.nat)
% 6.79/7.00 (declare-fun tptp.groups136491112297645522BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups2240296850493347238T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.79/7.00 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.79/7.00 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.79/7.00 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.79/7.00 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups5726676334696518183BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 6.79/7.00 (declare-fun tptp.groups2703838992350267259T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 6.79/7.00 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.79/7.00 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.79/7.00 (declare-fun tptp.the_Pr4378521158711661632nt_int ((-> tptp.product_prod_int_int Bool)) tptp.product_prod_int_int)
% 6.79/7.00 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.79/7.00 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.if_nat_rat (Bool (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.79/7.00 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.79/7.00 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.79/7.00 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.79/7.00 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.79/7.00 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.79/7.00 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.79/7.00 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.79/7.00 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.79/7.00 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.79/7.00 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.79/7.00 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.79/7.00 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.79/7.00 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.79/7.00 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.79/7.00 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.79/7.00 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 6.79/7.00 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.79/7.00 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.79/7.00 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.79/7.00 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.79/7.00 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.79/7.00 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.00 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.79/7.00 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.79/7.00 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.79/7.00 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.00 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.79/7.00 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.79/7.00 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.79/7.00 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.nil_int () tptp.list_int)
% 6.79/7.00 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.79/7.00 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.79/7.00 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.79/7.00 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.79/7.00 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.00 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.79/7.00 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.79/7.00 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.79/7.00 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.79/7.00 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.79/7.00 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.79/7.00 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.79/7.00 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.79/7.00 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.79/7.00 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.79/7.00 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.79/7.00 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.79/7.00 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.79/7.00 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.79/7.00 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.79/7.00 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.79/7.00 (declare-fun tptp.nth_Pr8522763379788166057eger_o (tptp.list_P8526636022914148096eger_o tptp.nat) tptp.produc6271795597528267376eger_o)
% 6.79/7.00 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.79/7.00 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.79/7.00 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.79/7.00 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.79/7.00 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.79/7.00 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.79/7.00 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.79/7.00 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.79/7.00 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.79/7.00 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.79/7.00 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.79/7.00 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.79/7.00 (declare-fun tptp.produc3607205314601156340eger_o (tptp.list_Code_integer tptp.list_o) tptp.list_P8526636022914148096eger_o)
% 6.79/7.00 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.79/7.00 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.79/7.00 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.79/7.00 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.79/7.00 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.79/7.00 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.79/7.00 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.79/7.00 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.79/7.00 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.79/7.00 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.79/7.00 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.replic4235873036481779905at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.79/7.00 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.79/7.00 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.79/7.00 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.79/7.00 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.79/7.00 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.79/7.00 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.79/7.00 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.79/7.00 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.79/7.00 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.79/7.00 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.79/7.00 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.79/7.00 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.79/7.00 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.79/7.00 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.79/7.00 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.79/7.00 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.79/7.00 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.79/7.00 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.79/7.00 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.79/7.00 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.79/7.00 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 6.79/7.00 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.79/7.01 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.79/7.01 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.79/7.01 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.79/7.01 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.79/7.01 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.79/7.01 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.79/7.01 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.79/7.01 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.79/7.01 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.79/7.01 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.79/7.01 (declare-fun tptp.one () tptp.num)
% 6.79/7.01 (declare-fun tptp.case_num_option_num (tptp.option_num (-> tptp.num tptp.option_num) (-> tptp.num tptp.option_num) tptp.num) tptp.option_num)
% 6.79/7.01 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.79/7.01 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.79/7.01 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.79/7.01 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.79/7.01 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.79/7.01 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.79/7.01 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.79/7.01 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.79/7.01 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.79/7.01 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.79/7.01 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.79/7.01 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.none_num () tptp.option_num)
% 6.79/7.01 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.79/7.01 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.79/7.01 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.79/7.01 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.79/7.01 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.79/7.01 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.79/7.01 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.79/7.01 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.79/7.01 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.79/7.01 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 6.79/7.01 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 6.79/7.01 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.79/7.01 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.79/7.01 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.79/7.01 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.79/7.01 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.79/7.01 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.01 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.79/7.01 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.79/7.01 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.79/7.01 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 6.79/7.01 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.79/7.01 (declare-fun tptp.ord_less_complex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le549003669493604880_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le3480810397992357184T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.79/7.01 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.79/7.01 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.79/7.01 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.79/7.01 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.79/7.01 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.79/7.01 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 6.79/7.01 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.79/7.01 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.79/7.01 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.79/7.01 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 6.79/7.01 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.79/7.01 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.79/7.01 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.79/7.01 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.79/7.01 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.79/7.01 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.79/7.01 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.79/7.01 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 6.79/7.01 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.79/7.01 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 6.79/7.01 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 6.79/7.01 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 6.79/7.01 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 6.79/7.01 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 6.79/7.01 (declare-fun tptp.produc2899441246263362727at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc6121120109295599847at_nat) tptp.produc5542196010084753463at_nat)
% 6.79/7.01 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.79/7.01 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.79/7.01 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.79/7.01 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.79/7.01 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.79/7.01 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.79/7.01 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.79/7.01 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.79/7.01 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.79/7.01 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.79/7.01 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 6.79/7.01 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.79/7.01 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 6.79/7.01 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 6.79/7.01 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 6.79/7.01 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.79/7.01 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.79/7.01 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.79/7.01 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.79/7.01 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.01 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.79/7.01 (declare-fun tptp.produc7828578312038201481er_o_o ((-> tptp.code_integer Bool Bool) tptp.produc6271795597528267376eger_o) Bool)
% 6.79/7.01 (declare-fun tptp.produc1043322548047392435omplex ((-> tptp.code_integer Bool tptp.set_complex) tptp.produc6271795597528267376eger_o) tptp.set_complex)
% 6.79/7.01 (declare-fun tptp.produc1253318751659547953et_int ((-> tptp.code_integer Bool tptp.set_int) tptp.produc6271795597528267376eger_o) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.produc5431169771168744661et_nat ((-> tptp.code_integer Bool tptp.set_nat) tptp.produc6271795597528267376eger_o) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.produc242741666403216561t_real ((-> tptp.code_integer Bool tptp.set_real) tptp.produc6271795597528267376eger_o) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.79/7.01 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.79/7.01 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.79/7.01 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.79/7.01 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.79/7.01 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 6.79/7.01 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.79/7.01 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.79/7.01 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.79/7.01 (declare-fun tptp.produc8739625826339149834_nat_o ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.79/7.01 (declare-fun tptp.produc27273713700761075at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.79/7.01 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.79/7.01 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.79/7.01 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.79/7.01 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.79/7.01 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.79/7.01 (declare-fun tptp.produc4927758841916487424_num_o ((-> tptp.nat tptp.num Bool) tptp.product_prod_nat_num) Bool)
% 6.79/7.01 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.79/7.01 (declare-fun tptp.produc6231982587499038204omplex ((-> tptp.nat tptp.num tptp.set_complex) tptp.product_prod_nat_num) tptp.set_complex)
% 6.79/7.01 (declare-fun tptp.produc1435849484188172666t_real ((-> tptp.nat tptp.num tptp.set_real) tptp.product_prod_nat_num) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.produc5703948589228662326_num_o ((-> tptp.num tptp.num Bool) tptp.product_prod_num_num) Bool)
% 6.79/7.01 (declare-fun tptp.produc2866383454006189126omplex ((-> tptp.num tptp.num tptp.set_complex) tptp.product_prod_num_num) tptp.set_complex)
% 6.79/7.01 (declare-fun tptp.produc6406642877701697732et_int ((-> tptp.num tptp.num tptp.set_int) tptp.product_prod_num_num) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.produc1361121860356118632et_nat ((-> tptp.num tptp.num tptp.set_nat) tptp.product_prod_num_num) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.produc8296048397933160132t_real ((-> tptp.num tptp.num tptp.set_real) tptp.product_prod_num_num) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 6.79/7.01 (declare-fun tptp.produc8508995932063986495nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.79/7.01 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.produc6174133586879617921nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.79/7.01 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.79/7.01 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.79/7.01 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.79/7.01 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.79/7.01 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 6.79/7.01 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.79/7.01 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.79/7.01 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.79/7.01 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 6.79/7.01 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 6.79/7.01 (declare-fun tptp.positive2 (tptp.real) Bool)
% 6.79/7.01 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.79/7.01 (declare-fun tptp.rep_real (tptp.real tptp.nat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 6.79/7.01 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.79/7.01 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.79/7.01 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.79/7.01 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.79/7.01 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.79/7.01 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.id_nat2 () tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.01 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 6.79/7.01 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.79/7.01 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.79/7.01 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.79/7.01 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.79/7.01 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.79/7.01 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.79/7.01 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.79/7.01 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.79/7.01 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.79/7.01 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.79/7.01 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.79/7.01 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.79/7.01 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.79/7.01 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.79/7.01 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.79/7.01 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.79/7.01 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.79/7.01 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.79/7.01 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.79/7.01 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.79/7.01 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.79/7.01 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.79/7.01 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.79/7.01 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.79/7.01 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.79/7.01 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 6.79/7.01 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 6.79/7.01 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 6.79/7.01 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.79/7.01 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 6.79/7.01 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.79/7.01 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 6.79/7.01 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.79/7.01 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.01 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 6.79/7.01 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.79/7.01 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.79/7.01 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.79/7.01 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 6.79/7.01 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 6.79/7.01 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.image_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 6.79/7.01 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 6.79/7.01 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.01 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 6.79/7.01 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.79/7.01 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.79/7.01 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.79/7.01 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.79/7.01 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.79/7.01 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.79/7.01 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.79/7.01 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.79/7.01 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.79/7.01 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.79/7.01 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.79/7.01 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.79/7.01 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.79/7.01 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.79/7.01 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.79/7.01 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.79/7.01 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.79/7.01 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.79/7.01 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.79/7.01 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.79/7.01 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.79/7.01 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.79/7.01 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 6.79/7.01 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.79/7.01 (declare-fun tptp.topolo7278393974255667507et_nat ((-> tptp.nat tptp.set_nat)) Bool)
% 6.79/7.01 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.79/7.01 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.79/7.01 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.79/7.01 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 6.79/7.01 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 6.79/7.01 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.79/7.01 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.79/7.01 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.79/7.01 (declare-fun tptp.diffs_rat ((-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.79/7.01 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.79/7.01 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.pi () tptp.real)
% 6.79/7.01 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.79/7.01 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.79/7.01 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.79/7.01 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.01 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_T_i_n_s_e_r_t (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_T_i_n_s_e_r_t2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_T5076183648494686801_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_T9217963907923527482_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_T_m_a_x_t (tptp.vEBT_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_T_m_a_x_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_T_m_e_m_b_e_r (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_T_m_e_m_b_e_r2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_T8099345112685741742_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_T5837161174952499735_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_T_m_i_n_N_u_l_l (tptp.vEBT_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_T5462971552011256508_l_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_T_m_i_n_t (tptp.vEBT_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_T_m_i_n_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.79/7.01 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.79/7.01 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.79/7.01 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_height (tptp.vEBT_VEBT) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_height_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.79/7.01 (declare-fun tptp.vEBT_V1502963449132264192at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.option4927543243414619207at_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.79/7.01 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.79/7.01 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.79/7.01 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.79/7.01 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.79/7.01 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.79/7.01 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.79/7.01 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.79/7.01 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.79/7.01 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.79/7.01 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.79/7.01 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.79/7.01 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.79/7.01 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.79/7.01 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.79/7.01 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.79/7.01 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.79/7.01 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.79/7.01 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.79/7.01 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.79/7.01 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.79/7.01 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.79/7.01 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.79/7.01 (declare-fun tptp.deg () tptp.nat)
% 6.79/7.01 (declare-fun tptp.m () tptp.nat)
% 6.79/7.01 (declare-fun tptp.ma () tptp.nat)
% 6.79/7.01 (declare-fun tptp.mi () tptp.nat)
% 6.79/7.01 (declare-fun tptp.na () tptp.nat)
% 6.79/7.01 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.79/7.01 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.79/7.01 (declare-fun tptp.xa () tptp.nat)
% 6.79/7.01 (assert (not (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)))
% 6.79/7.01 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.79/7.01 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat Y) X)))))))
% 6.79/7.01 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat X) Y)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t tptp.summary) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height tptp.summary))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))))))
% 6.79/7.01 (assert (forall ((Summary tptp.vEBT_VEBT) (Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height Summary))) (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)))))
% 6.79/7.01 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.79/7.01 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_1))))) (@ (@ tptp.vEBT_T_i_n_s_e_r_t tptp.summary) (@ (@ tptp.vEBT_VEBT_high (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)) tptp.mi) tptp.xa)) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat _let_1))))))))
% 6.79/7.01 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (= X2 Mi) (= X2 Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))))
% 6.79/7.01 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.79/7.01 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.79/7.01 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.79/7.01 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.79/7.01 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.79/7.01 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (@ _let_1 A)) (@ _let_1 B)))))
% 6.79/7.01 (assert (= tptp.vEBT_VEBT_high (lambda ((X tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.79/7.01 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M) N))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y2) _let_1)) X2)) N) Y2)))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.79/7.01 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L tptp.nat) (D tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D))) L))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.79/7.01 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.79/7.01 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 6.79/7.01 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 6.79/7.01 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.collec3392354462482085612at_nat P)) (@ P A))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.79/7.01 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.79/7.01 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.79/7.01 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A2))) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A2))) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A2))) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A2))) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A2))) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A2))) A2)))
% 6.79/7.01 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X3 tptp.complex)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))))
% 6.79/7.01 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 6.79/7.01 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 6.79/7.01 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 6.79/7.01 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.79/7.01 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.79/7.01 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2)))))) (@ P N))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.79/7.01 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X2) tptp.one) (= X2 tptp.one))))
% 6.79/7.01 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.79/7.01 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.79/7.01 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.79/7.01 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.79/7.01 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N2) (= M3 N2)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.79/7.01 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N2) (not (= M3 N2))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (L2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L2) (=> (= (@ (@ tptp.plus_plus_nat M) L2) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.79/7.01 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.79/7.01 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X3)))))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.79/7.01 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.79/7.01 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.79/7.01 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.79/7.01 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.79/7.01 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.79/7.01 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (exists ((K2 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M3) K2))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (exists ((N3 tptp.nat)) (= L2 (@ (@ tptp.plus_plus_nat K) N3))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) L2))))))
% 6.79/7.01 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.79/7.01 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.79/7.01 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X2))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.79/7.01 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.79/7.01 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.79/7.01 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.79/7.01 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.79/7.01 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.79/7.01 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.79/7.01 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.79/7.01 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.79/7.01 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.79/7.01 (assert (forall ((Y2 tptp.num)) (=> (not (= Y2 tptp.one)) (=> (forall ((X22 tptp.num)) (not (= Y2 (@ tptp.bit0 X22)))) (not (forall ((X32 tptp.num)) (not (= Y2 (@ tptp.bit1 X32)))))))))
% 6.79/7.01 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.79/7.01 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.79/7.01 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.79/7.01 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.79/7.01 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.79/7.01 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.79/7.01 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.79/7.01 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.79/7.01 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.79/7.01 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.79/7.01 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.79/7.01 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.79/7.01 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.79/7.01 (assert (forall ((B tptp.real) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.79/7.01 (assert (forall ((B tptp.int) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.79/7.01 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.79/7.01 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) tptp.one)))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.79/7.01 (assert (forall ((B tptp.real) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.79/7.01 (assert (forall ((B tptp.int) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.79/7.01 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 6.79/7.01 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 6.79/7.01 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N))))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 6.79/7.01 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.79/7.01 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.79/7.01 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 6.79/7.01 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N)))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat L2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L2)))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int L2)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L2)))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (= (@ (@ tptp.times_times_rat _let_1) A) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) N))) (let ((_let_2 (@ tptp.times_times_complex Y2))) (=> (= (@ (@ tptp.times_times_complex X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_complex _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) N))) (let ((_let_2 (@ tptp.times_times_real Y2))) (=> (= (@ (@ tptp.times_times_real X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_real _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) N))) (let ((_let_2 (@ tptp.times_times_rat Y2))) (=> (= (@ (@ tptp.times_times_rat X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_rat _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X2) N))) (let ((_let_2 (@ tptp.times_times_nat Y2))) (=> (= (@ (@ tptp.times_times_nat X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_nat _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X2) N))) (let ((_let_2 (@ tptp.times_times_int Y2))) (=> (= (@ (@ tptp.times_times_int X2) Y2) (@ _let_2 X2)) (= (@ (@ tptp.times_times_int _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_real (@ _let_1 M)) N)))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_int (@ _let_1 M)) N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 6.79/7.01 (assert (forall ((I tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I) J)) U)) K))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q2)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X2) Y2) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y2) N)) tptp.one_one_complex))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X2) Y2) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y2) N)) tptp.one_one_real))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X2) Y2) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_rat Y2) N)) tptp.one_one_rat))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X2) Y2) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y2) N)) tptp.one_one_nat))))
% 6.79/7.01 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X2) Y2) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y2) N)) tptp.one_one_int))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_complex A) N))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N)) M)))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N))) M)))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X2) X2)) X2)) X2))))
% 6.79/7.01 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X2) X2)) X2)) X2))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X2) X2)) X2)) X2))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.power_power_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X2) X2)) X2)) X2))))
% 6.79/7.01 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X2) X2)) X2)) X2))))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.79/7.01 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.79/7.01 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.79/7.01 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.79/7.01 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.79/7.01 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex A) A)) A))))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A) A)) A))))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat A) A)) A))))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A) A)) A))))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) A)) A))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1))))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat K) M)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X2) Y2)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y2) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y2)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) Y2)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y2)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X2) Y2)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y2) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y2)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X2) Y2)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y2) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X2)) Y2))))))
% 6.79/7.01 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X2) Y2)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y2) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y2)))))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y2) _let_2)))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y2)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.79/7.01 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)) tptp.mi) tptp.xa)) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat _let_1))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_1))))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2))) (@ (@ tptp.vEBT_T_i_n_s_e_r_t tptp.summary) _let_2)) tptp.one_one_nat))))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 6.79/7.01 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)) tptp.mi) tptp.xa)) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.79/7.01 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B) A)) C))))
% 6.79/7.01 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B) A)) C))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C))))
% 6.79/7.01 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) N) (= Deg N))))
% 6.79/7.01 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat _let_1) (@ tptp.vEBT_VEBT_height T))) (@ (@ tptp.times_times_nat _let_1) N))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.79/7.01 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))
% 6.79/7.01 (assert (forall ((X4 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X4))))
% 6.79/7.01 (assert (forall ((X4 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X4))))
% 6.79/7.01 (assert (forall ((X4 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X4) X_1))))
% 6.79/7.01 (assert (forall ((X4 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X4) X_1))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_real X2) Y2)) (@ (@ tptp.ord_less_real Y2) X2)))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_rat X2) Y2)) (@ (@ tptp.ord_less_rat Y2) X2)))))
% 6.79/7.01 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_int X2) Y2)) (@ (@ tptp.ord_less_int Y2) X2)))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B))))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) W)) (@ (@ tptp.times_times_complex Y2) Z)))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) W)) (@ (@ tptp.times_times_real Y2) Z)))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) W)) (@ (@ tptp.times_times_rat Y2) Z)))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex Y2) W)))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y2) W)))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y2) W)))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 6.79/7.01 (assert (forall ((M tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M) N)))))))
% 6.79/7.01 (assert (forall ((M tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M) N)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 6.79/7.01 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M) N)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B) tptp.one_one_real)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))))
% 6.79/7.01 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.79/7.01 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A) C))) (@ (@ tptp.times_times_real B) D2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) _let_2))))))
% 6.79/7.01 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))))
% 6.79/7.01 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))))
% 6.79/7.01 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X2))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X2))))
% 6.79/7.01 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)) tptp.mi) tptp.xa)) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat _let_1))))) (let ((_let_3 (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 _let_1))))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_3))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_3)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t tptp.summary) _let_2)) tptp.one_one_nat)))))))
% 6.79/7.01 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)) tptp.mi) tptp.xa))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high _let_2) _let_1))) (@ (@ tptp.vEBT_VEBT_low _let_2) _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y2) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X2)) Y2) (or (@ (@ tptp.vEBT_vebt_member T) Y2) (= X2 Y2)))))))))
% 6.79/7.01 (assert (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X4) tptp.na) (forall ((Xa tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t X4) Xa)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))))))))
% 6.79/7.01 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)) tptp.mi) tptp.xa))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_5) (@ (@ tptp.vEBT_VEBT_low _let_3) _let_2)))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_5))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_5)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t tptp.summary) _let_4)) tptp.one_one_nat)))))))))
% 6.79/7.01 (assert (forall ((Tree tptp.vEBT_VEBT) (X2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 6.79/7.01 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (D2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X2) D2)) (@ (@ tptp.vEBT_VEBT_low X2) D2)) D2) X2)))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((R tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R)) (@ (@ tptp.divide_divide_real A) R)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT T) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y2) _let_1)) X2)) N) X2)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.member_nat X2) (@ tptp.vEBT_set_vebt T))))))
% 6.79/7.01 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 6.79/7.01 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.79/7.01 (assert (=> (= tptp.mi tptp.ma) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))))
% 6.79/7.01 (assert (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I3)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I3)))))
% 6.79/7.01 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I3)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) tptp.na) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X4) (@ (@ tptp.ord_less_eq_nat X4) tptp.ma)))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.power_power_real X2) N3))))))
% 6.79/7.01 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 6.79/7.01 (assert (forall ((S2 tptp.set_real)) (=> (exists ((X4 tptp.real)) (@ (@ tptp.member_real X4) S2)) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (@ (@ tptp.ord_less_eq_real X3) Z2)))) (exists ((Y3 tptp.real)) (and (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S2) (@ (@ tptp.ord_less_eq_real X4) Y3))) (forall ((Z2 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (@ (@ tptp.ord_less_eq_real X3) Z2))) (@ (@ tptp.ord_less_eq_real Y3) Z2)))))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.79/7.01 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real B2) A3))))
% 6.79/7.01 (assert (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat B2) A3))))
% 6.79/7.01 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.times_times_nat B2) A3))))
% 6.79/7.01 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.times_times_int B2) A3))))
% 6.79/7.01 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex)) (= (= tptp.one_one_complex X2) (= X2 tptp.one_one_complex))))
% 6.79/7.01 (assert (forall ((X2 tptp.real)) (= (= tptp.one_one_real X2) (= X2 tptp.one_one_real))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat)) (= (= tptp.one_one_rat X2) (= X2 tptp.one_one_rat))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat)) (= (= tptp.one_one_nat X2) (= X2 tptp.one_one_nat))))
% 6.79/7.01 (assert (forall ((X2 tptp.int)) (= (= tptp.one_one_int X2) (= X2 tptp.one_one_int))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.79/7.01 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_rat I) K) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.79/7.01 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.79/7.01 (assert (forall ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.79/7.01 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.79/7.01 (assert (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.79/7.01 (assert (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.79/7.01 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real B2) A3))))
% 6.79/7.01 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat B2) A3))))
% 6.79/7.01 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A3))))
% 6.79/7.01 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int B2) A3))))
% 6.79/7.01 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.79/7.01 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_T_m_i_n_N_u_l_l T)) tptp.one_one_nat)))
% 6.79/7.01 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)) tptp.one_one_nat)))
% 6.79/7.01 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (= K L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C2))))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.79/7.01 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (exists ((C3 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A3) C3))))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.79/7.01 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (= K L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (= K L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.79/7.01 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.79/7.01 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)) tptp.mi) tptp.xa))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)) (not (or (= tptp.xa tptp.mi) (= tptp.xa tptp.ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_5) (@ (@ tptp.vEBT_VEBT_low _let_3) _let_2))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_5))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_5)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t tptp.summary) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))))))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X2 Mi) (= X2 Ma) (and (@ (@ tptp.ord_less_nat X2) Ma) (@ (@ tptp.ord_less_nat Mi) X2) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))))))))))
% 6.79/7.01 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (= X2 Mi) (= X2 Ma)))))))
% 6.79/7.01 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (@ (@ tptp.vEBT_VEBT_low X2) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X2)))))))))
% 6.79/7.01 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X2)) X2)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y2) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y2)) X2))))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))
% 6.79/7.01 (assert (= tptp.vEBT_VEBT_low (lambda ((X tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.79/7.01 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.79/7.01 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList2) S3))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) N))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) N))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) N))))))
% 6.79/7.01 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.79/7.01 (assert (forall ((X23 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X23) (@ tptp.suc Y22)) (= X23 Y22))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) B))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B) _let_1))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (= (@ (@ tptp.modulo_modulo_int _let_1) B) _let_1))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real A) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.minus_minus_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int A) B))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.79/7.01 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_real A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.79/7.01 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 6.79/7.01 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) B) A))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A))))
% 6.79/7.01 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 6.79/7.01 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.79/7.01 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.79/7.01 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.79/7.01 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.79/7.01 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.79/7.01 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K)))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2))))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) (@ tptp.suc J))))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N) K)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.79/7.01 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.79/7.01 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.79/7.01 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.79/7.01 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.79/7.01 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.79/7.01 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.79/7.01 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.79/7.01 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ (@ tptp.modulo_modulo_nat M) _let_1)))))
% 6.79/7.01 (assert (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (= A B) (= C D2)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (= A B) (= C D2)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A4) B4)) C))))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A4) B4)) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.79/7.01 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 6.79/7.01 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M3) N2)) M3) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M3) N2)) N2)))))
% 6.79/7.01 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P2) (=> (@ (@ tptp.ord_less_nat M) P2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P2) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P2))))) (@ P M)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.79/7.01 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Y2 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X2) (@ tptp.size_s6755466524823107622T_VEBT Y2))) (not (= X2 Y2)))))
% 6.79/7.01 (assert (forall ((X2 tptp.list_o) (Y2 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X2) (@ tptp.size_size_list_o Y2))) (not (= X2 Y2)))))
% 6.79/7.01 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y2))) (not (= X2 Y2)))))
% 6.79/7.01 (assert (forall ((X2 tptp.list_int) (Y2 tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X2) (@ tptp.size_size_list_int Y2))) (not (= X2 Y2)))))
% 6.79/7.01 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (=> (not (= (@ tptp.size_size_num X2) (@ tptp.size_size_num Y2))) (not (= X2 Y2)))))
% 6.79/7.01 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M3) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M3) N2)) N2)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A4) B4)) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A4) B4)) C))))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A4) B4)) C))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A4) B4)) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A4) B4)) C))))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) B4)) C))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N)) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N)) B))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D2) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (D2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D2) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D2) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D2)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D2)))))
% 6.79/7.01 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C) A)))))
% 6.79/7.01 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C) A)))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))))
% 6.79/7.01 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.79/7.01 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B) A) (= C (@ (@ tptp.minus_minus_real A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A) (= C (@ (@ tptp.minus_minus_rat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A) (= C (@ (@ tptp.minus_minus_nat A) B)))))
% 6.79/7.01 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A) (= C (@ (@ tptp.minus_minus_int A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B)) (= (@ (@ tptp.plus_plus_real A) B) C))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat A) B) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A) B) C))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C) (= A (@ (@ tptp.plus_plus_real C) B)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C) (= A (@ (@ tptp.plus_plus_rat C) B)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))))
% 6.79/7.01 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A2) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 6.79/7.01 (assert (forall ((J tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N) L2)))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M5 tptp.nat)) (and (= M (@ tptp.suc M5)) (@ (@ tptp.ord_less_nat N) M5))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K3) (=> (@ _let_1 J2) (=> (@ (@ P J2) K3) (@ _let_1 K3))))))) (@ (@ P I) J))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (=> (= J (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 6.79/7.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (R2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X3 tptp.nat)) (@ (@ R2 X3) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R2 X3))) (=> (@ _let_1 Y3) (=> (@ (@ R2 Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((N3 tptp.nat)) (@ (@ R2 N3) (@ tptp.suc N3))) (@ (@ R2 M) N)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 6.79/7.01 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M6) (exists ((M4 tptp.nat)) (= M6 (@ tptp.suc M4))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 6.79/7.01 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))
% 6.79/7.01 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (not (forall ((D3 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D3)))))))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D3 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D3)))))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C)))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C)))))
% 6.79/7.01 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K)) J)))))))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K)) J)))))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K)) J)))))))))
% 6.79/7.01 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K)) J)))))))))
% 6.79/7.01 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N) (@ (@ tptp.ord_less_eq_real I) (@ (@ tptp.minus_minus_real N) K)))))
% 6.79/7.01 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N) (@ (@ tptp.ord_less_eq_rat I) (@ (@ tptp.minus_minus_rat N) K)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N) K)))))
% 6.79/7.01 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N) K)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B)) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B)) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B)) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B)) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y2)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y2) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) A)) B))))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y2)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y2) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) A)) B))))))
% 6.79/7.01 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y2)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y2) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) A)) B))))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.minus_minus_real X2) Y2)))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) Y2)) (@ (@ tptp.minus_minus_rat X2) Y2)))))
% 6.79/7.01 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) Y2)) (@ (@ tptp.minus_minus_int X2) Y2)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D2))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D2))))
% 6.79/7.01 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D2))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y2) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X2) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y2) (@ _let_1 Q22))))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_real (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_num (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_int (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) A)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) A)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A)))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N5)) (@ F N))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N5))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.minus_minus_nat J) I) K) (= J (@ (@ tptp.plus_plus_nat K) I))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I)))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 6.79/7.01 (assert (forall ((J tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I) K)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 6.79/7.01 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K3)))))))
% 6.79/7.01 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M3) K2)))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.79/7.01 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.79/7.01 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.79/7.01 (assert (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.79/7.01 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 6.79/7.01 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 6.79/7.01 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1))))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 6.79/7.01 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) A)))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) A)))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) A)))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.79/7.01 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.79/7.01 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.79/7.01 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C))))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D2))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D2))))
% 6.79/7.01 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D2))))
% 6.79/7.01 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D2))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D2))))
% 6.79/7.01 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D2))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) X2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X2) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))
% 6.79/7.01 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))
% 6.79/7.01 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y2) N)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (exists ((Q3 tptp.nat)) (= X2 (@ (@ tptp.plus_plus_nat Y2) (@ (@ tptp.times_times_nat N) Q3))))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (forall ((S3 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S3))))))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (forall ((S3 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S3))))))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N)) Q2))) (@ _let_1 N)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N)))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I) K))))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.79/7.01 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.79/7.01 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.79/7.01 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M) N)))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y2)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y2) X2)) _let_1)))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y2)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y2) X2)) _let_1)))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y2)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y2) X2)) _let_1)))))
% 6.79/7.01 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y2)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y2) X2)) _let_1)))))
% 6.79/7.01 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.79/7.01 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N) Q2))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.79/7.01 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) Y2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_rat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat (@ _let_2 N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y2)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y2) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y2)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y2)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y2)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y2)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y2) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y2)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y2)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y2) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y2)))))))
% 6.79/7.01 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (X tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) (@ (@ tptp.vEBT_VEBT_high X) N2))) (@ (@ tptp.vEBT_VEBT_low X) N2)))))
% 6.79/7.01 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.79/7.01 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.79/7.01 (assert (forall ((L2 tptp.num) (R tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L2) (@ (@ tptp.product_Pair_nat_nat Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R))))))))))
% 6.79/7.01 (assert (forall ((L2 tptp.num) (R tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L2) (@ (@ tptp.product_Pair_int_int Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_int L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R))))))))))
% 6.79/7.01 (assert (forall ((L2 tptp.num) (R tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L2) (@ (@ tptp.produc1086072967326762835nteger Q2) R)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R))))))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N)))))))
% 6.79/7.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N))))))
% 6.79/7.01 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N)) N)) (@ (@ tptp.modulo_modulo_nat A2) N)))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.79/7.01 (assert (forall ((X23 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X23) (@ tptp.bit0 Y22)) (= X23 Y22))))
% 6.79/7.01 (assert (forall ((X33 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X33) (@ tptp.bit1 Y32)) (= X33 Y32))))
% 6.79/7.01 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Node Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W))))))
% 6.79/7.01 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))) tptp.one_one_int))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Y2) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat Y2) X2) (forall ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat Z4) X2)) (@ (@ tptp.ord_less_eq_nat Z4) Y2)))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Y2) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat X2) Y2) (forall ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat X2) Z4)) (@ (@ tptp.ord_less_eq_nat Y2) Z4)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.int) (N tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N)) N)) (@ (@ tptp.modulo_modulo_int A2) N)))))
% 6.79/7.01 (assert (forall ((Z tptp.extended_enat) (Y2 tptp.extended_enat) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y2) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y2) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y2)) Z))))))
% 6.79/7.01 (assert (forall ((X2 tptp.product_prod_num_num)) (=> (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M4 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit0 N3))))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit1 N3))))) (=> (forall ((M4 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit0 N3))))) (not (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit1 N3))))))))))))))))
% 6.79/7.01 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.79/7.01 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.79/7.01 (assert (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (@ (@ tptp.ord_less_eq_num A) B)) (not (@ (@ tptp.ord_less_eq_num B) A)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.79/7.01 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.79/7.01 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.79/7.01 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.79/7.01 (assert (forall ((B4 tptp.real) (A4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B4) A4)) (@ (@ tptp.ord_less_real A4) B4))))
% 6.79/7.01 (assert (forall ((B4 tptp.rat) (A4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B4) A4)) (@ (@ tptp.ord_less_rat A4) B4))))
% 6.79/7.01 (assert (forall ((B4 tptp.num) (A4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B4) A4)) (@ (@ tptp.ord_less_num A4) B4))))
% 6.79/7.01 (assert (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))))
% 6.79/7.01 (assert (forall ((B4 tptp.int) (A4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B4) A4)) (@ (@ tptp.ord_less_int A4) B4))))
% 6.79/7.01 (assert (forall ((X23 tptp.num)) (not (= tptp.one (@ tptp.bit0 X23)))))
% 6.79/7.01 (assert (forall ((X23 tptp.num) (X33 tptp.num)) (not (= (@ tptp.bit0 X23) (@ tptp.bit1 X33)))))
% 6.79/7.01 (assert (forall ((X33 tptp.num)) (not (= tptp.one (@ tptp.bit1 X33)))))
% 6.79/7.01 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real B) A)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I4)))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X Bool)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I4)))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I4)))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I4)))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X2 tptp.product_prod_nat_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I2)))) (=> (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X2)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X2 tptp.complex)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I2)))) (=> (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs2)) (@ P X2)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I2)))) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs2)) (@ P X2)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X2)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X2 Bool)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I2)))) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ P X2)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I2)))) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ P X2)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X2 tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I2)))) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ P X2)))))
% 6.79/7.01 (assert (forall ((X2 tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs2)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I4) X2))))))
% 6.79/7.01 (assert (forall ((X2 tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I4) X2))))))
% 6.79/7.01 (assert (forall ((X2 tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I4) X2))))))
% 6.79/7.01 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I4) X2))))))
% 6.79/7.01 (assert (forall ((X2 Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I4) X2))))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I4) X2))))))
% 6.79/7.01 (assert (forall ((X2 tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I4) X2))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_int Xs2) N))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N)) (@ tptp.set_Pr5648618587558075414at_nat Xs2)))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs2) N)) (@ tptp.set_complex2 Xs2)))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N)) (@ tptp.set_real2 Xs2)))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N)) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N)) (@ tptp.set_o2 Xs2)))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N)) (@ tptp.set_nat2 Xs2)))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N)) (@ tptp.set_int2 Xs2)))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (= N (@ tptp.suc (@ tptp.suc Va))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))))))))))
% 6.79/7.01 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.79/7.01 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.79/7.01 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.79/7.01 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.79/7.01 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.79/7.01 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.79/7.01 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.79/7.01 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.79/7.01 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.79/7.01 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2))))
% 6.79/7.01 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) B3) (forall ((X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) B3) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 (@ tptp.set_complex2 Xs2)) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) B3) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 (@ tptp.set_real2 Xs2)) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) B3) (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs2)) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) B3) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 Xs2)) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) B3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 Xs2)) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs2 Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (not (= Xs2 Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (not (= Xs2 Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys))) (not (= Xs2 Ys)))))
% 6.79/7.01 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy)) tptp.one_one_nat)))
% 6.79/7.01 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.79/7.01 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.79/7.01 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.79/7.01 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.79/7.01 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.79/7.01 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.79/7.01 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.79/7.01 (assert (forall ((P (-> tptp.list_o Bool)) (Xs2 tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.79/7.01 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs2 tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.79/7.01 (assert (forall ((P (-> tptp.list_int Bool)) (Xs2 tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) (@ (@ tptp.nth_VEBT_VEBT Ys) I2)))) (= Xs2 Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I2) (@ (@ tptp.nth_o Ys) I2)))) (= Xs2 Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I2) (@ (@ tptp.nth_nat Ys) I2)))) (= Xs2 Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I2) (@ (@ tptp.nth_int Ys) I2)))) (= Xs2 Ys)))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 tptp.vEBT_VEBT)) (@ (@ P I4) X5)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 Bool)) (@ (@ P I4) X5)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_o Xs) I4)))))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 tptp.nat)) (@ (@ P I4) X5)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_nat Xs) I4)))))))))
% 6.79/7.01 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 tptp.int)) (@ (@ P I4) X5)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_int Xs) I4)))))))))
% 6.79/7.01 (assert (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z5 tptp.list_VEBT_VEBT)) (= Y5 Z5)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) (@ (@ tptp.nth_VEBT_VEBT Ys3) I4))))))))
% 6.79/7.01 (assert (= (lambda ((Y5 tptp.list_o) (Z5 tptp.list_o)) (= Y5 Z5)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) (@ (@ tptp.nth_o Ys3) I4))))))))
% 6.79/7.01 (assert (= (lambda ((Y5 tptp.list_nat) (Z5 tptp.list_nat)) (= Y5 Z5)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) (@ (@ tptp.nth_nat Ys3) I4))))))))
% 6.79/7.01 (assert (= (lambda ((Y5 tptp.list_int) (Z5 tptp.list_int)) (= Y5 Z5)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) (@ (@ tptp.nth_int Ys3) I4))))))))
% 6.79/7.01 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M4) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))))
% 6.79/7.01 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 6.79/7.01 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 6.79/7.01 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 6.79/7.01 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2))) _let_1) TreeList) Summary)))))
% 6.79/7.01 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.79/7.01 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (forall ((Y tptp.product_prod_nat_nat)) (not (= X2 (@ tptp.some_P7363390416028606310at_nat Y)))) (= X2 tptp.none_P5556105721700978146at_nat))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_nat)) (= (forall ((Y tptp.nat)) (not (= X2 (@ tptp.some_nat Y)))) (= X2 tptp.none_nat))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_num)) (= (forall ((Y tptp.num)) (not (= X2 (@ tptp.some_num Y)))) (= X2 tptp.none_num))))
% 6.79/7.01 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (not (= X2 tptp.none_P5556105721700978146at_nat)) (exists ((Y tptp.product_prod_nat_nat)) (= X2 (@ tptp.some_P7363390416028606310at_nat Y))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_nat)) (= (not (= X2 tptp.none_nat)) (exists ((Y tptp.nat)) (= X2 (@ tptp.some_nat Y))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_num)) (= (not (= X2 tptp.none_num)) (exists ((Y tptp.num)) (= X2 (@ tptp.some_num Y))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.some_nat M) (@ tptp.vEBT_vebt_mint T)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X2))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X2) Y2) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)) (@ tptp.some_nat Z)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.79/7.01 (assert (forall ((X23 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X23) (@ tptp.some_P7363390416028606310at_nat Y22)) (= X23 Y22))))
% 6.79/7.01 (assert (forall ((X23 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.some_nat X23) (@ tptp.some_nat Y22)) (= X23 Y22))))
% 6.79/7.01 (assert (forall ((X23 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.some_num X23) (@ tptp.some_num Y22)) (= X23 Y22))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.ord_less_eq_nat Mini) X2))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.ord_less_eq_nat X2) Maxi))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2)))))
% 6.79/7.01 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 6.79/7.01 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 6.79/7.01 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 6.79/7.01 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P K) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I))))))
% 6.79/7.01 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I))))))
% 6.79/7.01 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.79/7.01 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.79/7.01 (assert (forall ((X23 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X23)))))
% 6.79/7.01 (assert (forall ((X23 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X23)))))
% 6.79/7.01 (assert (forall ((X23 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X23)))))
% 6.79/7.01 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X23 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X23)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.79/7.01 (assert (forall ((Option tptp.option_nat) (X23 tptp.nat)) (=> (= Option (@ tptp.some_nat X23)) (not (= Option tptp.none_nat)))))
% 6.79/7.01 (assert (forall ((Option tptp.option_num) (X23 tptp.num)) (=> (= Option (@ tptp.some_num X23)) (not (= Option tptp.none_num)))))
% 6.79/7.01 (assert (forall ((Y2 tptp.option4927543243414619207at_nat)) (=> (not (= Y2 tptp.none_P5556105721700978146at_nat)) (not (forall ((X22 tptp.product_prod_nat_nat)) (not (= Y2 (@ tptp.some_P7363390416028606310at_nat X22))))))))
% 6.79/7.01 (assert (forall ((Y2 tptp.option_nat)) (=> (not (= Y2 tptp.none_nat)) (not (forall ((X22 tptp.nat)) (not (= Y2 (@ tptp.some_nat X22))))))))
% 6.79/7.01 (assert (forall ((Y2 tptp.option_num)) (=> (not (= Y2 tptp.none_num)) (not (forall ((X22 tptp.num)) (not (= Y2 (@ tptp.some_num X22))))))))
% 6.79/7.01 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P4 tptp.none_P5556105721700978146at_nat) (exists ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 6.79/7.01 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (exists ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (or (@ P4 tptp.none_nat) (exists ((X tptp.nat)) (@ P4 (@ tptp.some_nat X)))))))
% 6.79/7.01 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (exists ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))))
% 6.79/7.01 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P4 tptp.none_P5556105721700978146at_nat) (forall ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 6.79/7.01 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (forall ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (and (@ P4 tptp.none_nat) (forall ((X tptp.nat)) (@ P4 (@ tptp.some_nat X)))))))
% 6.79/7.01 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (forall ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y2 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y2 tptp.none_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y2 (@ tptp.some_nat B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y2 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y2 tptp.none_num) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.num)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y2 (@ tptp.some_num B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.nat) (B5 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_nat A5)) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y2 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y2 tptp.none_nat) _let_1) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (= X2 (@ tptp.some_nat A5)) (=> (= Y2 (@ tptp.some_nat B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y2 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y2 tptp.none_num) _let_1) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (=> (= X2 (@ tptp.some_nat A5)) (=> (= Y2 (@ tptp.some_num B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_num A5)) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y2 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y2 tptp.none_nat) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.nat)) (=> (= X2 (@ tptp.some_num A5)) (=> (= Y2 (@ tptp.some_nat B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.79/7.01 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y2 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y2))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y2 tptp.none_num) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= X2 (@ tptp.some_num A5)) (=> (= Y2 (@ tptp.some_num B5)) (@ (@ P X2) Y2)))) _let_1))))))
% 6.79/7.01 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 6.79/7.01 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P I2) (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int))))) (@ P I))))))
% 6.79/7.01 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 6.79/7.01 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 6.79/7.01 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I tptp.int)) (=> (@ P K) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P I2) (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int))))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I))))))
% 6.79/7.01 (assert (forall ((X23 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X23)) X23)))
% 6.79/7.01 (assert (forall ((X23 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X23)) X23)))
% 6.79/7.01 (assert (forall ((X23 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X23)) X23)))
% 6.79/7.01 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 6.79/7.01 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 6.79/7.01 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 6.79/7.01 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X2) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) tptp.none_nat)))))))
% 6.79/7.01 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X2) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) tptp.none_nat)))))))
% 6.79/7.01 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X2) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ tptp.some_nat Ma))))))
% 6.79/7.01 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat X2) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ tptp.some_nat Mi))))))
% 6.79/7.01 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 6.79/7.01 (assert (= tptp.ord_less_nat (lambda ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Y2)) (@ (@ tptp.ord_less_nat Y2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Y2)) (@ (@ tptp.ord_less_nat Y2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X2) Sx)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X2) Sx)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Sx)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Px)))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_eq_nat Ma) X2) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X2) tptp.none_nat))))))
% 6.79/7.01 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Ma))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Mi))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X2) Y2) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)) (@ tptp.some_nat Z)))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y2) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)) (@ tptp.some_nat Z)))))
% 6.79/7.01 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.79/7.01 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.none_nat)))
% 6.79/7.01 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.none_nat)))
% 6.79/7.01 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.79/7.01 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.79/7.01 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.79/7.01 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat F) (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F A) B)))))
% 6.79/7.01 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F A) B)))))
% 6.79/7.01 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F) (@ tptp.some_nat A)) (@ tptp.some_nat B)) (@ tptp.some_nat (@ (@ F A) B)))))
% 6.79/7.01 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y2 tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X2) Xa2) Xb) Y2) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa2 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A5 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A5)) (forall ((B5 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B5)) (not (= Y2 (@ tptp.some_P7363390416028606310at_nat (@ (@ X2 A5) B5)))))))))))))))
% 6.79/7.01 (assert (forall ((X2 (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X2) Xa2) Xb) Y2) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A5 tptp.num)) (=> (= Xa2 (@ tptp.some_num A5)) (forall ((B5 tptp.num)) (=> (= Xb (@ tptp.some_num B5)) (not (= Y2 (@ tptp.some_num (@ (@ X2 A5) B5)))))))))))))))
% 6.79/7.01 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y2 tptp.option_nat)) (let ((_let_1 (not (= Y2 tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X2) Xa2) Xb) Y2) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A5 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A5)) (forall ((B5 tptp.nat)) (=> (= Xb (@ tptp.some_nat B5)) (not (= Y2 (@ tptp.some_nat (@ (@ X2 A5) B5)))))))))))))))
% 6.79/7.01 (assert (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw) (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)))
% 6.79/7.01 (assert (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw) (@ tptp.some_num V)) tptp.none_num) tptp.none_num)))
% 6.79/7.01 (assert (forall ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw) (@ tptp.some_nat V)) tptp.none_nat) tptp.none_nat)))
% 6.79/7.01 (assert (forall ((X2 tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V2 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X3)) (@ tptp.some_P7363390416028606310at_nat Y3)))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat Bool)) (Uv2 tptp.option_nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Y3 tptp.nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X3)) (@ tptp.some_nat Y3)))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.produc7036089656553540234on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num Bool)) (Uv2 tptp.option_num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num Bool)) (X3 tptp.num) (Y3 tptp.num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X3)) (@ tptp.some_num Y3)))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.produc5542196010084753463at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A5)) (@ tptp.some_P7363390416028606310at_nat B5)))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A5)) (@ tptp.some_nat B5)))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.produc1193250871479095198on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A5 tptp.num) (B5 tptp.num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A5)) (@ tptp.some_num B5)))))))))))
% 6.79/7.01 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat Z4) X) (@ (@ tptp.ord_less_eq_nat Z4) Y))))))))
% 6.79/7.01 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat X) Z4) (@ (@ tptp.ord_less_eq_nat Y) Z4))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B3) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B3))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A2) B3) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B3))))
% 6.79/7.01 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X2) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.79/7.01 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X2) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.79/7.01 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.79/7.01 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs2) Ys)) N) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs2) Ys)) N) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Z tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A2) Z) (=> (@ tptp.finite_finite_nat B3) (=> (= A2 B3) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A2) X2) X_1))))))))
% 6.79/7.01 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A2) Z) (=> (@ tptp.finite_finite_nat A2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A2) X2) X_1)))))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2))) (let ((_let_12 (@ (@ tptp.ord_less_nat X2) Mi))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.79/7.01 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs2) (@ (@ tptp.ord_less_nat X4) A))))))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs2) (@ (@ tptp.ord_less_nat A) X4))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_set_nat A2) B3)))))
% 6.79/7.01 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3))) (= (@ (@ tptp.minus_1356011639430497352at_nat _let_1) B3) _let_1))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B3) _let_1))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X2) Y)))) tptp.bot_bot_set_nat)))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X2)))) tptp.bot_bot_set_nat)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs2))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs2))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs2))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) tptp.bot_bot_set_int) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) tptp.bot_bot_set_real) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A2) tptp.bot_bo2099793752762293965at_nat) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A2) tptp.bot_bot_set_int)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real tptp.bot_bot_set_real) A2) tptp.bot_bot_set_real)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat tptp.bot_bo2099793752762293965at_nat) A2) tptp.bot_bo2099793752762293965at_nat)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A2) tptp.bot_bot_set_nat)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) A2) tptp.bot_bot_set_int)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) A2) tptp.bot_bot_set_real)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A2) A2) tptp.bot_bo2099793752762293965at_nat)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) A2) tptp.bot_bot_set_nat)))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.79/7.01 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.79/7.01 (assert (forall ((C tptp.real)) (= (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C)) (@ tptp.times_times_real C))))
% 6.79/7.01 (assert (forall ((C tptp.rat)) (= (lambda ((X tptp.rat)) (@ (@ tptp.times_times_rat X) C)) (@ tptp.times_times_rat C))))
% 6.79/7.01 (assert (forall ((C tptp.nat)) (= (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C)) (@ tptp.times_times_nat C))))
% 6.79/7.01 (assert (forall ((C tptp.int)) (= (lambda ((X tptp.int)) (@ (@ tptp.times_times_int X) C)) (@ tptp.times_times_int C))))
% 6.79/7.01 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.79/7.01 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ _let_1 A2)))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)) (@ _let_1 A2)))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ _let_1 A2)))))
% 6.79/7.01 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) (@ _let_1 A2)))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ _let_1 A2)))))
% 6.79/7.01 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (not (@ _let_1 B3))))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)) (not (@ _let_1 B3))))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (not (@ _let_1 B3))))))
% 6.79/7.01 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) (not (@ _let_1 B3))))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (not (@ _let_1 B3))))))
% 6.79/7.01 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.79/7.01 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.79/7.01 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.79/7.01 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.79/7.01 (assert (= tptp.minus_1356011639430497352at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.79/7.01 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.79/7.01 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ tptp.collect_complex (@ (@ tptp.minus_8727706125548526216plex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B6)))))))
% 6.79/7.01 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6)))))))
% 6.79/7.01 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.minus_1139252259498527702_nat_o (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A6))) (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) B6)))))))
% 6.79/7.01 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6)))))))
% 6.79/7.01 (assert (= tptp.minus_1356011639430497352at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (@ (@ tptp.minus_2270307095948843157_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A6))) (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) B6)))))))
% 6.79/7.01 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A2) B3) (exists ((B5 tptp.complex)) (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B3) (exists ((B5 tptp.real)) (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (exists ((B5 tptp.int)) (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B3) A2))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) B3) (exists ((B5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat B5) (@ (@ tptp.minus_1356011639430497352at_nat B3) A2))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (exists ((B5 tptp.nat)) (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B3) A2))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs) N))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (= (@ tptp.size_size_list_o Xs) N))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (= (@ tptp.size_size_list_int Xs) N))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (= (@ tptp.size_size_list_nat Xs) N))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))))))
% 6.79/7.01 (assert (= (lambda ((X tptp.complex)) X) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.79/7.01 (assert (= (lambda ((X tptp.real)) X) (@ tptp.times_times_real tptp.one_one_real)))
% 6.79/7.01 (assert (= (lambda ((X tptp.rat)) X) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.79/7.01 (assert (= (lambda ((X tptp.nat)) X) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.79/7.01 (assert (= (lambda ((X tptp.int)) X) (@ tptp.times_times_int tptp.one_one_int)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))))
% 6.79/7.01 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.79/7.01 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.79/7.01 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 6.79/7.01 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 6.79/7.01 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 6.79/7.01 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 6.79/7.01 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 6.79/7.01 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z) _let_2)) _let_2))))))
% 6.79/7.01 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z) _let_2)) _let_2))))))
% 6.79/7.01 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))))
% 6.79/7.01 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z) _let_2)) _let_2))))))
% 6.79/7.01 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z) _let_2)) _let_2))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A2) tptp.bot_bot_set_real))))
% 6.79/7.01 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A6) B6) (= A6 B6)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_set_nat B3) C4) (@ (@ tptp.ord_less_set_nat A2) C4)))))
% 6.79/7.01 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B6) (not (@ (@ tptp.ord_less_eq_set_nat B6) A6))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C4) (@ _let_1 C4))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (@ (@ tptp.ord_less_eq_set_nat A2) B3))))
% 6.79/7.01 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B6) (not (= A6 B6))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (@ (@ tptp.ord_less_eq_set_nat B3) A2))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (D4 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) C4) (=> (@ (@ tptp.ord_le3146513528884898305at_nat D4) B3) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) (@ (@ tptp.minus_1356011639430497352at_nat C4) D4))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (C4 tptp.set_nat) (D4 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_set_nat C4) D4))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) A2)))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) C4) (= (@ (@ tptp.minus_1356011639430497352at_nat B3) (@ (@ tptp.minus_1356011639430497352at_nat C4) A2)) A2)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C4) (= (@ (@ tptp.minus_minus_set_nat B3) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X2) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (=> (not (= X2 Mi)) (=> (not (= X2 Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))))))))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high X2) _let_4))) (let ((_let_6 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_3) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= X2 Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (= X2 Ma)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ _let_6 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_5)) (@ (@ tptp.vEBT_VEBT_low X2) _let_4)))) tptp.one_one_nat)))))))))))))))))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) Mi) X2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_5))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_6))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary) _let_5)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))
% 6.79/7.01 (assert (forall ((Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X2))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) Mi) X2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_5) (@ (@ tptp.vEBT_VEBT_low _let_3) _let_2))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_5)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))))))))
% 6.79/7.01 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))))
% 6.79/7.01 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.power_power_real Z4) N) tptp.one_one_real)))))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B3)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B3)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B3)))))
% 6.79/7.01 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (= (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B3)) (@ tptp.finite_finite_int A2)))))
% 6.79/7.01 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.79/7.01 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B3) (= (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) (@ tptp.finite6177210948735845034at_nat A2)))))
% 6.79/7.01 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ tptp.finite_finite_nat A2)))))
% 6.79/7.01 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc)) X2) (or (= X2 Mi) (= X2 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4)))))))))
% 6.79/7.01 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 6.79/7.01 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X2))))
% 6.79/7.01 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X2))))
% 6.79/7.01 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X) (@ (@ tptp.vEBT_VEBT_membermima T2) X)))))
% 6.79/7.01 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X2) (@ (@ tptp.vEBT_VEBT_membermima Tree) X2))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 6.79/7.01 (assert (= tptp.ord_le7866589430770878221at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le549003669493604880_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A6))) (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) B6))))))
% 6.79/7.01 (assert (= tptp.ord_less_set_complex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ (@ tptp.ord_less_complex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B6))))))
% 6.79/7.01 (assert (= tptp.ord_less_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6))))))
% 6.79/7.01 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6))))))
% 6.79/7.01 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_less_set_complex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.79/7.01 (assert (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X4) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X4)) N3)))))))
% 6.79/7.01 (assert (forall ((M7 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M7) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_o)) (=> (@ (@ tptp.member_list_o X4) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X4)) N3)))))))
% 6.79/7.01 (assert (forall ((M7 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M7) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X4)) N3)))))))
% 6.79/7.01 (assert (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_int)) (=> (@ (@ tptp.member_list_int X4) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X4)) N3)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((B7 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B7) A7) (@ P B7))) (@ P A7)))) (@ P A2)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((B7 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B7) A7) (@ P B7))) (@ P A7)))) (@ P A2)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (forall ((B7 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex B7) A7) (@ P B7))) (@ P A7)))) (@ P A2)))))
% 6.79/7.01 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary)) X2) tptp.one_one_nat)))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) Y2)) tptp.one_one_nat)))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real A) X3) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (@ (@ tptp.ord_less_eq_set_nat A) X3) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (@ (@ tptp.ord_less_eq_rat A) X3) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (@ (@ tptp.ord_less_eq_num A) X3) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat A) X3) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int A) X3) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real X3) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (@ (@ tptp.ord_less_eq_set_nat X3) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (@ (@ tptp.ord_less_eq_rat X3) A) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (@ (@ tptp.ord_less_eq_num X3) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat X3) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int X3) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) L2)) tptp.one_one_nat)))))
% 6.79/7.01 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int)) (=> (@ tptp.finite_finite_int T3) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S2) T3)))))))
% 6.79/7.01 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S2) T3)))))))
% 6.79/7.01 (assert (forall ((T3 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat T3) (=> (not (@ tptp.finite6177210948735845034at_nat S2)) (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat S2) T3)))))))
% 6.79/7.01 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat T3) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S2) T3)))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (let ((_let_1 (not (= Y2 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa2) Y2) (=> (forall ((Uu2 Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uu2) B5)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B5 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y2 tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc N3))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y2 (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (let ((_let_1 (not (= Y2 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa2) Y2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A5 Bool)) (=> (exists ((Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A5 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y2 tptp.none_nat))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (=> (exists ((Va3 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va3)))) (not (and (=> B5 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y2 tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y2 (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.complex)) (Y2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y2 I4)) tptp.one_one_complex))))))))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.complex)) (Y2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y2 I4)) tptp.one_one_complex))))))))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.complex)) (Y2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y2 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y2 I4)) tptp.one_one_complex))))))))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.complex)) (Y2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y2 I4) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y2 I4)) tptp.one_one_complex))))))))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.real)) (Y2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y2 I4)) tptp.one_one_real))))))))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.real)) (Y2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y2 I4)) tptp.one_one_real))))))))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.real)) (Y2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y2 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y2 I4)) tptp.one_one_real))))))))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.real)) (Y2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y2 I4) tptp.one_one_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y2 I4)) tptp.one_one_real))))))))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (Y2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.one_one_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_rat (@ X2 I4)) (@ Y2 I4)) tptp.one_one_rat))))))))))
% 6.79/7.01 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.one_one_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_rat (@ X2 I4)) (@ Y2 I4)) tptp.one_one_rat))))))))))
% 6.79/7.01 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t X2) Xa2) Y2) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= Y2 (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))))) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) _let_1) (=> (=> (exists ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) (not (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_5))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (= Y2 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_6))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary2) _let_5)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))))))))))
% 6.79/7.01 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.79/7.01 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5)))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5))))))
% 6.79/7.01 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2))))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.79/7.01 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))))
% 6.79/7.01 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 6.79/7.01 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 6.79/7.01 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 6.79/7.01 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 6.79/7.01 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.79/7.01 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.79/7.01 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X2) Y2)) (and (= X2 tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat)))))
% 6.79/7.01 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y2) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat)))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.79/7.01 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.79/7.01 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.79/7.01 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.79/7.01 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.79/7.01 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.79/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 6.79/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 6.79/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 6.79/7.02 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 6.79/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.79/7.02 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.79/7.02 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.79/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.79/7.02 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))))
% 6.79/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))))
% 6.79/7.02 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_real B) A))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat B) A))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_int B) A))))
% 6.79/7.02 (assert (forall ((A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.79/7.02 (assert (forall ((A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.79/7.02 (assert (forall ((A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.79/7.02 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.79/7.02 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.79/7.02 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.79/7.02 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.79/7.02 (assert (forall ((C tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.times_times_complex C) A) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.79/7.02 (assert (forall ((C tptp.real) (A tptp.real)) (= (= (@ (@ tptp.times_times_real C) A) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.79/7.02 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.79/7.02 (assert (forall ((C tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.79/7.02 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.79/7.02 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.79/7.02 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.79/7.02 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.79/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real)))))
% 6.79/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat)))))
% 6.79/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int)))))
% 6.79/7.02 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.79/7.02 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.79/7.02 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.79/7.02 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.79/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.79/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.79/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.79/7.02 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.79/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) B) A))))
% 6.79/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))))
% 6.79/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) B) A))))
% 6.79/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))))
% 6.79/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.79/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.79/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.79/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.79/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.79/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.79/7.02 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) A) B))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) A) B))))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) A) B))))
% 6.79/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 6.79/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))))
% 6.79/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 6.79/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B)))))))))
% 6.79/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))))
% 6.79/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 6.79/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 6.79/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 6.79/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.79/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))))
% 6.79/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.79/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 6.79/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 6.79/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 6.79/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.79/7.02 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.79/7.02 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.79/7.02 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.79/7.02 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.79/7.02 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.79/7.02 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.79/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.79/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.79/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.79/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.79/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.79/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.79/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))))
% 6.79/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 6.79/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N)) (and (= M _let_1) (= N _let_1))))))
% 6.79/7.02 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))))
% 6.79/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.79/7.02 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))))
% 6.79/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))))
% 6.79/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.79/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 6.79/7.02 (assert (forall ((X2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X2) M) _let_1) (or (= M tptp.zero_zero_nat) (= X2 _let_1))))))
% 6.79/7.02 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.79/7.02 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X2) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 6.79/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N)))))))))
% 6.79/7.02 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.79/7.02 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.79/7.02 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.79/7.02 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.79/7.02 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.79/7.02 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real A) B)))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real B) A)))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B) A)))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ _let_1 B))))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))))
% 6.79/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.79/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.79/7.02 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.79/7.02 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.79/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.79/7.02 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.82/7.02 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 6.82/7.02 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.02 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.82/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M)) N) M))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N)) N) M))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.82/7.02 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 6.82/7.02 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.82/7.02 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.82/7.02 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.82/7.02 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.82/7.02 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y2) _let_1)) (= X2 Y2))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y2) _let_1)) (= X2 Y2))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (= (@ (@ tptp.power_power_nat X2) _let_1) (@ (@ tptp.power_power_nat Y2) _let_1)) (= X2 Y2))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y2) _let_1)) (= X2 Y2))))))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int))))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.82/7.02 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (forall ((X2 tptp.complex)) (= (= tptp.zero_zero_complex X2) (= X2 tptp.zero_zero_complex))))
% 6.82/7.02 (assert (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat)) (= (= tptp.zero_zero_rat X2) (= X2 tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((X2 tptp.int)) (= (= tptp.zero_zero_int X2) (= X2 tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X3)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3)) X3)))))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X2) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y2 (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y2 (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.82/7.02 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))))
% 6.82/7.02 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) Deg3))))))))
% 6.82/7.02 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X2))) (let ((_let_4 (= X2 tptp.one_one_nat))) (let ((_let_5 (= X2 tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X2) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.82/7.02 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)))
% 6.82/7.02 (assert (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.82/7.02 (assert (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E2))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.82/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (= A B)))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (= A B)))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (= A B)))))
% 6.82/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.82/7.02 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))))
% 6.82/7.02 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B tptp.zero_zero_complex))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))))
% 6.82/7.02 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.82/7.02 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.82/7.02 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.82/7.02 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.82/7.02 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.82/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.82/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.82/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.82/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.82/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.82/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.82/7.02 (assert (= (lambda ((Y5 tptp.complex) (Z5 tptp.complex)) (= Y5 Z5)) (lambda ((A3 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B2) tptp.zero_zero_complex))))
% 6.82/7.02 (assert (= (lambda ((Y5 tptp.real) (Z5 tptp.real)) (= Y5 Z5)) (lambda ((A3 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B2) tptp.zero_zero_real))))
% 6.82/7.02 (assert (= (lambda ((Y5 tptp.rat) (Z5 tptp.rat)) (= Y5 Z5)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B2) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (= (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B2) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.82/7.02 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.82/7.02 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.82/7.02 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X3) Y3) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P M) N))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.nat)) (=> (not (= Y2 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y2 (@ tptp.suc Nat3))))))))
% 6.82/7.02 (assert (forall ((Nat tptp.nat) (X23 tptp.nat)) (=> (= Nat (@ tptp.suc X23)) (not (= Nat tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.82/7.02 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((X23 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X23)))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (=> (not (= X2 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va3 tptp.nat)) (not (= X2 (@ tptp.suc (@ tptp.suc Va3))))))))))
% 6.82/7.02 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.82/7.02 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.82/7.02 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2))))))) (@ P N)))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 6.82/7.02 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ tptp.vEBT_Leaf A) B)) X2) (@ _let_1 (@ (@ (@ tptp.if_nat (= X2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 6.82/7.02 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.82/7.02 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.82/7.02 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.82/7.02 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.82/7.02 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.82/7.02 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.complex)) (Y2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_complex))))))))))
% 6.82/7.02 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.complex)) (Y2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_complex))))))))))
% 6.82/7.02 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.complex)) (Y2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_complex))))))))))
% 6.82/7.02 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.complex)) (Y2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_complex))))))))))
% 6.82/7.02 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.real)) (Y2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_real))))))))))
% 6.82/7.02 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.real)) (Y2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_real))))))))))
% 6.82/7.02 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.real)) (Y2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_real))))))))))
% 6.82/7.02 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.real)) (Y2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_real))))))))))
% 6.82/7.02 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (Y2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_rat))))))))))
% 6.82/7.02 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y2 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X2 I4)) (@ Y2 I4)) tptp.zero_zero_rat))))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))))
% 6.82/7.02 (assert (forall ((A Bool) (Uw Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))))
% 6.82/7.02 (assert (forall ((B Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))
% 6.82/7.02 (assert (forall ((B Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X2) Y2) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X2) Y2) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y2) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X2) Y2) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y2) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X2) Y2) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_real X2) Y2) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_rat X2) Y2) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_nat X2) Y2) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_int X2) Y2) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real B) A))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y2)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X2) Y2)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X2) Y2)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y2) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C2 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real A) C))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat A) C))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y2)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.82/7.02 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.82/7.02 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y2)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)) (not (= C tptp.zero_zero_real))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C tptp.zero_zero_rat))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.82/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (= (@ (@ tptp.times_times_complex A) C) B)))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C)) (= (@ (@ tptp.times_times_real A) C) B)))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))))
% 6.82/7.02 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (= B (@ (@ tptp.times_times_complex A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C) A) (= B (@ (@ tptp.times_times_real A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B) (= A (@ (@ tptp.divide1717551699836669952omplex B) C))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B) (= A (@ (@ tptp.divide_divide_real B) C))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))))
% 6.82/7.02 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B) C) A)))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B) C) A)))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))))
% 6.82/7.02 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.82/7.02 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X2) Y2) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X2) Z) (@ (@ tptp.times_times_complex W) Y2)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X2) Y2) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X2) Z) (@ (@ tptp.times_times_real W) Y2)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X2) Y2) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X2) Z) (@ (@ tptp.times_times_rat W) Y2)))))))
% 6.82/7.02 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) A))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B)) A))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B)) A))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B)) B))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B)) B))))
% 6.82/7.02 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.82/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.82/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M3 tptp.nat)) (= N (@ tptp.suc M3))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ tptp.vEBT_Leaf A) B)) X2) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 6.82/7.02 (assert (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf false) false)) tptp.one_one_nat))
% 6.82/7.02 (assert (forall ((Uv Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf true) Uv)) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((Uu Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf Uu) true)) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((X23 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((X23 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K3) (not (@ P I3)))) (@ P K3)))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.plus_plus_nat I) K3) J))))))
% 6.82/7.02 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.82/7.02 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.82/7.02 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.82/7.02 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.82/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.82/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D2) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (@ (@ tptp.times_times_nat D2) Q3))))))
% 6.82/7.02 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X3)))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3)) X3)))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X3)))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2)) X3)))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2)) X3)))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A5 Bool) (Uw2 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A5 Bool) (B5 Bool) (Va3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) (@ tptp.suc (@ tptp.suc Va3)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve)) Vf)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X3)))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B5 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B5)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N3))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2)) Ve)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2)) X3))))))))))))
% 6.82/7.02 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts2) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 6.82/7.02 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux))))
% 6.82/7.02 (assert (forall ((B Bool) (A Bool) (Va tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va))))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2)))))))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.vEBT_Leaf A) B)) X2) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= X2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))))))))))
% 6.82/7.02 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.none_nat)))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X2) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real Y2) E2)))) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat Y2) E2)))) (@ (@ tptp.ord_less_eq_rat X2) Y2))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (X2 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y2) W))))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_eq_rat X2) Y2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y2) W))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y2) W))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat X2) Y2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y2) W))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y2) W)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_rat X2) Y2) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y2) W)))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) A)))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) A)))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) A)))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) A)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.one_one_real))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Y2)) X2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Y2)) X2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Y2)) X2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y2) X2)) X2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y2) X2)) X2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y2) X2)) X2)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2)))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2))) tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2))) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2))) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y2 tptp.zero_zero_real))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y2) Y2))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y2 tptp.zero_zero_rat))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y2) Y2))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y2 tptp.zero_zero_int))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real Z) Y2)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.times_times_rat Z) Y2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y2)) X2) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y2)) X2) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B)) (= A tptp.zero_zero_real))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.one_one_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))))
% 6.82/7.02 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.82/7.02 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.82/7.02 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.82/7.02 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.82/7.02 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Z)) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y2) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real Y2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat Y2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X2 tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y2))) Y2)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y2))) Y2)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y2))) Y2)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.complex) (X2 tptp.complex) (Z tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y2))) Y2)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y2)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y2))) Y2)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y2)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y2))) Y2)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y2))) (@ (@ tptp.times_times_complex Y2) Z)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y2))) (@ (@ tptp.times_times_real Y2) Z)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y2))) (@ (@ tptp.times_times_rat Y2) Z)))))))
% 6.82/7.02 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.82/7.02 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.82/7.02 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y2))) (@ (@ tptp.times_times_complex Y2) Z)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y2))) (@ (@ tptp.times_times_real Y2) Z)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y2))) (@ (@ tptp.times_times_rat Y2) Z)))))))
% 6.82/7.02 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y2) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real Y2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat Y2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Z)) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.modulo364778990260209775nteger A) B) A)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.modulo_modulo_nat A) B) A)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.modulo_modulo_int A) B) A)))))
% 6.82/7.02 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.82/7.02 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.02 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.82/7.02 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) K3) (not (@ P I3)))) (@ P (@ tptp.suc K3))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))))
% 6.82/7.02 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M))))))
% 6.82/7.02 (assert (forall ((X2 tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs2)))))
% 6.82/7.02 (assert (forall ((X2 tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.82/7.02 (assert (forall ((X2 Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))))
% 6.82/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D)) (@ P D)))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D)) (not (@ P D)))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N) K)))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N)) (and (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M)))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I) (@ _let_1 (@ (@ tptp.power_power_nat I) N))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N) M) (= N tptp.one_one_nat)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) M)))))
% 6.82/7.02 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N) Q2))))))
% 6.82/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M) N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 6.82/7.02 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B3) N))))))))
% 6.82/7.02 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 6.82/7.02 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts2) S)) X2) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2))))
% 6.82/7.02 (assert (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz))))
% 6.82/7.02 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts2) S)) X2) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 Bool)) (let ((_let_1 (not Y2))) (=> (= (@ tptp.vEBT_VEBT_minNull X2) Y2) (=> (=> (= X2 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2))) Y2) (=> (=> (exists ((Uu2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true))) Y2) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) Y2))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (=> (@ (@ tptp.ord_less_real Z3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) X2)) Y2)))) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (forall ((Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (=> (@ (@ tptp.ord_less_rat Z3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) X2)) Y2)))) (@ (@ tptp.ord_less_eq_rat X2) Y2))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y2)) X2) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y2)) X2) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.times_times_real Z) Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.times_times_rat Z) Y2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) Z)))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)) (= A tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (A tptp.real) (Y2 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X2) A) (=> (@ (@ tptp.ord_less_eq_real Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y2))) A)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (A tptp.rat) (Y2 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X2) A) (=> (@ (@ tptp.ord_less_eq_rat Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y2))) A)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (A tptp.int) (Y2 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X2) A) (=> (@ (@ tptp.ord_less_eq_int Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y2))) A)))))))))
% 6.82/7.02 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.82/7.02 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y2))) (@ (@ tptp.times_times_real Y2) Z))) tptp.zero_zero_real))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y2))) (@ (@ tptp.times_times_rat Y2) Z))) tptp.zero_zero_rat))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y2))) (@ (@ tptp.times_times_real Y2) Z))) tptp.zero_zero_real))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y2)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y2))) (@ (@ tptp.times_times_rat Y2) Z))) tptp.zero_zero_rat))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X2) Y2) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> A5 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y2 tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y2 tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y2 (@ tptp.some_nat Mi2)))))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) A)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) tptp.one_one_real)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X2) Y2) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> B5 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y2 tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y2 tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y2 (@ tptp.some_nat Ma2)))))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.82/7.02 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.82/7.02 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.82/7.02 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.82/7.02 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))))
% 6.82/7.02 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A) N)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))))
% 6.82/7.02 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.02 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.82/7.02 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N))))))))
% 6.82/7.02 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 6.82/7.02 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M3) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M3) N2)) N2))))))
% 6.82/7.02 (assert (= tptp.plus_plus_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N2))))))
% 6.82/7.02 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N)))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P I4))))))))))
% 6.82/7.02 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N2))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P J3))))))))))
% 6.82/7.02 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S)) X2) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2))))
% 6.82/7.02 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S)) X2) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X2) (or (= X2 Mi) (= X2 Ma)))))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve2)) Vf2) tptp.none_nat)))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd)) Ve2) tptp.none_nat)))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (A tptp.real) (Y2 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X2) A) (=> (@ (@ tptp.ord_less_real Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y2))) A)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (A tptp.rat) (Y2 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X2) A) (=> (@ (@ tptp.ord_less_rat Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y2))) A)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (A tptp.int) (Y2 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X2) A) (=> (@ (@ tptp.ord_less_int Y2) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y2))) A)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_i_n_N_u_l_l X2) Y2) (=> (=> (= X2 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2))) _let_1) (=> (=> (exists ((Uu2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true))) _let_1) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) _let_1))))))))))
% 6.82/7.02 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.82/7.02 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.02 (assert (forall ((U tptp.real) (V tptp.real) (R tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_eq_real R) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R) (@ (@ tptp.minus_minus_real V) U))) S))) V))))))
% 6.82/7.02 (assert (forall ((U tptp.rat) (V tptp.rat) (R tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R) (=> (@ (@ tptp.ord_less_eq_rat R) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_eq_rat X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_eq_int X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X2) _let_2) (@ (@ tptp.power_power_real Y2) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= X2 Y2))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X2) _let_2) (@ (@ tptp.power_power_rat Y2) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= X2 Y2))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X2) _let_2) (@ (@ tptp.power_power_nat Y2) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= X2 Y2))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X2) _let_2) (@ (@ tptp.power_power_int Y2) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= X2 Y2))))))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C))) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C))) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_nat))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_int))))))
% 6.82/7.02 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.02 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 6.82/7.02 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M3 tptp.nat)) (@ (@ (@ tptp.if_complex (= M3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.02 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M3 tptp.nat)) (@ (@ (@ tptp.if_real (= M3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.02 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.02 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.02 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N))) M) tptp.one_one_nat))))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.none_nat)))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.none_nat)))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_real X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_rat X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y2) (@ (@ tptp.ord_less_nat X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_int X2) Y2))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.zero_zero_real))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y2 tptp.zero_zero_int))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y2 tptp.zero_zero_real)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y2 tptp.zero_zero_rat)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y2 tptp.zero_zero_int)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) tptp.zero_zero_real)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))) tptp.zero_zero_rat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.82/7.02 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y2 (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y2) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3))) (= Y2 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.82/7.02 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X2) N)) (@ _let_1 M)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X2) N)) (@ _let_1 N)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) Y2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y2) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (= Y2 (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (= Y2 (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (= Y2 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.82/7.02 (assert (forall ((M tptp.code_integer) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.82/7.02 (assert (forall ((M tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B) (@ _let_1 B)))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B) (@ _let_1 B)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y2 (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y2) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (= Y2 (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((U tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X2) Y2)) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.82/7.02 (assert (forall ((U tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X2) Y2)) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y2)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (not (= Y2 _let_1)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X2) Xa2) Y2) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= Y2 (@ (@ tptp.plus_plus_nat _let_1) (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_2) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (not (= Y2 (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ _let_5 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3)))) tptp.one_one_nat)))))))))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X2) Xa2) Y2) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) B5))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) _let_1) (=> (=> (exists ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2)) (not (= Y2 (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_5) (@ (@ tptp.vEBT_VEBT_low _let_3) _let_2))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_5)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary2) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))))))))))
% 6.82/7.02 (assert (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A3 Bool) (B2 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A3) B2))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N2))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N2) _let_1)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 N2)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N2))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N2) _let_3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))))))
% 6.82/7.02 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma2))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma2)))))))))))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B))))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X2) Xa2) Y2) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) B5))) _let_1) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ tptp.ord_less_nat Xa2))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList2) Summary2))) (not (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_3 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa2) (@ _let_3 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ tptp.ord_less_nat X2))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= X2 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X2 Ma)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_4 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi) X2) (@ _let_4 Ma))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) tptp.zero_zero_nat)) tptp.zero_zero_nat)))))))))))))
% 6.82/7.02 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (@ tptp.numeral_numeral_nat _let_1)) (= _let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))))))
% 6.82/7.02 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.82/7.02 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C)))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_i_n_t X2) Y2) (=> (forall ((A5 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (exists ((B5 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= Y2 (@ _let_1 (@ (@ (@ tptp.if_nat A5) tptp.zero_zero_nat) (@ _let_1 tptp.one_one_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (not (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B5))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B5 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y2 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X2 _let_2) (=> (and (=> _let_12 (= Y2 (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= X2 _let_2) (=> (= Xa2 _let_1) (=> (and (=> A5 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y2 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (=> (= Xa2 _let_1) (=> (and (=> B5 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y2 tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X2 _let_2) (=> (and (=> _let_12 (= Y2 (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (let ((_let_1 (not (= Y2 tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_a_x_t X2) Y2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (= Y2 (@ _let_1 (@ (@ (@ tptp.if_nat B5) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (not (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.82/7.02 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 6.82/7.02 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 6.82/7.02 (assert (forall ((X2 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X2) X2))) (= X2 tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))))
% 6.82/7.02 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ _let_1 K)))))
% 6.82/7.02 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.82/7.02 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.82/7.02 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 6.82/7.02 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.82/7.02 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 6.82/7.02 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.82/7.02 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 6.82/7.02 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.82/7.02 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))))
% 6.82/7.02 (assert (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2))))))
% 6.82/7.02 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L2)) L2))))
% 6.82/7.02 (assert (forall ((M tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D2) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M (@ (@ tptp.times_times_int D2) Q4))))))
% 6.82/7.02 (assert (forall ((M tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D2) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (@ (@ tptp.times_times_int D2) Q3))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N)) A))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) N3)) Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.82/7.02 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))))
% 6.82/7.02 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 B)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (@ _let_1 A))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((K tptp.int) (I tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I) K)) (@ (@ tptp.ord_less_eq_int K) I))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.82/7.02 (assert (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L2) K) (=> (@ _let_1 L2) (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)))))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)) (or (= K tptp.zero_zero_int) (= L2 tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L2)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B4)) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A4) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.82/7.02 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B4))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A4) B))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X2) K)) X2)))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.82/7.02 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L2)))))
% 6.82/7.02 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L2)) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I) K) I) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 6.82/7.02 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A2) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ tptp.divide_divide_int B3) N))))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.vEBT_Leaf A) B)) X2) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real X3) N) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N) A)) (= Y4 X3)))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N) A)))))))
% 6.82/7.02 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 6.82/7.02 (assert (forall ((B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q5)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ _let_1 R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ _let_1 R) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L2) _let_1))))))
% 6.82/7.02 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L2)) L2))))))
% 6.82/7.02 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (= (@ (@ tptp.modulo_modulo_int A) B) R))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R) (= (@ (@ tptp.modulo_modulo_int A) B) R))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3))))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.82/7.02 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L2)) L2)) tptp.one_one_int))))))
% 6.82/7.02 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N))))))
% 6.82/7.02 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 6.82/7.02 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ tptp.vEBT_Leaf A) B)) (@ _let_1 (@ (@ (@ tptp.if_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (= X2 (@ (@ tptp.minus_minus_real Y2) Z)) (= Y2 (@ (@ tptp.plus_plus_real X2) Z)))))
% 6.82/7.02 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))))
% 6.82/7.02 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_T_m_a_x_t T)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 6.82/7.02 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_T_m_i_n_t T)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A)))))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ tptp.vEBT_Leaf A) B)) (@ _let_1 (@ (@ (@ tptp.if_nat A) tptp.zero_zero_nat) (@ _let_1 tptp.one_one_nat)))))))
% 6.82/7.02 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 T) X2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 6.82/7.02 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_1) (=> (= Y2 (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat _let_3)))) (let ((_let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_4))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_3))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_4))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_7))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary2) _let_6)) tptp.one_one_nat))) tptp.one_one_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_5))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary2) _let_5)) tptp.one_one_nat))) tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (= Y2 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ tptp.numeral_numeral_nat _let_3))) (let ((_let_5 (@ (@ tptp.divide_divide_nat _let_1) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_5))) (let ((_let_7 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ tptp.plus_plus_nat _let_4) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_3)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ _let_7 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_5)))) tptp.one_one_nat))))))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ tptp.ord_less_nat Xa2))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_5 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa2) (@ _let_5 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y2 (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X2 _let_2) (=> (= Y2 (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y2 (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S3))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y2 (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S3))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.82/7.02 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.82/7.02 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S3))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X2 _let_1) (=> (= Y2 (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y2 (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y2 (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))) (@ (@ tptp.ord_less_rat A) B))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat))))
% 6.82/7.02 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real))))
% 6.82/7.02 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D2 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D2)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat B) D2))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D2)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D2))))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D2)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D2))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D2)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D2))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D2)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D2))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D2)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B) D2))))))
% 6.82/7.02 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.82/7.02 (assert (forall ((L2 tptp.set_nat) (H2 tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L2) H2) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))))
% 6.82/7.02 (assert (forall ((L2 tptp.rat) (H2 tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L2) H2) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 6.82/7.02 (assert (forall ((L2 tptp.num) (H2 tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L2) H2) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L2) H2)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 6.82/7.02 (assert (forall ((L2 tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L2) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 6.82/7.02 (assert (forall ((L2 tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L2) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L2) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 6.82/7.02 (assert (forall ((L2 tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L2) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L2) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 6.82/7.02 (assert (forall ((I tptp.set_nat) (L2 tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or4548717258645045905et_nat L2) U)) (and (@ (@ tptp.ord_less_eq_set_nat L2) I) (@ (@ tptp.ord_less_eq_set_nat I) U)))))
% 6.82/7.02 (assert (forall ((I tptp.rat) (L2 tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I) (@ (@ tptp.set_or633870826150836451st_rat L2) U)) (and (@ (@ tptp.ord_less_eq_rat L2) I) (@ (@ tptp.ord_less_eq_rat I) U)))))
% 6.82/7.02 (assert (forall ((I tptp.num) (L2 tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I) (@ (@ tptp.set_or7049704709247886629st_num L2) U)) (and (@ (@ tptp.ord_less_eq_num L2) I) (@ (@ tptp.ord_less_eq_num I) U)))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (and (@ (@ tptp.ord_less_eq_nat L2) I) (@ (@ tptp.ord_less_eq_nat I) U)))))
% 6.82/7.02 (assert (forall ((I tptp.int) (L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (and (@ (@ tptp.ord_less_eq_int L2) I) (@ (@ tptp.ord_less_eq_int I) U)))))
% 6.82/7.02 (assert (forall ((I tptp.real) (L2 tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or1222579329274155063t_real L2) U)) (and (@ (@ tptp.ord_less_eq_real L2) I) (@ (@ tptp.ord_less_eq_real I) U)))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (M7 tptp.nat)) (=> (@ P X2) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M7))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M4)))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.num)) (not (= X2 (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A5) (@ (@ tptp.product_Pair_nat_num B5) Acc)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.nat)) (not (= X2 (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A5) (@ (@ tptp.product_Pair_nat_nat B5) Acc)))))))))
% 6.82/7.02 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N6) (@ (@ tptp.ord_less_nat X) M3)))))))
% 6.82/7.02 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N4) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N4))))
% 6.82/7.02 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N6) (@ (@ tptp.ord_less_eq_nat X) M3)))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ P K2) (@ (@ tptp.ord_less_nat K2) I)))))))
% 6.82/7.02 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) U)))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B) D2) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B) D2)))) (@ _let_1 D2))))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D2) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D2)))) (@ _let_1 D2))))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D2) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D2)))) (@ _let_1 D2))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D2) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D2)))) (@ _let_1 D2))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D2) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D2)))) (@ _let_1 D2))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D2) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D2)))) (@ _let_1 D2))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X5 tptp.int)) (@ P X5)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) A2) (@ P (@ (@ tptp.minus_minus_int Y) X))))))))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X5 tptp.int)) (@ P X5)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B3) (@ P (@ (@ tptp.plus_plus_int Y) X))))))))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X4) D4)) T)))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D4))))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X4) D4)) T))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D4)))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X4 T) (= (@ (@ tptp.minus_minus_int X4) D4) T))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X4 T)) (not (= (@ (@ tptp.minus_minus_int X4) D4) T)))))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z3) (not (@ (@ tptp.ord_less_real T) X4)))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z3) (not (@ (@ tptp.ord_less_rat T) X4)))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z3) (not (@ (@ tptp.ord_less_num T) X4)))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z3) (not (@ (@ tptp.ord_less_nat T) X4)))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z3) (not (@ (@ tptp.ord_less_int T) X4)))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X4))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X4))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z3) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z3) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z3) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z3) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z3) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z3) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z3) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z3) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z3) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z3) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z3) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (@ (@ tptp.ord_less_real T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X4) (@ (@ tptp.ord_less_rat T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X4) (@ (@ tptp.ord_less_num T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X4) (@ (@ tptp.ord_less_nat T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (@ (@ tptp.ord_less_int T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (not (@ (@ tptp.ord_less_real X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X4) (not (@ (@ tptp.ord_less_rat X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X4) (not (@ (@ tptp.ord_less_num X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X4) (not (@ (@ tptp.ord_less_nat X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (not (@ (@ tptp.ord_less_int X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (not (= X4 T)))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (not (@ (@ tptp.ord_less_eq_real X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X4) (not (@ (@ tptp.ord_less_eq_rat X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X4) (not (@ (@ tptp.ord_less_eq_num X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X4) (not (@ (@ tptp.ord_less_eq_nat X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (not (@ (@ tptp.ord_less_eq_int X4) T)))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X4) (@ (@ tptp.ord_less_eq_real T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X4) (@ (@ tptp.ord_less_eq_rat T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X4) (@ (@ tptp.ord_less_eq_num T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X4) (@ (@ tptp.ord_less_eq_nat T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (@ (@ tptp.ord_less_eq_int T) X4))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z3) (@ (@ tptp.ord_less_eq_real X4) T))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z3) (@ (@ tptp.ord_less_eq_rat X4) T))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z3) (@ (@ tptp.ord_less_eq_num X4) T))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z3) (@ (@ tptp.ord_less_eq_nat X4) T))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z3) (@ (@ tptp.ord_less_eq_int X4) T))))))
% 6.82/7.02 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z3) (not (@ (@ tptp.ord_less_eq_real T) X4)))))))
% 6.82/7.02 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z3) (not (@ (@ tptp.ord_less_eq_rat T) X4)))))))
% 6.82/7.02 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z3) (not (@ (@ tptp.ord_less_eq_num T) X4)))))))
% 6.82/7.02 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X4)))))))
% 6.82/7.02 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z3) (not (@ (@ tptp.ord_less_eq_int T) X4)))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K3 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X3 tptp.real) (K3 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K3 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X3 tptp.real) (K3 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D4))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X4) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D4))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X4) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.82/7.02 (assert (forall ((D2 tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D2))))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((X_12 tptp.int)) (@ P6 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.82/7.02 (assert (forall ((D2 tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D2))))) (=> (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.82/7.02 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) (@ (@ tptp.times_times_int K) D2))))))))))
% 6.82/7.02 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K) D2))))))))))
% 6.82/7.02 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D2))))) (= (exists ((X5 tptp.int)) (@ P X5)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P X))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D4)))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X4) D4)) T))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X4 T)) (not (= (@ (@ tptp.plus_plus_int X4) D4) T)))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X4 T) (= (@ (@ tptp.plus_plus_int X4) D4) T))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D4))))))))))
% 6.82/7.02 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X4) D4)) T)))))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A5 tptp.real) (B5 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (=> (@ (@ P B5) C2) (=> (@ (@ tptp.ord_less_eq_real A5) B5) (=> (@ (@ tptp.ord_less_eq_real B5) C2) (@ _let_1 C2))))))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A5 tptp.real) (B5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X3) (@ (@ tptp.ord_less_eq_real X3) B5) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B5) A5)) D5)) (@ (@ P A5) B5)))))))) (@ (@ P A) B))))))
% 6.82/7.02 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.82/7.02 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.82/7.02 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.82/7.02 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.82/7.02 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.82/7.02 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_rat X2) Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_int X2) Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y2) Z)) (@ (@ tptp.ord_less_eq_real X2) Y2)))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y2) Z)) (@ (@ tptp.ord_less_eq_rat X2) Y2)))))
% 6.82/7.02 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y2) Z)) (@ (@ tptp.ord_less_eq_int X2) Y2)))))
% 6.82/7.02 (assert (forall ((Q2 tptp.nat) (R tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R)) (= R tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R)) (= R tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.82/7.02 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.82/7.02 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.82/7.02 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.82/7.02 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.82/7.02 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.82/7.02 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M3) N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.unique5026877609467782581ep_nat N2) (@ (@ tptp.unique5055182867167087721od_nat M3) (@ tptp.bit0 N2)))))))
% 6.82/7.02 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M3) N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.unique5024387138958732305ep_int N2) (@ (@ tptp.unique5052692396658037445od_int M3) (@ tptp.bit0 N2)))))))
% 6.82/7.02 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M3) N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.unique4921790084139445826nteger N2) (@ (@ tptp.unique3479559517661332726nteger M3) (@ tptp.bit0 N2)))))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y2) Z)) (@ (@ tptp.ord_less_real X2) Y2)))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y2) Z)) (@ (@ tptp.ord_less_rat X2) Y2)))))
% 6.82/7.02 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y2) Z)) (@ (@ tptp.ord_less_int X2) Y2)))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R)) tptp.one_one_int)))))))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B Bool) (A4 tptp.code_integer) (B4 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A4) B4)) (and (= A A4) (= B B4)))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num) (A4 tptp.num) (B4 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A4) B4)) (and (= A A4) (= B B4)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.num) (A4 tptp.nat) (B4 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A4) B4)) (and (= A A4) (= B B4)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (A4 tptp.nat) (B4 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A4) B4)) (and (= A A4) (= B B4)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int) (B4 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A4) B4)) (and (= A A4) (= B B4)))))
% 6.82/7.02 (assert (forall ((X1 tptp.code_integer) (X23 Bool) (Y1 tptp.code_integer) (Y22 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o X1) X23) (@ (@ tptp.produc6677183202524767010eger_o Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.82/7.02 (assert (forall ((X1 tptp.num) (X23 tptp.num) (Y1 tptp.num) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num X1) X23) (@ (@ tptp.product_Pair_num_num Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.82/7.02 (assert (forall ((X1 tptp.nat) (X23 tptp.num) (Y1 tptp.nat) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num X1) X23) (@ (@ tptp.product_Pair_nat_num Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.82/7.02 (assert (forall ((X1 tptp.nat) (X23 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X23) (@ (@ tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.82/7.02 (assert (forall ((X1 tptp.int) (X23 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X23) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= Q2 Q5))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= R R4))))))
% 6.82/7.02 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R)) (= (@ (@ tptp.divide_divide_int K) L2) Q2))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R)) (= (@ (@ tptp.modulo_modulo_int K) L2) R))))
% 6.82/7.02 (assert (forall ((L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q2) L2)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B Bool) (A4 tptp.code_integer) (B4 Bool)) (=> (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A4) B4)) (not (=> (= A A4) (= B (not B4)))))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num) (A4 tptp.num) (B4 tptp.num)) (=> (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.num) (A4 tptp.nat) (B4 tptp.num)) (=> (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (A4 tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.produc6271795597528267376eger_o Bool)) (P2 tptp.produc6271795597528267376eger_o)) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (@ P (@ (@ tptp.produc6677183202524767010eger_o A5) B5))) (@ P P2))))
% 6.82/7.02 (assert (forall ((P (-> tptp.product_prod_num_num Bool)) (P2 tptp.product_prod_num_num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (@ P (@ (@ tptp.product_Pair_num_num A5) B5))) (@ P P2))))
% 6.82/7.02 (assert (forall ((P (-> tptp.product_prod_nat_num Bool)) (P2 tptp.product_prod_nat_num)) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (@ P (@ (@ tptp.product_Pair_nat_num A5) B5))) (@ P P2))))
% 6.82/7.02 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P2 tptp.product_prod_nat_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A5) B5))) (@ P P2))))
% 6.82/7.02 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P2 tptp.product_prod_int_int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A5) B5))) (@ P P2))))
% 6.82/7.02 (assert (forall ((P2 tptp.produc6271795597528267376eger_o)) (exists ((X3 tptp.code_integer) (Y3 Bool)) (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)))))
% 6.82/7.02 (assert (forall ((P2 tptp.product_prod_num_num)) (exists ((X3 tptp.num) (Y3 tptp.num)) (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)))))
% 6.82/7.02 (assert (forall ((P2 tptp.product_prod_nat_num)) (exists ((X3 tptp.nat) (Y3 tptp.num)) (= P2 (@ (@ tptp.product_Pair_nat_num X3) Y3)))))
% 6.82/7.02 (assert (forall ((P2 tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= P2 (@ (@ tptp.product_Pair_nat_nat X3) Y3)))))
% 6.82/7.02 (assert (forall ((P2 tptp.product_prod_int_int)) (exists ((X3 tptp.int) (Y3 tptp.int)) (= P2 (@ (@ tptp.product_Pair_int_int X3) Y3)))))
% 6.82/7.02 (assert (forall ((Y2 tptp.produc6271795597528267376eger_o)) (not (forall ((A5 tptp.code_integer) (B5 Bool)) (not (= Y2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.product_prod_num_num)) (not (forall ((A5 tptp.num) (B5 tptp.num)) (not (= Y2 (@ (@ tptp.product_Pair_num_num A5) B5)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.product_prod_nat_num)) (not (forall ((A5 tptp.nat) (B5 tptp.num)) (not (= Y2 (@ (@ tptp.product_Pair_nat_num A5) B5)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.product_prod_nat_nat)) (not (forall ((A5 tptp.nat) (B5 tptp.nat)) (not (= Y2 (@ (@ tptp.product_Pair_nat_nat A5) B5)))))))
% 6.82/7.02 (assert (forall ((Y2 tptp.product_prod_int_int)) (not (forall ((A5 tptp.int) (B5 tptp.int)) (not (= Y2 (@ (@ tptp.product_Pair_int_int A5) B5)))))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L2)) (@ (@ tptp.modulo_modulo_int K) L2)))))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))) (= (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L2) Q2)) R)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (@ (@ tptp.ord_less_int R) L2))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R) (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R)))))))))))
% 6.82/7.02 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_height (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi) X2) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X2) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.82/7.02 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X2 tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat X2) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M4 tptp.nat)) (@ (@ P M4) tptp.zero_zero_nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M4) N3)) (@ (@ P M4) N3)))) (@ (@ P M) N)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K) _let_1)) L2)))))))
% 6.82/7.02 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.82/7.02 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.82/7.02 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.82/7.02 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.82/7.02 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.82/7.02 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.82/7.02 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.82/7.02 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (and (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 6.82/7.02 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C) A)))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 6.82/7.02 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 6.82/7.02 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y2)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X2) Y2)) Z) (and (@ (@ tptp.ord_less_real X2) Z) (@ (@ tptp.ord_less_real Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X2) Y2)) Z) (and (@ (@ tptp.ord_less_rat X2) Z) (@ (@ tptp.ord_less_rat Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.num) (Y2 tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X2) Y2)) Z) (and (@ (@ tptp.ord_less_num X2) Z) (@ (@ tptp.ord_less_num Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X2) Y2)) Z) (and (@ (@ tptp.ord_less_nat X2) Z) (@ (@ tptp.ord_less_nat Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X2) Y2)) Z) (and (@ (@ tptp.ord_less_int X2) Z) (@ (@ tptp.ord_less_int Y2) Z)))))
% 6.82/7.02 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.82/7.02 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.82/7.02 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.82/7.02 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_o) (I tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I) X2)) (@ tptp.size_size_list_o Xs2))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) (@ tptp.size_size_list_nat Xs2))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat) (X2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs2) I) X2)) (@ tptp.size_size_list_int Xs2))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 6.82/7.02 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (not (= I J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) J) (@ (@ tptp.nth_nat Xs2) J)))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (not (= I J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) J) (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I) (@ (@ tptp.nth_nat Xs2) I)) Xs2)))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) (@ (@ tptp.nth_VEBT_VEBT Xs2) I)) Xs2)))
% 6.82/7.02 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)))
% 6.82/7.02 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.82/7.02 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.82/7.02 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.82/7.02 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.82/7.02 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.02 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.02 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.02 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.02 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.82/7.02 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.82/7.02 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2) Xs2))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_o) (I tptp.nat) (X2 Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I) (= (@ (@ (@ tptp.list_update_o Xs2) I) X2) Xs2))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) I) (= (@ (@ (@ tptp.list_update_nat Xs2) I) X2) Xs2))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) I) (= (@ (@ (@ tptp.list_update_int Xs2) I) X2) Xs2))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ _let_1 L2)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.82/7.02 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.82/7.02 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.82/7.02 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) I) X2))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I) X2)) I) X2))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) I) X2))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I) X2)) I) X2))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_VEBT_VEBT2 Xs2))))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_o2 Xs2))))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_nat2 Xs2))))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_int2 Xs2))))))))
% 6.82/7.02 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (D2 tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat D2) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat C) D2)) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (D2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D2)) (@ (@ tptp.ord_max_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.num) (A tptp.num) (D2 tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A) (=> (@ (@ tptp.ord_less_eq_num D2) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D2)) (@ (@ tptp.ord_max_num A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (D2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D2)) (@ (@ tptp.ord_max_nat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (D2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D2)) (@ (@ tptp.ord_max_int A) B))))))
% 6.82/7.02 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.82/7.02 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.82/7.02 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (not (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A)))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))))
% 6.82/7.02 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A)))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A)))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A)))))
% 6.82/7.02 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= A3 (@ (@ tptp.ord_max_rat A3) B2)))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= A3 (@ (@ tptp.ord_max_num A3) B2)))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.ord_max_nat A3) B2)))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.ord_max_int A3) B2)))))
% 6.82/7.02 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.82/7.02 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.82/7.02 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.82/7.02 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.82/7.02 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.82/7.02 (assert (forall ((Z tptp.extended_enat) (X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) B2))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) B2))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) B2))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) B2))))
% 6.82/7.02 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) B2))))
% 6.82/7.02 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.82/7.02 (assert (forall ((Z tptp.extended_enat) (X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y2)) (or (@ _let_1 X2) (@ _let_1 Y2))))))
% 6.82/7.02 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B) C)) A) (not (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 6.82/7.02 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 6.82/7.02 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)) (not (= A3 B2))))))
% 6.82/7.02 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (= A3 (@ (@ tptp.ord_max_real A3) B2)) (not (= A3 B2))))))
% 6.82/7.02 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (= A3 (@ (@ tptp.ord_max_rat A3) B2)) (not (= A3 B2))))))
% 6.82/7.02 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (= A3 (@ (@ tptp.ord_max_num A3) B2)) (not (= A3 B2))))))
% 6.82/7.02 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_max_nat A3) B2)) (not (= A3 B2))))))
% 6.82/7.02 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.ord_max_int A3) B2)) (not (= A3 B2))))))
% 6.82/7.02 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X2) Y2)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X2) Z)) (@ (@ tptp.plus_plus_real Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X2) Y2)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X2) Z)) (@ (@ tptp.plus_plus_rat Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X2) Y2)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X2) Z)) (@ (@ tptp.plus_plus_nat Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X2) Y2)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X2) Z)) (@ (@ tptp.plus_plus_int Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X2))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y2) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y2) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.82/7.02 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y2) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X2))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y2) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.82/7.02 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X2) Y2)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X2) Z)) (@ (@ tptp.minus_minus_rat Y2) Z)))))
% 6.82/7.02 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X2) Y2)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X2) Z)) (@ (@ tptp.minus_minus_int Y2) Z)))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N) Q2)))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.82/7.02 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.82/7.02 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.82/7.02 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B2)) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_max_set_nat (lambda ((A3 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B2)) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B2)) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_max_num (lambda ((A3 tptp.num) (B2 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B2)) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B2)) B2) A3))))
% 6.82/7.02 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B2)) B2) A3))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L2 tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L2) R)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L2)) R)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M)) M) (@ (@ tptp.ord_max_nat N) M))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A2) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) I) X2))) A2)))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_complex) (A2 tptp.set_complex) (X2 tptp.complex) (I tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (=> (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) I) X2))) A2)))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_real) (A2 tptp.set_real) (X2 tptp.real) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) A2) (=> (@ (@ tptp.member_real X2) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I) X2))) A2)))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_int) (A2 tptp.set_int) (X2 tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (=> (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I) X2))) A2)))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (I tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2))) A2)))))
% 6.82/7.02 (assert (forall ((Xs2 tptp.list_nat) (A2 tptp.set_nat) (X2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (=> (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I) X2))) A2)))))
% 6.82/7.02 (assert (= tptp.neg_numeral_dbl_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) X))))
% 6.82/7.02 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat X) X))))
% 6.82/7.02 (assert (= tptp.neg_numeral_dbl_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) X))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat) (X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) N) X2))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (Xs2 tptp.list_complex) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N) X2))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N) X2))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N) X2))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X2) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N) X2))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N) X2))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N) X2))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I) X2)))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_o Xs2) I) X2)))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_nat Xs2) I) X2)))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ (@ tptp.list_update_int Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_int Xs2) I) X2)))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X2 Bool) (J tptp.nat)) (let ((_let_1 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I) X2)) J) (and (=> _let_1 X2) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J))))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J)))))))))
% 6.82/7.02 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (J tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs2) J)))))))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N))) tptp.one_one_real))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N))) tptp.one_one_rat))))
% 6.82/7.02 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) tptp.one_one_int))))
% 6.82/7.02 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ P A5) B5) (@ (@ P B5) A5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) tptp.zero_zero_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.plus_plus_nat A5) B5))))) (@ (@ P A) B))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) Summary2))))))))
% 6.82/7.02 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X2) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X2) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (not (and (=> _let_4 (= Y2 (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y2 (@ _let_1 true))) (=> (not _let_3) (= Y2 _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3))) (=> (= X2 _let_1) (not (= Y2 _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) (=> (= X2 _let_1) (not (= Y2 _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2)) (not (= Y2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (not (= Y2 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 6.82/7.02 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (=> (and (=> _let_4 (= Y2 (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y2 (@ _let_1 true))) (=> (not _let_3) (= Y2 _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3))) (=> (= X2 _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) (=> (= X2 _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (=> (= Y2 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 6.82/7.02 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.82/7.02 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.82/7.02 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 6.82/7.02 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat)) (X23 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) (@ tptp.some_P7363390416028606310at_nat X23)) (@ (@ tptp.plus_plus_nat (@ X2 X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((X2 (-> tptp.nat tptp.nat)) (X23 tptp.nat)) (= (@ (@ tptp.size_option_nat X2) (@ tptp.some_nat X23)) (@ (@ tptp.plus_plus_nat (@ X2 X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((X2 (-> tptp.num tptp.nat)) (X23 tptp.num)) (= (@ (@ tptp.size_option_num X2) (@ tptp.some_num X23)) (@ (@ tptp.plus_plus_nat (@ X2 X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.82/7.02 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.82/7.02 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.82/7.02 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.82/7.02 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.82/7.02 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.82/7.02 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.82/7.02 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.82/7.02 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.02 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 6.82/7.02 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.82/7.02 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.82/7.02 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.82/7.02 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.82/7.02 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.82/7.02 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) A)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) A)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) A)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) A)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))))
% 6.82/7.02 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.82/7.02 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.82/7.02 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.82/7.02 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.82/7.02 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.82/7.02 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.82/7.02 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.82/7.02 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 6.82/7.02 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 6.82/7.02 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 6.82/7.02 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 6.82/7.02 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N))) (@ _let_1 N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N)) (not (@ _let_1 N))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ _let_2 A))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ _let_2 A))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (= (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ _let_2 A))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ (@ tptp.divide_divide_nat N) _let_1))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N) _let_1)))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N) M)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (not (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (not (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (not (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (or (@ (@ tptp.ord_less_nat M) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) tptp.one_one_Code_integer))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_2 (= A tptp.zero_zero_real)))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_2 (= A tptp.zero_zero_rat)))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_2 (= A tptp.zero_zero_int)))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int)) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) C) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) C) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.82/7.03 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B2 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real B) C))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat B) C))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D2) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real A) C))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat A) C))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (exists ((K2 tptp.code_integer)) (= A3 (@ (@ tptp.times_3573771949741848930nteger B2) K2))))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_real (lambda ((B2 tptp.real) (A3 tptp.real)) (exists ((K2 tptp.real)) (= A3 (@ (@ tptp.times_times_real B2) K2))))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (exists ((K2 tptp.rat)) (= A3 (@ (@ tptp.times_times_rat B2) K2))))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (exists ((K2 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B2) K2))))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A3 tptp.int)) (exists ((K2 tptp.int)) (= A3 (@ (@ tptp.times_times_int B2) K2))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K3))))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K3 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K3))))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K3 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K3))))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K3))))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K3 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K3))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B8 tptp.nat) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B8) C5)) (@ (@ tptp.dvd_dvd_nat B8) B) (@ (@ tptp.dvd_dvd_nat C5) C))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B8 tptp.int) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B8) C5)) (@ (@ tptp.dvd_dvd_int B8) B) (@ (@ tptp.dvd_dvd_int C5) C))))))
% 6.82/7.03 (assert (forall ((P2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P2) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.times_times_nat X3) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 6.82/7.03 (assert (forall ((P2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P2) (@ (@ tptp.times_times_int A) B)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.times_times_int X3) Y3)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.82/7.03 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.82/7.03 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C)))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int C) B)) (@ _let_1 (@ (@ tptp.minus_minus_int B) C))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y2) Z)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y2) Z)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y2) Z)))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (= A B)))))))
% 6.82/7.03 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (= A B)))))))
% 6.82/7.03 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (= A B)))))))
% 6.82/7.03 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (= A B)))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (= A B)))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (= A B)))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D2)) (@ (@ tptp.divide6298287555418463151nteger B) D2)) (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D2) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D2)) (@ (@ tptp.divide_divide_nat B) D2)) (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D2) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D2)) (@ (@ tptp.divide_divide_int B) D2)) (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y2) N)))))
% 6.82/7.03 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y2) N)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y2) N)))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y2) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y2) N)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y2) N)))))
% 6.82/7.03 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X1 tptp.nat) (X23 tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X23)) (@ (@ F X1) X23))))
% 6.82/7.03 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X1 tptp.nat) (X23 tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X23)) (@ (@ F X1) X23))))
% 6.82/7.03 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (X1 tptp.int) (X23 tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int X1) X23)) (@ (@ F X1) X23))))
% 6.82/7.03 (assert (forall ((F (-> tptp.int tptp.int Bool)) (X1 tptp.int) (X23 tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int X1) X23)) (@ (@ F X1) X23))))
% 6.82/7.03 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X1 tptp.int) (X23 tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int X1) X23)) (@ (@ F X1) X23))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N)))))))
% 6.82/7.03 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N)))))))
% 6.82/7.03 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N)))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.82/7.03 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M) N)) (=> (@ _let_1 N) (@ _let_1 M))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) A)))) (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) B)))) (@ (@ tptp.dvd_dvd_complex A) B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B)))) (@ (@ tptp.dvd_dvd_real A) B))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) A)))) (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.82/7.03 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc27273713700761075at_nat P) Z)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc8739625826339149834_nat_o P) Z)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4245557441103728435nt_int P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.int tptp.int Bool)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4947309494688390418_int_o P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Q (-> tptp.int Bool)) (P (-> tptp.int tptp.int tptp.int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc8211389475949308722nt_int P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X) Y)) __flatten_var_0))) F)))
% 6.82/7.03 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X) Y)) __flatten_var_0))) F)))
% 6.82/7.03 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y)))) F)))
% 6.82/7.03 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((X tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y)))) F)))
% 6.82/7.03 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (lambda ((X tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y)))) F)))
% 6.82/7.03 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 6.82/7.03 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 6.82/7.03 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 6.82/7.03 (assert (forall ((F (-> tptp.int tptp.int Bool)) (G (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc4947309494688390418_int_o F) G))))
% 6.82/7.03 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.product_prod_int_int tptp.int))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc8211389475949308722nt_int F) G))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) A)))) (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) B)))) (and (@ (@ tptp.dvd_dvd_complex A) B) (not (@ (@ tptp.dvd_dvd_complex B) A))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B)))) (and (@ (@ tptp.dvd_dvd_real A) B) (not (@ (@ tptp.dvd_dvd_real B) A))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) A)))) (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri6519982836138164636nteger M) A)) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int M) A)) (@ _let_1 A)))))
% 6.82/7.03 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.82/7.03 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.82/7.03 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.82/7.03 (assert (forall ((D2 tptp.code_integer) (S tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X4) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X4) S)))) (=> (@ (@ tptp.ord_less_real Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X4) S)))) (=> (@ (@ tptp.ord_less_rat Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X4) S)))) (=> (@ (@ tptp.ord_less_nat Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X4) S)))) (=> (@ (@ tptp.ord_less_int Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.code_integer) (S tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X4) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X4) S))))) (=> (@ (@ tptp.ord_less_real Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X4) S))))) (=> (@ (@ tptp.ord_less_rat Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X4) S))))) (=> (@ (@ tptp.ord_less_nat Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X4) S))))) (=> (@ (@ tptp.ord_less_int Z3) X4) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.code_integer) (S tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X4) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X4) S)))) (=> (@ (@ tptp.ord_less_real X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X4) S)))) (=> (@ (@ tptp.ord_less_rat X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X4) S)))) (=> (@ (@ tptp.ord_less_nat X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X4) S)))) (=> (@ (@ tptp.ord_less_int X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.code_integer) (S tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X4) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X4) S))))) (=> (@ (@ tptp.ord_less_real X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X4) S))))) (=> (@ (@ tptp.ord_less_rat X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X4) S))))) (=> (@ (@ tptp.ord_less_nat X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X4) S))))) (=> (@ (@ tptp.ord_less_int X4) Z3) (= _let_1 _let_1)))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B C)))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C) A)) (= B C)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C) A)) (= B C)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (D2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D2) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D2) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))))
% 6.82/7.03 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger C) B)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B)) (@ _let_1 C))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C) A)) (= B C)))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C) A)) (= B C)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C) A)) (= B C)))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B2) A3) tptp.zero_zero_nat))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B2) A3) tptp.zero_zero_int))))
% 6.82/7.03 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B2) A3) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y2) M))))))
% 6.82/7.03 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y2) M))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y2) M))))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y2) M))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y2) M))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (@ (@ tptp.dvd_dvd_int C) (@ (@ tptp.minus_minus_int A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer C) (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (or (@ (@ tptp.ord_less_nat N) M) (@ _let_1 N))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 M)))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N)))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))))))
% 6.82/7.03 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N) (not (@ (@ tptp.dvd_dvd_int N) M))))))
% 6.82/7.03 (assert (forall ((D2 tptp.nat) (A tptp.nat) (B tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D2))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X2) (@ (@ tptp.plus_plus_nat (@ _let_2 Y2)) D2)) (= (@ _let_2 X2) (@ (@ tptp.plus_plus_nat (@ _let_1 Y2)) D2))) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D2)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D2)))))))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D3)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D3))))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X3)) (@ _let_2 Y3)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X3)) (@ _let_1 Y3)) D3)))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X2) _let_1) (@ (@ tptp.divide_divide_nat Y2) _let_1)) (=> (= (@ _let_2 X2) (@ _let_2 Y2)) (= X2 Y2)))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C2 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C2)))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C2)))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C2)))))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.code_integer Bool)) (L2 tptp.code_integer)) (= (exists ((X tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L2) X))) (exists ((X tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L2) (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.zero_z3403309356797280102nteger)) (@ P X))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.complex Bool)) (L2 tptp.complex)) (= (exists ((X tptp.complex)) (@ P (@ (@ tptp.times_times_complex L2) X))) (exists ((X tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L2) (@ (@ tptp.plus_plus_complex X) tptp.zero_zero_complex)) (@ P X))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.real Bool)) (L2 tptp.real)) (= (exists ((X tptp.real)) (@ P (@ (@ tptp.times_times_real L2) X))) (exists ((X tptp.real)) (and (@ (@ tptp.dvd_dvd_real L2) (@ (@ tptp.plus_plus_real X) tptp.zero_zero_real)) (@ P X))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.rat Bool)) (L2 tptp.rat)) (= (exists ((X tptp.rat)) (@ P (@ (@ tptp.times_times_rat L2) X))) (exists ((X tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L2) (@ (@ tptp.plus_plus_rat X) tptp.zero_zero_rat)) (@ P X))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.nat Bool)) (L2 tptp.nat)) (= (exists ((X tptp.nat)) (@ P (@ (@ tptp.times_times_nat L2) X))) (exists ((X tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L2) (@ (@ tptp.plus_plus_nat X) tptp.zero_zero_nat)) (@ P X))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.int Bool)) (L2 tptp.int)) (= (exists ((X tptp.int)) (@ P (@ (@ tptp.times_times_int L2) X))) (exists ((X tptp.int)) (and (@ (@ tptp.dvd_dvd_int L2) (@ (@ tptp.plus_plus_int X) tptp.zero_zero_int)) (@ P X))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) C) (= B (@ (@ tptp.times_3573771949741848930nteger C) A)))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C) (= B (@ (@ tptp.times_times_nat C) A)))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C) (= B (@ (@ tptp.times_times_int C) A)))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B)))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B)))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B)))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D2) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D2)))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D2) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D2)))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D2) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D2)))))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 6.82/7.03 (assert (forall ((D2 tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D4) (forall ((X4 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X4) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D2) D4) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D4))) T))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D4) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D4))) T))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D4))) T))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D4) (forall ((X4 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X4) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T)))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D2) D4) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D4))) T)))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D4) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D4))) T)))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D4))) T)))))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B)))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B)))))
% 6.82/7.03 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B)) (= (@ (@ tptp.times_times_nat A) B) C)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B)) (= (@ (@ tptp.times_times_int A) B) C)))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B))))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C) (= A (@ (@ tptp.times_times_nat C) B))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C) (= A (@ (@ tptp.times_times_int C) B))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K) N)))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D3))))))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N)) (not (@ (@ tptp.dvd_dvd_nat N) M)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N))))))
% 6.82/7.03 (assert (forall ((X2 tptp.product_prod_nat_nat)) (not (forall ((K3 tptp.nat) (M4 tptp.nat)) (not (= X2 (@ (@ tptp.product_Pair_nat_nat K3) M4)))))))
% 6.82/7.03 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D tptp.nat)) (@ (@ tptp.dvd_dvd_nat D) M)))))))
% 6.82/7.03 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.82/7.03 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.82/7.03 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B5 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B5 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B5) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B5) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B5)))))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B5 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B5 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B5) tptp.one_one_nat) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_nat A) B5) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B5)))))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B5 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B5 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B5) tptp.one_one_int) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_int A) B5) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B5)))))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5))))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5))))))))
% 6.82/7.03 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.82/7.03 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.82/7.03 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.82/7.03 (assert (= (lambda ((Y5 tptp.code_integer) (Z5 tptp.code_integer)) (= Y5 Z5)) (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide6298287555418463151nteger A3) _let_1) (@ (@ tptp.divide6298287555418463151nteger B2) _let_1))))))))
% 6.82/7.03 (assert (= (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_nat A3) _let_1) (@ (@ tptp.divide_divide_nat B2) _let_1))))))))
% 6.82/7.03 (assert (= (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) (lambda ((A3 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_int A3) _let_1) (@ (@ tptp.divide_divide_int B2) _let_1))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (=> (not (= X2 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X2))) (=> (not (= X2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (not (= X2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X2) (@ (@ tptp.power_8256067586552552935nteger X2) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X2) (@ (@ tptp.power_power_rat X2) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X2) (@ (@ tptp.power_power_nat X2) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X2) (@ (@ tptp.power_power_real X2) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X2) (@ (@ tptp.power_power_complex X2) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X2) (@ (@ tptp.power_power_int X2) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M)) M) (= N tptp.one_one_nat)))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N)) M) (= N tptp.one_one_nat)))))
% 6.82/7.03 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 6.82/7.03 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W))))))
% 6.82/7.03 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W))))))
% 6.82/7.03 (assert (forall ((Q2 tptp.nat) (N tptp.nat) (R tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))))
% 6.82/7.03 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.82/7.03 (assert (forall ((R tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R) N) (=> (@ (@ tptp.ord_less_eq_nat R) M) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M) R)) (= (@ (@ tptp.modulo_modulo_nat M) N) R))))))
% 6.82/7.03 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2)) (or (@ (@ tptp.dvd_dvd_int L2) K) (and (= L2 tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X4))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T)))))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X4))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T))))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) D4)) T))))))))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) D4)) T)))))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) A)))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)) A)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)) A)))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.zero_zero_int)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.one_one_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.one_one_int)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.one_one_Code_integer)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se8260200283734997820nteger M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2793503036327961859nteger M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7882103937844011126it_nat M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1345352211410354436nteger M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2161824704523386999it_nat M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.82/7.03 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_Code_integer))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_nat))))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_int))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 6.82/7.03 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.82/7.03 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X2 (@ tptp.suc N3))))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N))))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 6.82/7.03 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.03 (assert (forall ((X2 (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X2) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.03 (assert (forall ((X2 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X2) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))))
% 6.82/7.03 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.82/7.03 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.82/7.03 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.82/7.03 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.82/7.03 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.82/7.03 (assert (forall ((S2 tptp.set_real)) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) S2) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S2) (@ (@ tptp.ord_less_real Xa) X3))))))))))
% 6.82/7.03 (assert (forall ((S2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat S2) (=> (not (= S2 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) S2) (not (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) S2) (@ (@ tptp.ord_less_rat Xa) X3))))))))))
% 6.82/7.03 (assert (forall ((S2 tptp.set_num)) (=> (@ tptp.finite_finite_num S2) (=> (not (= S2 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) S2) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S2) (@ (@ tptp.ord_less_num Xa) X3))))))))))
% 6.82/7.03 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) S2) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S2) (@ (@ tptp.ord_less_nat Xa) X3))))))))))
% 6.82/7.03 (assert (forall ((S2 tptp.set_int)) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) S2) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S2) (@ (@ tptp.ord_less_int Xa) X3))))))))))
% 6.82/7.03 (assert (forall ((X7 tptp.set_real)) (=> (not (= X7 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) X7) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X7) (@ (@ tptp.ord_less_real X3) Xa))))) (not (@ tptp.finite_finite_real X7))))))
% 6.82/7.03 (assert (forall ((X7 tptp.set_rat)) (=> (not (= X7 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) X7) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X7) (@ (@ tptp.ord_less_rat X3) Xa))))) (not (@ tptp.finite_finite_rat X7))))))
% 6.82/7.03 (assert (forall ((X7 tptp.set_num)) (=> (not (= X7 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) X7) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X7) (@ (@ tptp.ord_less_num X3) Xa))))) (not (@ tptp.finite_finite_num X7))))))
% 6.82/7.03 (assert (forall ((X7 tptp.set_nat)) (=> (not (= X7 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X7) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X7) (@ (@ tptp.ord_less_nat X3) Xa))))) (not (@ tptp.finite_finite_nat X7))))))
% 6.82/7.03 (assert (forall ((X7 tptp.set_int)) (=> (not (= X7 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X7) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X7) (@ (@ tptp.ord_less_int X3) Xa))))) (not (@ tptp.finite_finite_int X7))))))
% 6.82/7.03 (assert (= tptp.nat_triangle (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (forall ((X2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y2 (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y2) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X2 _let_2) (not (and (=> _let_8 (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.82/7.03 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M3) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M3)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M3) N2)) N2))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.82/7.03 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A3) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))))))))))
% 6.82/7.03 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A3) _let_1))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))))))))))
% 6.82/7.03 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 6.82/7.03 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I))))))
% 6.82/7.03 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.82/7.03 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (C (-> tptp.code_integer Bool Bool))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc7828578312038201481er_o_o C) P2))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_num_num) (C (-> tptp.num tptp.num Bool))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc5703948589228662326_num_o C) P2))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_nat_num) (C (-> tptp.nat tptp.num Bool))) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc4927758841916487424_num_o C) P2))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat Bool))) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc6081775807080527818_nat_o C) P2))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= P2 (@ (@ tptp.product_Pair_int_int A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc4947309494688390418_int_o C) P2))))
% 6.82/7.03 (assert (forall ((F (-> tptp.code_integer Bool Bool)) (A tptp.code_integer) (B Bool)) (=> (@ (@ F A) B) (@ (@ tptp.produc7828578312038201481er_o_o F) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))
% 6.82/7.03 (assert (forall ((F (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (@ (@ F A) B) (@ (@ tptp.produc5703948589228662326_num_o F) (@ (@ tptp.product_Pair_num_num A) B)))))
% 6.82/7.03 (assert (forall ((F (-> tptp.nat tptp.num Bool)) (A tptp.nat) (B tptp.num)) (=> (@ (@ F A) B) (@ (@ tptp.produc4927758841916487424_num_o F) (@ (@ tptp.product_Pair_nat_num A) B)))))
% 6.82/7.03 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ F A) B) (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.82/7.03 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ F A) B) (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.82/7.03 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P2)))))
% 6.82/7.03 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ tptp.member_real Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P2)))))
% 6.82/7.03 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ tptp.member_nat Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P2)))))
% 6.82/7.03 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ tptp.member_int Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P2)))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P2)))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ tptp.member_real Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P2)))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ tptp.member_nat Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P2)))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ tptp.member_int Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P2)))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_nat_num) (Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex))) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A5) B5)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc6231982587499038204omplex C) P2)))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_nat_num) (Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real))) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A5) B5)) (@ (@ tptp.member_real Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P2)))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1043322548047392435omplex C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc242741666403216561t_real C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 6.82/7.03 (assert (forall ((Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc5431169771168744661et_nat C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1253318751659547953et_int C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc2866383454006189126omplex C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8296048397933160132t_real C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.82/7.03 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1361121860356118632et_nat C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6406642877701697732et_int C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6231982587499038204omplex C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1435849484188172666t_real C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 6.82/7.03 (assert (forall ((P2 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X2 tptp.product_prod_nat_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A5) B5) P2) (@ (@ (@ C A5) B5) X2))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P2) X2))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.82/7.03 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.82/7.03 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.82/7.03 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.82/7.03 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.82/7.03 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M N))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) B))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) B))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y2)) (@ _let_1 Y2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X2))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y2)) (@ _let_1 Y2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X2))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y2)) (@ _let_1 Y2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y2)) (@ _let_1 Y2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y2)) (@ _let_1 Y2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X2)) Y2) (@ (@ tptp.dvd_dvd_int X2) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X2)) Y2) (@ (@ tptp.dvd_dvd_real X2) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X2)) Y2) (@ (@ tptp.dvd_dvd_complex X2) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X2)) Y2) (@ (@ tptp.dvd_dvd_Code_integer X2) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X2)) Y2) (@ (@ tptp.dvd_dvd_rat X2) Y2))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.82/7.03 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 6.82/7.03 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.82/7.03 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.82/7.03 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.82/7.03 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.82/7.03 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X2 A))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.82/7.03 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.82/7.03 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.82/7.03 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.82/7.03 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.82/7.03 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.82/7.03 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) N)))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X2)) N)))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X2)) N)))
% 6.82/7.03 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X2)) N)))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (or P Q)) (@ (@ tptp.ord_max_Code_integer (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.82/7.03 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 6.82/7.03 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 6.82/7.03 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.82/7.03 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.82/7.03 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.82/7.03 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.82/7.03 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.82/7.03 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.82/7.03 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.82/7.03 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.82/7.03 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.82/7.03 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.divide_divide_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X2))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int B) A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.82/7.03 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N) (@ tptp.zero_n2687167440665602831ol_nat (not (= N _let_1)))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((X2 tptp.product_prod_nat_nat) (N tptp.nat) (Y2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N) Y2))) (and (= X2 Y2) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y2 tptp.complex)) (= (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y2))) (and (= X2 Y2) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y2 tptp.real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y2))) (and (= X2 Y2) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y2 tptp.int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y2))) (and (= X2 Y2) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y2))) (and (= X2 Y2) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((X2 tptp.vEBT_VEBT) (N tptp.nat) (Y2 tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y2))) (and (= X2 Y2) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.82/7.03 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 6.82/7.03 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I) X2))))
% 6.82/7.03 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I) X2))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.82/7.03 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y2)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y2)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N))))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y2)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y2)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y2)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y2)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y2)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y2)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y2)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y2)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y2)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y2)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 6.82/7.03 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K)))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K)))))
% 6.82/7.03 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K)))))
% 6.82/7.03 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K))))))
% 6.82/7.03 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N)))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)))) (not (= M tptp.one)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)))) (not (= M tptp.one)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)))) (not (= M tptp.one)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (not (= M tptp.one)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M tptp.one)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M tptp.one)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M tptp.one)))))
% 6.82/7.03 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.82/7.03 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P2))) P2)))
% 6.82/7.03 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P2))) P2)))
% 6.82/7.03 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P2))) P2)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.plus_plus_int _let_1) _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.plus_plus_complex _let_1) _let_1) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)))
% 6.82/7.03 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.82/7.03 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.82/7.03 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.82/7.03 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.82/7.03 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.82/7.03 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.82/7.03 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)))
% 6.82/7.03 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.power_power_complex A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.82/7.03 (assert (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real)))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_complex)))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int _let_1) N) _let_1)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real _let_1) N) _let_1)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex _let_1) N) _let_1)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N) _let_1)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat _let_1) N) _let_1)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N) tptp.one_one_real))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N) tptp.one_one_complex))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N) tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.03 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.82/7.03 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P2 Q2))))
% 6.82/7.03 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P2 Q2))))
% 6.82/7.03 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) (@ tptp.zero_n356916108424825756nteger Q2)) (= P2 Q2))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n3304061248610475627l_real (and P Q)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (and P Q)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P Q)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P Q)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.82/7.03 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P2)) (not (forall ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P2)) (not (forall ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P2)) (not (forall ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P2)) (not (forall ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P2)) (not (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P2)) (not (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P2)) (not (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P2)) (not (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc6231982587499038204omplex C) P2)) (not (forall ((X3 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X3) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P2)) (not (forall ((X3 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X3) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y3)))))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_eq_real B) (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_real B))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B) B)) (or (= A B) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) A) (@ (@ tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_rat B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))))
% 6.82/7.03 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.82/7.03 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.82/7.03 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.82/7.03 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.82/7.03 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 6.82/7.03 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 6.82/7.03 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.82/7.03 (assert (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 6.82/7.03 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B))) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B))) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A4) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A4)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A4) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A4)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.82/7.03 (assert (forall ((C (-> tptp.code_integer Bool Bool)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.produc7828578312038201481er_o_o C) P2) (not (forall ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.82/7.03 (assert (forall ((C (-> tptp.num tptp.num Bool)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.produc5703948589228662326_num_o C) P2) (not (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.82/7.03 (assert (forall ((C (-> tptp.nat tptp.num Bool)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.produc4927758841916487424_num_o C) P2) (not (forall ((X3 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.82/7.03 (assert (forall ((C (-> tptp.nat tptp.nat Bool)) (P2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o C) P2) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.82/7.03 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P2 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P2) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.82/7.03 (assert (forall ((F (-> tptp.code_integer Bool Bool)) (A tptp.code_integer) (B Bool)) (=> (@ (@ tptp.produc7828578312038201481er_o_o F) (@ (@ tptp.produc6677183202524767010eger_o A) B)) (@ (@ F A) B))))
% 6.82/7.03 (assert (forall ((F (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (@ (@ tptp.produc5703948589228662326_num_o F) (@ (@ tptp.product_Pair_num_num A) B)) (@ (@ F A) B))))
% 6.82/7.03 (assert (forall ((F (-> tptp.nat tptp.num Bool)) (A tptp.nat) (B tptp.num)) (=> (@ (@ tptp.produc4927758841916487424_num_o F) (@ (@ tptp.product_Pair_nat_num A) B)) (@ (@ F A) B))))
% 6.82/7.03 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.82/7.03 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.82/7.03 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P2 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P2) Z) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ (@ (@ C X3) Y3) Z))))))))
% 6.82/7.03 (assert (forall ((R2 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat) (C tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o R2) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R2 A) B) C))))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.82/7.03 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.82/7.03 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.82/7.03 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))))
% 6.82/7.03 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.82/7.03 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.82/7.03 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))
% 6.82/7.03 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((P (-> tptp.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (and (=> P2 (@ P tptp.one_one_complex)) (=> (not P2) (@ P tptp.zero_zero_complex))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (and (=> P2 (@ P tptp.one_one_real)) (=> (not P2) (@ P tptp.zero_zero_real))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (and (=> P2 (@ P tptp.one_one_rat)) (=> (not P2) (@ P tptp.zero_zero_rat))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (and (=> P2 (@ P tptp.one_one_nat)) (=> (not P2) (@ P tptp.zero_zero_nat))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (and (=> P2 (@ P tptp.one_one_int)) (=> (not P2) (@ P tptp.zero_zero_int))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (and (=> P2 (@ P tptp.one_one_Code_integer)) (=> (not P2) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (not (or (and P2 (not (@ P tptp.one_one_complex))) (and (not P2) (not (@ P tptp.zero_zero_complex))))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (not (or (and P2 (not (@ P tptp.one_one_real))) (and (not P2) (not (@ P tptp.zero_zero_real))))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (not (or (and P2 (not (@ P tptp.one_one_rat))) (and (not P2) (not (@ P tptp.zero_zero_rat))))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (not (or (and P2 (not (@ P tptp.one_one_nat))) (and (not P2) (not (@ P tptp.zero_zero_nat))))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (not (or (and P2 (not (@ P tptp.one_one_int))) (and (not P2) (not (@ P tptp.zero_zero_int))))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (not (or (and P2 (not (@ P tptp.one_one_Code_integer))) (and (not P2) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.82/7.03 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.82/7.03 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.82/7.03 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.82/7.03 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.82/7.03 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.82/7.03 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.82/7.03 (assert (forall ((W tptp.num) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X2)) (@ (@ tptp.times_times_int X2) (@ tptp.uminus_uminus_int _let_1))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real X2) (@ tptp.uminus_uminus_real _let_1))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (X2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex X2) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X2)) (@ (@ tptp.times_3573771949741848930nteger X2) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat X2) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B)))))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.times_times_int X2) X2) tptp.one_one_int) (or (= X2 tptp.one_one_int) (= X2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.times_times_real X2) X2) tptp.one_one_real) (or (= X2 tptp.one_one_real) (= X2 (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X2) X2) tptp.one_one_complex) (or (= X2 tptp.one_one_complex) (= X2 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X2) X2) tptp.one_one_Code_integer) (or (= X2 tptp.one_one_Code_integer) (= X2 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X2) X2) tptp.one_one_rat) (or (= X2 tptp.one_one_rat) (= X2 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.82/7.03 (assert (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B3 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B3 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((B3 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B3 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((B3 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B3 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B3 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 6.82/7.03 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.82/7.03 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.82/7.03 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.82/7.03 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.82/7.03 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.82/7.03 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.82/7.03 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.82/7.03 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.82/7.03 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.82/7.03 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (N tptp.nat) (X2 tptp.product_prod_nat_nat)) (=> (= (@ tptp.size_s5460976970255530739at_nat Xs2) N) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replic4235873036481779905at_nat N) X2))))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_complex) (N tptp.nat) (X2 tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_complex N) X2))))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_real) (N tptp.nat) (X2 tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_real N) X2))))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N) X2))))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_o) (N tptp.nat) (X2 Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_o N) X2))))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_nat) (N tptp.nat) (X2 tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_nat N) X2))))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_int) (N tptp.nat) (X2 tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_int N) X2))))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X3 X2))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X2) Xs2))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_o) (X2 Bool)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (= X3 X2))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X2) Xs2))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (= X3 X2))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs2)) X2) Xs2))))
% 6.82/7.03 (assert (forall ((Xs2 tptp.list_int) (X2 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (= X3 X2))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs2)) X2) Xs2))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B)))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))))))
% 6.82/7.03 (assert (forall ((U tptp.real) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X2) X2))))
% 6.82/7.03 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L2) (@ tptp.uminus_uminus_int L2))))
% 6.82/7.03 (assert (= tptp.numeral_numeral_nat (lambda ((K2 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K2)))))
% 6.82/7.03 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K) L2) tptp.zero_zero_int)))))
% 6.82/7.03 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L2)) tptp.zero_zero_int)) (not (= (@ _let_1 L2) tptp.zero_zero_int))))))
% 6.82/7.03 (assert (= tptp.minus_minus_real (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real Y)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.03 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.82/7.03 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.82/7.03 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.82/7.03 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C) B) (@ tptp.uminus_uminus_real A))))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C) B) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B))))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))))
% 6.82/7.03 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))))
% 6.82/7.03 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))))
% 6.82/7.03 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.82/7.03 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))))
% 6.82/7.03 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))))
% 6.82/7.03 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))))
% 6.82/7.03 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.82/7.03 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.82/7.03 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))))
% 6.82/7.03 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.82/7.03 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.82/7.03 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.82/7.03 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.82/7.03 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.power_power_real A) N)))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ (@ tptp.power_power_complex A) N)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ (@ tptp.power_power_int X2) _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ (@ tptp.power_power_real X2) _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ (@ tptp.power_power_complex X2) _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ (@ tptp.power_power_rat X2) _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X2) _let_1))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X2) _let_1))))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X2) _let_1))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X2) _let_1))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X2)) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y2) (@ tptp.uminus_uminus_real X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X2) Y2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.uminus_uminus_real X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X2)) Y2))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int B) _let_1)))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= _let_2 tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) B))))))))))
% 6.82/7.03 (assert (= tptp.pred_numeral (lambda ((K2 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K2)) tptp.one_one_nat))))
% 6.82/7.03 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.82/7.03 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.82/7.03 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.82/7.03 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.82/7.03 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.82/7.03 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.82/7.03 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.82/7.03 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.82/7.03 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.82/7.03 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.82/7.03 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.82/7.03 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.82/7.03 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.82/7.03 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_int Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_real Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X2) _let_1) (@ (@ tptp.power_power_complex Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus1482373934393186551omplex Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus1351360451143612070nteger Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y2) _let_1)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_rat Y2)))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.82/7.03 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 6.82/7.03 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.modulo_modulo_nat A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.modulo_modulo_int A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n356916108424825756nteger (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 6.82/7.03 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.82/7.03 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.82/7.03 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.82/7.03 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.82/7.03 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.82/7.03 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.82/7.03 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.82/7.03 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.82/7.03 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (or (= A tptp.one_one_int) (= A (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (or (= A tptp.one_one_real) (= A (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (or (= A tptp.one_one_complex) (= A (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (or (= A tptp.one_one_Code_integer) (= A (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.82/7.03 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.82/7.03 (assert (forall ((U tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) K))))
% 6.82/7.03 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))))
% 6.82/7.03 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L2) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L2))))))
% 6.82/7.03 (assert (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))))
% 6.82/7.03 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.if_int (= R tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R))))))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A5 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.nat) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B5)) (@ (@ tptp.times_times_nat _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.82/7.03 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A5 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A5) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.int) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B5)) (@ (@ tptp.times_times_int _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.82/7.03 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A5 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A5) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B5)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.82/7.03 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2) (=> (@ (@ tptp.ord_le3102999989581377725nteger X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X2) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) _let_1))))
% 6.82/7.03 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L2)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L2) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.82/7.03 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M3) N2)) (@ (@ tptp.modulo_modulo_nat M3) N2)))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.82/7.03 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 6.82/7.03 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.82/7.03 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.82/7.03 (assert (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 6.82/7.03 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) (@ tptp.uminus5710092332889474511et_nat Y2)) (@ (@ tptp.ord_less_eq_set_nat Y2) X2))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.82/7.03 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.82/7.03 (assert (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one)))))
% 6.82/7.03 (assert (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))))
% 6.82/7.03 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.82/7.03 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.82/7.03 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one)))))
% 6.82/7.03 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.82/7.03 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.82/7.03 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.82/7.03 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.82/7.03 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.82/7.03 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.82/7.03 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.82/7.03 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.82/7.03 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.82/7.03 (assert (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R tptp.zero_zero_int)))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu5851722552734809277nc_int _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu8295874005876285629c_real _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu5219082963157363817nc_rat _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu3811975205180677377ec_int _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu6075765906172075777c_real _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu3179335615603231917ec_rat _let_1))))))
% 6.82/7.03 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 6.82/7.03 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.82/7.03 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.82/7.03 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.82/7.03 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Y2 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y2)) X2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) Y2))))
% 6.82/7.03 (assert (forall ((Y2 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y2) (@ tptp.uminus5710092332889474511et_nat X2)) (@ (@ tptp.ord_less_eq_set_nat X2) (@ tptp.uminus5710092332889474511et_nat Y2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y2)) (@ tptp.uminus5710092332889474511et_nat X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.set_int) (Y2 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X2) Y2) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X2) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.set_real) (Y2 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X2) Y2) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X2) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat X2) Y2) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X2) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X2) Y2) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X2) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))
% 6.82/7.03 (assert (= tptp.ring_1_of_int_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K2) _let_1))))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K2) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 6.82/7.03 (assert (= tptp.ring_1_of_int_real (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 6.82/7.03 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 6.82/7.03 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.82/7.03 (assert (= tptp.ring_1_of_int_rat (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y2 (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y2) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X2 _let_1) (=> (and (=> _let_8 (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 6.82/7.03 (assert (= tptp.int_ge_less_than (lambda ((D tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D) Z6) (@ (@ tptp.ord_less_int Z6) Z4))))))))
% 6.82/7.03 (assert (= tptp.int_ge_less_than2 (lambda ((D tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D) Z4) (@ (@ tptp.ord_less_int Z6) Z4))))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.82/7.03 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.82/7.03 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.82/7.03 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.82/7.03 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.82/7.03 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.82/7.03 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2)) (@ (@ tptp.ord_less_real X2) Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (= (@ tptp.ln_ln_real X2) (@ tptp.ln_ln_real Y2)) (= X2 Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X2) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X2) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X2) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X2) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (= (@ _let_1 (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (= (@ tptp.ln_ln_real X2) tptp.zero_zero_real) (= X2 tptp.one_one_real)))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 6.82/7.03 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.82/7.03 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.82/7.03 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.82/7.03 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.82/7.03 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.82/7.03 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.82/7.03 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y2) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y2) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y2) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= (@ tptp.ring_1_of_int_int Y2) _let_1) (= Y2 _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.ring_17405671764205052669omplex Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.ring_1_of_int_real Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.ring_1_of_int_rat Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y2)) (= _let_1 Y2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.82/7.03 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (= (@ tptp.ring_1_of_int_int Y2) _let_1) (= Y2 _let_1)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y2) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y2) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y2) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y2) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y2)) (= _let_1 Y2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N) (@ tptp.ring_1_of_int_real Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N) (@ tptp.ring_17405671764205052669omplex Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N) (@ tptp.ring_18347121197199848620nteger Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N) (@ tptp.ring_1_of_int_rat Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y2))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y2) (@ (@ tptp.times_times_real Y2) _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y2) (@ (@ tptp.times_times_rat Y2) _let_1)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y2) (@ (@ tptp.times_times_int Y2) _let_1)))))
% 6.82/7.03 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.82/7.03 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X2)) (=> (@ _let_1 X2) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2)))))
% 6.82/7.03 (assert (forall ((D2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D2)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D2))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (= (@ tptp.ln_ln_real X2) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (= X2 tptp.one_one_real)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2))))))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real K)))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.82/7.03 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)))))
% 6.82/7.03 (assert (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M3)) tptp.one_one_real)))))
% 6.82/7.03 (assert (= tptp.ord_less_int (lambda ((N2 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M3)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D2))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X2) D2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X2) D2))) _let_1))))))
% 6.82/7.03 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) Y2)) Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2)))) tptp.one_one_real)))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2))) (@ tptp.uminus_uminus_real X2))))))
% 6.82/7.03 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K)))))
% 6.82/7.03 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ _let_1 K)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)))))))
% 6.82/7.03 (assert (= tptp.artanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X3)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X3) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X3)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X3)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X3) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X3)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.82/7.03 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.times_3573771949741848930nteger A) A)))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.times_times_real A) A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.times_times_rat A) A)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.82/7.03 (assert (forall ((M tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))))
% 6.82/7.03 (assert (forall ((M tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))))
% 6.82/7.03 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K)) (@ _let_1 K)))))
% 6.82/7.03 (assert (forall ((M tptp.rat) (K tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M))) (= (@ _let_1 (@ tptp.abs_abs_rat K)) (@ _let_1 K)))))
% 6.82/7.03 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.82/7.03 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.82/7.03 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M)) K) (@ (@ tptp.dvd_dvd_Code_integer M) K))))
% 6.82/7.03 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 6.82/7.03 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) (@ tptp.tanh_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X2)) (@ tptp.tanh_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.82/7.03 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X2)) (@ _let_1 X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X2)) (@ _let_1 X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X2))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N)) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N)) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.82/7.03 (assert (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1))))))
% 6.82/7.03 (assert (forall ((W tptp.num) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1))))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.82/7.03 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (= (@ tptp.abs_abs_int X2) (@ tptp.abs_abs_int Y2)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_int Y2))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (= (@ tptp.abs_abs_real X2) (@ tptp.abs_abs_real Y2)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_real Y2))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X2) (@ tptp.abs_abs_Code_integer Y2)) (or (= X2 Y2) (= X2 (@ tptp.uminus1351360451143612070nteger Y2))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (= (@ tptp.abs_abs_rat X2) (@ tptp.abs_abs_rat Y2)) (or (= X2 Y2) (= X2 (@ tptp.uminus_uminus_rat Y2))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 6.82/7.03 (assert (forall ((L2 tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L2) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L2) K))))
% 6.82/7.03 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L2) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L2) K))))
% 6.82/7.03 (assert (forall ((L2 tptp.code_integer) (K tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L2) (@ tptp.abs_abs_Code_integer K)) (@ (@ tptp.dvd_dvd_Code_integer L2) K))))
% 6.82/7.03 (assert (forall ((L2 tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L2) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L2) K))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D2))))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D2))))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D2))))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D2))))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 6.82/7.03 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 6.82/7.03 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.one_one_real)))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) E2))) (= X2 tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) E2))) (= X2 tptp.zero_zero_rat))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X2) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y2)) X2) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y2) X2))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y2)) X2) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y2) X2))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y2)) X2) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y2) X2))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y2)) X2) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y2) X2))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.abs_abs_real A) B) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (or (= A B) (= A (@ tptp.uminus_uminus_real B)))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) B) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B)))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.abs_abs_rat A) B) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (or (= A B) (= A (@ tptp.uminus_uminus_rat B)))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.abs_abs_int A) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (or (= A B) (= A (@ tptp.uminus_uminus_int B)))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.abs_abs_real B)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B A) (= B (@ tptp.uminus_uminus_real A)))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.abs_abs_Code_integer B)) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (or (= B A) (= B (@ tptp.uminus1351360451143612070nteger A)))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.abs_abs_rat B)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (or (= B A) (= B (@ tptp.uminus_uminus_rat A)))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.abs_abs_int B)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B A) (= B (@ tptp.uminus_uminus_int A)))))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.82/7.03 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.82/7.03 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X2)) Y2) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) Y2))))))
% 6.82/7.03 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X2)) Y2) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X2) Y2))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 6.82/7.03 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 6.82/7.03 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 6.82/7.03 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.82/7.03 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.82/7.03 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.82/7.03 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.82/7.03 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.82/7.03 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.82/7.03 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.82/7.03 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.82/7.03 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.82/7.03 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.82/7.03 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R)) X2) (@ (@ tptp.ord_le3102999989581377725nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R)) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real A) R))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R)) X2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat A) R))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R)) X2) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.plus_plus_int A) R))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D2)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D2))))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D2))))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D2)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D2))))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D2)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D2))))))
% 6.82/7.03 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.82/7.03 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.82/7.03 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R)) X2) (@ (@ tptp.ord_le6747313008572928689nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R)) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real A) R))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R)) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat A) R))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R)) X2) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.plus_plus_int A) R))))))
% 6.82/7.03 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.82/7.03 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D3) (and (@ (@ tptp.ord_less_real A) Y4) (@ (@ tptp.ord_less_real Y4) B))))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (U tptp.real) (V tptp.real)) (=> (= X2 Y2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) U)) Y2))) V)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X2)))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X2)))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2)))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X2)))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X2)))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X2)))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2)))))
% 6.82/7.03 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X2)))))
% 6.82/7.03 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y4) (@ (@ tptp.ord_less_eq_real Y4) B))))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) (@ tptp.abs_abs_Code_integer Y2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y2) _let_1))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) (@ tptp.abs_abs_rat Y2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))))))
% 6.82/7.03 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X2) tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X2) tptp.one_one_rat))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X2) tptp.one_one_real))))
% 6.82/7.03 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X2) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 6.82/7.03 (assert (forall ((Y2 tptp.code_integer) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y2) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y2) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) Y2))))))
% 6.82/7.03 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) Y2))))))
% 6.82/7.03 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) Y2))))))
% 6.82/7.03 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) Y2))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X2 tptp.code_integer)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3) (@ (@ P X3) (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X2)) (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X2 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ P X3) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X2 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (@ (@ P X3) (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X2)) (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X2 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ (@ P X3) (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X2)) (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 6.82/7.03 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 6.82/7.03 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.82/7.03 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.82/7.03 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N3 tptp.nat)) (and (not (@ P N3)) (@ P (@ tptp.suc N3))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z3)))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z3)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) X2))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z3)))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z3)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y2))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X2) _let_1)) (= (@ tptp.archim8280529875227126926d_real X2) Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y2))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X2) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X2) Y2)))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X2) N))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X2) N))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) X2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) X2))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 6.82/7.03 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X2)) (@ _let_1 X2)))))
% 6.82/7.03 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X2)) (@ _let_1 X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 6.82/7.04 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.82/7.04 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X2)) (@ tptp.arctan Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X2)) (@ tptp.arctan Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.82/7.04 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y2) X2) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X2) Y2)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X2)) (@ tptp.archim7778729529865785530nd_rat Y2)))))
% 6.82/7.04 (assert (= tptp.abs_abs_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I4)) I4))))
% 6.82/7.04 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L2))) (@ tptp.abs_abs_int L2)))))
% 6.82/7.04 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L2))) (@ _let_2 (@ _let_1 L2)))))))
% 6.82/7.04 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K)) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.82/7.04 (assert (forall ((Z tptp.real) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M)))))))
% 6.82/7.04 (assert (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ (@ tptp.ord_less_nat I2) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I2))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K)))))))))
% 6.82/7.04 (assert (forall ((D2 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) Z))) tptp.one_one_int)) D2))))))
% 6.82/7.04 (assert (forall ((D2 tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D2))) Z)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I2))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X2)) (@ tptp.arctan Y2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X2) Y2)))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X2)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X2)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.04 (assert (forall ((R tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R))) (=> (not (= R tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D2)))))))))
% 6.82/7.04 (assert (forall ((R tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (=> (not (= R tptp.zero_zero_real)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D2)))))))))
% 6.82/7.04 (assert (forall ((R tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R))) (=> (not (= R tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D2)))))))))
% 6.82/7.04 (assert (forall ((R tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R))) (=> (not (= R tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D2)))))))))
% 6.82/7.04 (assert (forall ((R tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R))) (=> (not (= R tptp.zero_zero_int)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D2)))))))))
% 6.82/7.04 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int M) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N) (@ (@ tptp.plus_plus_int N) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.82/7.04 (assert (= tptp.nat_set_decode (lambda ((X tptp.nat)) (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat _let_1) N2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A2)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A2))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G) K5)))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) K5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G) K5)))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) K5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) K5)) (@ (@ tptp.groups5690904116761175830ex_int G) K5)))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))))
% 6.82/7.04 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 6.82/7.04 (assert (forall ((R tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int R) (@ F N2)))) A2))))
% 6.82/7.04 (assert (forall ((R tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex R) (@ F N2)))) A2))))
% 6.82/7.04 (assert (forall ((R tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat R) (@ F N2)))) A2))))
% 6.82/7.04 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R) (@ F N2)))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int (@ F N2)) R))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N2)) R))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N2)) R))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) R))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B3 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I4)) (@ G J3)))) B3))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B3 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B3)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I4)) (@ G J3)))) B3))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I4)) (@ G J3)))) B3))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ G J3)))) B3))) A2))))
% 6.82/7.04 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_int (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_complex (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) A2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_real (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) A2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) R))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) R))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((F (-> tptp.real tptp.rat)) (I5 tptp.set_real) (G (-> tptp.real tptp.rat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) I5) (@ (@ tptp.groups1300246762558778688al_rat G) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I5) (@ (@ tptp.groups2906978787729119204at_rat G) I5)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_nat I) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G (-> tptp.int tptp.rat)) (I tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I5) (@ (@ tptp.groups3906332499630173760nt_rat G) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.complex tptp.rat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I5) (@ (@ tptp.groups5058264527183730370ex_rat G) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.real tptp.nat)) (I5 tptp.set_real) (G (-> tptp.real tptp.nat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I5) (@ (@ tptp.groups1935376822645274424al_nat G) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G (-> tptp.int tptp.nat)) (I tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I5) (@ (@ tptp.groups4541462559716669496nt_nat G) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.complex tptp.nat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I5) (@ (@ tptp.groups5693394587270226106ex_nat G) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.real tptp.int)) (I5 tptp.set_real) (G (-> tptp.real tptp.int)) (I tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I5) (@ (@ tptp.groups1932886352136224148al_int G) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I5) (@ (@ tptp.groups3539618377306564664at_int G) I5)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_nat I) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.complex tptp.int)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.int)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) I5) (@ (@ tptp.groups5690904116761175830ex_int G) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_nat) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I (-> tptp.int tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A2) tptp.zero_zero_real) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A2) (= (@ F X) tptp.zero_zero_real))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A2) (= (@ F X) tptp.zero_zero_real))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A2) tptp.zero_zero_real) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A2) (= (@ F X) tptp.zero_zero_real))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F) A2) tptp.zero_zero_rat) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A2) (= (@ F X) tptp.zero_zero_rat))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A2) tptp.zero_zero_rat) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A2) (= (@ F X) tptp.zero_zero_rat))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A2) tptp.zero_zero_rat) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A2) (= (@ F X) tptp.zero_zero_rat))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F) A2) tptp.zero_zero_rat) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A2) (= (@ F X) tptp.zero_zero_rat))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F) A2) tptp.zero_zero_nat) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A2) (= (@ F X) tptp.zero_zero_nat))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.zero_zero_nat) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A2) (= (@ F X) tptp.zero_zero_nat))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.zero_zero_nat) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A2) (= (@ F X) tptp.zero_zero_nat))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_int (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups3539618377306564664at_int G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_int (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups5690904116761175830ex_int G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_int (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X22) Y23)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups2073611262835488442omplex H2) S2)) (@ (@ tptp.groups2073611262835488442omplex G) S2))))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X22) Y23)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups3049146728041665814omplex H2) S2)) (@ (@ tptp.groups3049146728041665814omplex G) S2))))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X22) Y23)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups8778361861064173332t_real H2) S2)) (@ (@ tptp.groups8778361861064173332t_real G) S2))))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X22) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups5808333547571424918x_real H2) S2)) (@ (@ tptp.groups5808333547571424918x_real G) S2))))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X22) Y23)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups2906978787729119204at_rat H2) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) S2))))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X22) Y23)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups3906332499630173760nt_rat H2) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G) S2))))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R2 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X22) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups5058264527183730370ex_rat H2) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) S2))))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R2 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X22 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X22) Y23)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups4541462559716669496nt_nat H2) S2)) (@ (@ tptp.groups4541462559716669496nt_nat G) S2))))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R2 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X22 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X22) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups5693394587270226106ex_nat H2) S2)) (@ (@ tptp.groups5693394587270226106ex_nat G) S2))))))))
% 6.82/7.04 (assert (forall ((R2 (-> tptp.int tptp.int Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R2 tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X22 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R2 X15) X22) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_int X15) Y15)) (@ (@ tptp.plus_plus_int X22) Y23)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (@ (@ R2 (@ H2 X3)) (@ G X3)))) (@ (@ R2 (@ (@ tptp.groups3539618377306564664at_int H2) S2)) (@ (@ tptp.groups3539618377306564664at_int G) S2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) (@ (@ tptp.groups8097168146408367636l_real G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) (@ (@ tptp.groups1300246762558778688al_rat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2)))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_real) (S2 tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T4) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S2) (@ (@ tptp.groups5754745047067104278omplex H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_int) (S2 tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T3 tptp.set_int) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T4) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S2) (@ (@ tptp.groups3049146728041665814omplex H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_real) (S2 tptp.set_int) (I (-> tptp.real tptp.int)) (J (-> tptp.int tptp.real)) (T3 tptp.set_real) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T4) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S2) (@ (@ tptp.groups5754745047067104278omplex H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S2 tptp.set_int) (I (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T3 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T4) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S2) (@ (@ tptp.groups3049146728041665814omplex H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_real) (S2 tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups8097168146408367636l_real H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_int) (S2 tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T3 tptp.set_int) (G (-> tptp.real tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups8778361861064173332t_real H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_complex) (S2 tptp.set_real) (I (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.real tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T3) T4)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups5808333547571424918x_real H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_real) (S2 tptp.set_int) (I (-> tptp.real tptp.int)) (J (-> tptp.int tptp.real)) (T3 tptp.set_real) (G (-> tptp.int tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S2) (@ (@ tptp.groups8097168146408367636l_real H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S2 tptp.set_int) (I (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S2) (@ (@ tptp.groups8778361861064173332t_real H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_complex) (S2 tptp.set_int) (I (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.int tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T3) T4)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S2) (@ (@ tptp.groups5808333547571424918x_real H2) T3)))))))))))))
% 6.82/7.04 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.rat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.nat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (B3 tptp.real) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) B3) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (B3 tptp.real) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) B3) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (B3 tptp.real) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) B3) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.rat)) (B3 tptp.rat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S) B3) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B3 tptp.rat) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) B3) (=> (@ (@ tptp.member_nat I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (B3 tptp.rat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) B3) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B3 tptp.rat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) B3) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (B3 tptp.nat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) B3) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.nat)) (B3 tptp.nat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S) B3) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.nat)) (B3 tptp.nat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S) B3) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B3)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G X) tptp.zero_zero_complex))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.zero_zero_complex))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G X) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ G X) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G X) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ G X) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G X) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex H2))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int C4) B3)) (= (@ H2 B5) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H2))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat H2))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_nat))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat H2))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A5) tptp.zero_zero_nat))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int C4) B3)) (= (@ H2 B5) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex H2))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int C4) B3)) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H2))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat H2))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_nat))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat H2))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A5) tptp.zero_zero_nat))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int C4) B3)) (= (@ H2 B5) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S2) (@ (@ tptp.groups5754745047067104278omplex H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ H2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S2) (@ (@ tptp.groups3049146728041665814omplex H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups8097168146408367636l_real H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ H2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S2) (@ (@ tptp.groups8778361861064173332t_real H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G) S2) (@ (@ tptp.groups5808333547571424918x_real H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) S2) (@ (@ tptp.groups1300246762558778688al_rat H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ H2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G) S2) (@ (@ tptp.groups3906332499630173760nt_rat H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G) S2) (@ (@ tptp.groups5058264527183730370ex_rat H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S2) (@ (@ tptp.groups1935376822645274424al_nat H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ H2 X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) S2) (@ (@ tptp.groups4541462559716669496nt_nat H2) T3))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) T3) (@ (@ tptp.groups5754745047067104278omplex H2) S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3049146728041665814omplex G) T3) (@ (@ tptp.groups3049146728041665814omplex H2) S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G) T3) (@ (@ tptp.groups8097168146408367636l_real H2) S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups8778361861064173332t_real G) T3) (@ (@ tptp.groups8778361861064173332t_real H2) S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G) T3) (@ (@ tptp.groups5808333547571424918x_real H2) S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) T3) (@ (@ tptp.groups1300246762558778688al_rat H2) S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G) T3) (@ (@ tptp.groups3906332499630173760nt_rat H2) S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G) T3) (@ (@ tptp.groups5058264527183730370ex_rat H2) S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) T3) (@ (@ tptp.groups1935376822645274424al_nat H2) S2))))))))
% 6.82/7.04 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) T3) (@ (@ tptp.groups4541462559716669496nt_nat H2) S2))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat F))) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.groups975429370522433651at_int F))) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B5)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B5)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B5)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B5)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B3) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B3) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I4 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I4 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X2) I5) tptp.one_one_real) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I4 tptp.complex)) (@ (@ tptp.times_times_real (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X2) I5) tptp.one_one_real) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_real (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X2) I5) tptp.one_one_real) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I4 tptp.int)) (@ (@ tptp.times_times_real (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X2) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((I4 tptp.complex)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X2) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X2) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 6.82/7.04 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.82/7.04 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_real (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.82/7.04 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_rat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_nat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.82/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_int (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (Y2 tptp.real) (X2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X2) (= Y2 Z)))))))
% 6.82/7.04 (assert (forall ((W tptp.rat) (Y2 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X2) (= Y2 Z)))))))
% 6.82/7.04 (assert (forall ((W tptp.nat) (Y2 tptp.nat) (X2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X2))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X2) (= Y2 Z)))))))
% 6.82/7.04 (assert (forall ((W tptp.int) (Y2 tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X2) (= Y2 Z)))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M3 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_int M3) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S2)))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N)))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N)))))))
% 6.82/7.04 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))))
% 6.82/7.04 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))))
% 6.82/7.04 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))))
% 6.82/7.04 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.82/7.04 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.82/7.04 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.82/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.82/7.04 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) tptp.one_one_int) tptp.one_one_int)))
% 6.82/7.04 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.82/7.04 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.82/7.04 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.exp_real X2) tptp.one_one_real) (= X2 tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.82/7.04 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.82/7.04 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A2) tptp.zero_zero_complex))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A2) tptp.zero_zero_rat))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A2) tptp.zero_zero_real))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1745604003318907178nteger N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D2 (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D2 I4)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D2 I4)))) A2) tptp.zero_zero_complex))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D2 (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D2 I4)))) A2) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D2 I4)))) A2) tptp.zero_zero_rat))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D2 (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D2 I4)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D2 I4)))) A2) tptp.zero_zero_real))))))
% 6.82/7.04 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N))) _let_1)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.82/7.04 (assert (forall ((A2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A2))) (= (@ (@ tptp.times_times_complex _let_1) A2) (@ (@ tptp.times_times_complex A2) _let_1)))))
% 6.82/7.04 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.exp_real A2))) (= (@ (@ tptp.times_times_real _let_1) A2) (@ (@ tptp.times_times_real A2) _let_1)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int) (R tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ tptp.bit_concat_bit N))) (= (= (@ (@ _let_2 K) L2) (@ (@ _let_2 R) S)) (and (= (@ _let_1 K) (@ _let_1 R)) (= L2 S)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) B)) (@ _let_1 B)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (exists ((X3 tptp.real)) (= (@ tptp.exp_real X3) Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X2))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A2) (@ (@ tptp.groups6591440286371151544t_real G) A2))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 6.82/7.04 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N) M)) _let_2) _let_1) A))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y2)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X2) Y2) (@ (@ tptp.times_times_complex Y2) X2)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y2)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (= (@ (@ tptp.times_times_real X2) Y2) (@ (@ tptp.times_times_real Y2) X2)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y2)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat)) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups977919841031483927at_nat (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups977919841031483927at_nat F) A2)) (@ (@ tptp.groups977919841031483927at_nat G) A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A2) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.one_one_nat) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) tptp.one_one_nat) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A2) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A2) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) A)) (@ _let_1 A))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.exp_real X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))) tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2))) tptp.one_one_complex)))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C)))) tptp.zero_zero_complex))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.exp_real X2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.rat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y2) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.minus_minus_real Y2) tptp.one_one_real)) (= (@ tptp.exp_real X3) Y2))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y2)) X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y2)) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) X2))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)))))
% 6.82/7.04 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ tptp.modulo_modulo_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.82/7.04 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.82/7.04 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.04 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.modulo_modulo_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.82/7.04 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))) (let ((_let_2 (@ tptp.exp_real X))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.82/7.04 (assert (= tptp.tanh_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (@ tptp.exp_complex X))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.82/7.04 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A))))
% 6.82/7.04 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1))) _let_1)))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 6.82/7.04 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.82/7.04 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N)) (= N tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N)) (= N tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N)) (= N tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.82/7.04 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 6.82/7.04 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.82/7.04 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.82/7.04 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 6.82/7.04 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))
% 6.82/7.04 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M3 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.member_nat N2) S2)))))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (S2 tptp.set_nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M4) (exists ((N7 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N7) (@ (@ tptp.member_nat N7) S2))))) (not (@ tptp.finite_finite_nat S2)))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M3 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.member_nat N2) S2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 6.82/7.04 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.82/7.04 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int K2) _let_1))) _let_1)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.82/7.04 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer))))))))))
% 6.82/7.04 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X2))))))))
% 6.82/7.04 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I4) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D2)))) _let_1)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X2))))))
% 6.82/7.04 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.log _let_1) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X2)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.82/7.04 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 tptp.zero_zero_int) (= L tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K2 _let_2)) L) (@ (@ (@ tptp.if_int (= L _let_2)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N)) (= M N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) (@ tptp.semiri681578069525770553at_rat N)) (= M N))))
% 6.82/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) B) _let_1))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B))) (= (@ (@ tptp.bit_se727722235901077358nd_nat _let_1) B) _let_1))))
% 6.82/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.82/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.82/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.82/7.04 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.82/7.04 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X2) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.82/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.82/7.04 (assert (forall ((U tptp.real) (Deg tptp.nat) (T tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (=> (= U (@ (@ tptp.power_power_real _let_1) Deg)) (=> (@ (@ tptp.vEBT_invar_vebt T) Deg) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_height T))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ _let_2 (@ _let_2 U))))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 6.82/7.04 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.82/7.04 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.82/7.04 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.82/7.04 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.82/7.04 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 6.82/7.04 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.82/7.04 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.82/7.04 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.82/7.04 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.82/7.04 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2)))
% 6.82/7.04 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) (@ tptp.uminus_uminus_int tptp.one_one_int)) X2)))
% 6.82/7.04 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.82/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.82/7.04 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.82/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat M)) N))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W) (@ tptp.semiri681578069525770553at_rat X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X2) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X2) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X2) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X2) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X2) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.82/7.04 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.82/7.04 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))))
% 6.82/7.04 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.82/7.04 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.82/7.04 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.82/7.04 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 6.82/7.04 (assert (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.82/7.04 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.82/7.04 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y2))) tptp.one_one_int)))
% 6.82/7.04 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) tptp.one_one_nat)))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) tptp.one_one_int) tptp.one_one_int)))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.82/7.04 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))))
% 6.82/7.04 (assert (forall ((N tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M))))
% 6.82/7.04 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) A) tptp.one_one_real)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_real X2) Y2)))))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) A))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_real A) X2)))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X2) (= (@ _let_2 (@ (@ tptp.log A) X2)) (@ _let_1 X2))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.82/7.04 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y2))) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) tptp.zero_zero_nat)))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y2))))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y2) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y2) _let_1) (= Y2 _let_1)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y2) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y2) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) (@ tptp.semiri1314217659103216013at_int Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.semiri5074537144036343181t_real Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y2)) (= _let_1 Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.semiri8010041392384452111omplex Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.semiri681578069525770553at_rat Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real A) X2))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) A))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2)))))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M))))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M))))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M))))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M))))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M)))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.inc M)))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.82/7.04 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int)))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X2)) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y2))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 6.82/7.04 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.82/7.04 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.82/7.04 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 6.82/7.04 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_nat X2) _let_1)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_eq_nat X2) _let_1)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.82/7.04 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.82/7.04 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.82/7.04 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 6.82/7.04 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y2))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y2)))))))
% 6.82/7.04 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int B))) (let ((_let_2 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat B))) (let ((_let_2 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.82/7.04 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B2) A3))))
% 6.82/7.04 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B2) A3))))
% 6.82/7.04 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int B) C))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat B) C))))))
% 6.82/7.04 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y2) (@ (@ tptp.times_times_int Y2) _let_1)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y2) (@ (@ tptp.times_times_real Y2) _let_1)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X2))) (= (@ (@ tptp.times_times_nat _let_1) Y2) (@ (@ tptp.times_times_nat Y2) _let_1)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X2))) (= (@ (@ tptp.times_times_complex _let_1) Y2) (@ (@ tptp.times_times_complex Y2) _let_1)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y2) (@ (@ tptp.times_times_rat Y2) _let_1)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N) M)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.82/7.04 (assert (forall ((Z tptp.int)) (not (forall ((M4 tptp.nat) (N3 tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.82/7.04 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X2)) (@ _let_1 X2)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 6.82/7.04 (assert (forall ((P (-> tptp.num Bool)) (X2 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X3 tptp.num)) (=> (@ P X3) (@ P (@ tptp.inc X3)))) (@ P X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X2))) (= (@ _let_1 (@ tptp.inc Y2)) (@ tptp.inc (@ _let_1 Y2))))))
% 6.82/7.04 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X2)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X2)))))))
% 6.82/7.04 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (= (@ (@ tptp.bit_se3949692690581998587nteger A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 6.82/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.04 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I)) (@ tptp.semiri5074537144036343181t_real J)))))
% 6.82/7.04 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.82/7.04 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.82/7.04 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) Z)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y2) Ya)) Z)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2))))))
% 6.82/7.04 (assert (= tptp.log (lambda ((A3 tptp.real) (X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real A3)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.82/7.04 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_se2000444600071755411sk_int N2)))))
% 6.82/7.04 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.82/7.04 (assert (forall ((Z tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))))
% 6.82/7.04 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N3))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))) (@ P Z)))))
% 6.82/7.04 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.82/7.04 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.82/7.04 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X2)) (@ tptp.semiri4216267220026989637d_enat Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.semiri5074537144036343181t_real Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ tptp.semiri1316708129612266289at_nat Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.ord_max_nat X2) Y2)) (@ (@ tptp.ord_max_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ tptp.semiri681578069525770553at_rat Y2)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.82/7.04 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.82/7.04 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.82/7.04 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X2)) (@ tptp.bit1 X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X2)) (@ tptp.bit0 (@ tptp.inc X2)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y2) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.plus_plus_num X2) tptp.one) (@ tptp.inc X2))))
% 6.82/7.04 (assert (forall ((Y2 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) Z)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y2) Ya)) Z)))))
% 6.82/7.04 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) K))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))))))
% 6.82/7.04 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X2) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X2) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X2)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N))))
% 6.82/7.04 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (forall ((Y4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X2)))))))
% 6.82/7.04 (assert (forall ((M tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2)))))
% 6.82/7.04 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 6.82/7.04 (assert (= tptp.ord_less_int (lambda ((W2 tptp.int) (Z4 tptp.int)) (exists ((N2 tptp.nat)) (= Z4 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 6.82/7.04 (assert (forall ((D2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D2) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D2)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num X2))) (= (@ _let_1 (@ tptp.inc Y2)) (@ (@ tptp.plus_plus_num (@ _let_1 Y2)) X2)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.82/7.04 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X2) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 B))))))))
% 6.82/7.04 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X2)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X2)) tptp.one_one_complex))))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X2)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X2)) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X2)) tptp.one_one_rat))))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X2)) tptp.one_one_nat))))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X2)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X2)) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.82/7.04 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.82/7.04 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.82/7.04 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K (@ tptp.semiri1314217659103216013at_int N3)))))))
% 6.82/7.04 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))))
% 6.82/7.04 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M3)))))
% 6.82/7.04 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M3)) tptp.one_one_real)))))
% 6.82/7.04 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B)))) (let ((_let_4 (@ (@ tptp.ord_less_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) _let_1))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D2))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X2) D2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X2) D2))) _let_1))))))
% 6.82/7.04 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.one_one_int) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.one_one_nat) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ _let_1 X2)) (@ _let_1 Y2)))))))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.minus_minus_real (@ _let_1 X2)) (@ _let_1 Y2)))))))))))
% 6.82/7.04 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E)))))))
% 6.82/7.04 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))))
% 6.82/7.04 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (let ((_let_3 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_1) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) X2))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_3)) (@ _let_2 (@ _let_2 U))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X2)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 C) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M4)) X2)) C))) (= X2 tptp.zero_zero_real)))))))
% 6.82/7.04 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.82/7.04 (assert (forall ((P (-> tptp.int Bool)) (X2 tptp.nat) (Y2 tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X2) Y2))) (and (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y2)))) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ P tptp.zero_zero_int))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2)))) tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X2))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.log A) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X2)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 6.82/7.04 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.82/7.04 (assert (forall ((A tptp.int) (D2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D2))))))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (D2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D2))))))))
% 6.82/7.04 (assert (forall ((A tptp.rat) (D2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D2))))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D2))))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (D2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D2))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.82/7.04 (assert (forall ((A tptp.int) (D2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D2)))) _let_1))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D2)))) _let_1))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real X2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 X2) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X2)))))))
% 6.82/7.04 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M3)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.04 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M3)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.04 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M3)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.04 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M3)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.04 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M3 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M3)))) (@ (@ (@ tptp.if_rat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))
% 6.82/7.04 (assert (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 6.82/7.04 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.archim7802044766580827645g_real (@ _let_1 X2)) (@ tptp.archim7802044766580827645g_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X2) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ tptp.suc N2))))))))))
% 6.82/7.04 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q4)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.82/7.04 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q4)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.82/7.04 (assert (forall ((H2 tptp.real) (Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q4)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.82/7.04 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I) K))))
% 6.82/7.04 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I) K))))
% 6.82/7.04 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I) K))))
% 6.82/7.04 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))))
% 6.82/7.04 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I) K))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)) X2) (exists ((N2 tptp.int)) (= X2 (@ tptp.ring_1_of_int_rat N2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)) X2) (exists ((N2 tptp.int)) (= X2 (@ tptp.ring_1_of_int_real N2))))))
% 6.82/7.04 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height T)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X2)) (@ tptp.set_ord_lessThan_rat Y2)) (@ (@ tptp.ord_less_eq_rat X2) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X2)) (@ tptp.set_ord_lessThan_num Y2)) (@ (@ tptp.ord_less_eq_num X2) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X2)) (@ tptp.set_ord_lessThan_int Y2)) (@ (@ tptp.ord_less_eq_int X2) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X2)) (@ tptp.set_ord_lessThan_nat Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X2)) (@ tptp.set_or5984915006950818249n_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.82/7.04 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.82/7.04 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.82/7.04 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 6.82/7.04 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) Z))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) Z))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) Z))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) Z))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real V)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 6.82/7.04 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X2))))
% 6.82/7.04 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 6.82/7.04 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.82/7.04 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 6.82/7.04 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.82/7.04 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) tptp.zero_zero_nat)))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ F tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ F tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.82/7.04 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) tptp.one_one_nat)))
% 6.82/7.04 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.82/7.04 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 6.82/7.04 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.82/7.04 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X2))))
% 6.82/7.04 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X2))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.82/7.04 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X2))))
% 6.82/7.04 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X2))))
% 6.82/7.04 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_rat X) U2))))))
% 6.82/7.04 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_num X) U2))))))
% 6.82/7.04 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_int X) U2))))))
% 6.82/7.04 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) U2))))))
% 6.82/7.04 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_real X) U2))))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y2)) (@ tptp.archim7802044766580827645g_real X2)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y2) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y2)) (@ tptp.archim2889992004027027881ng_rat X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y2)) (@ (@ tptp.ord_less_rat X2) Y2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.82/7.04 (assert (forall ((M tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M) N))))
% 6.82/7.04 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M) N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.04 (assert (forall ((M tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M) N))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.82/7.04 (assert (forall ((B tptp.complex) (A tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B) A))) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex A))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) A))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) A))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 6.82/7.04 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 6.82/7.04 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) Y2))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X2))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X2))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X2)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.82/7.04 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N))) (=> (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 6.82/7.04 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 6.82/7.04 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) (@ (@ tptp.plus_plus_real R) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R))) (@ (@ tptp.plus_plus_rat R) tptp.one_one_rat))))
% 6.82/7.04 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) tptp.one_one_real)) R)))
% 6.82/7.04 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R))) tptp.one_one_rat)) R)))
% 6.82/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.82/7.04 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (R tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I4)) R))) _let_1)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (N tptp.nat) (R tptp.complex)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex F) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) R)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F I4)) R))) _let_1)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (R tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I4)) R))) _let_1)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (R tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I4)) R))) _let_1)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1)))))
% 6.82/7.04 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.archim7802044766580827645g_real X2) Z))))))
% 6.82/7.04 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X2) Z))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X2) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X2) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1))))))
% 6.82/7.04 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I4)))))))
% 6.82/7.04 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T) (@ (@ tptp.ord_less_eq_rat T) _let_1)) (@ P I4)))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.82/7.04 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.82/7.04 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 6.82/7.04 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_complex (@ _let_2 X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_rat (@ _let_2 X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_int (@ _let_2 X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_real (@ _let_2 X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (not (= X2 tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (not (= X2 tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (not (= X2 tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))))
% 6.82/7.04 (assert (forall ((Q2 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real P2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q2)))) Q2)))))
% 6.82/7.04 (assert (forall ((Q2 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_eq_rat P2) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q2)))) Q2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 6.82/7.04 (assert (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P5)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.82/7.04 (assert (forall ((Z tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.82/7.04 (assert (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.82/7.04 (assert (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P5)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y2) N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_complex X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (N tptp.nat) (Y2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_rat Y2) N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_rat X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y2) N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_int X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y2) N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_real X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.power_power_complex Y2) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) P5)) (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (N tptp.nat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) P5)) (@ (@ tptp.power_power_rat Y2) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) P5)) (@ (@ tptp.power_power_int Y2) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) P5)) (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.82/7.04 (assert (forall ((Q2 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q2)))) tptp.one_one_real)) Q2)) P2))))
% 6.82/7.04 (assert (forall ((Q2 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q2)))) tptp.one_one_rat)) Q2)) P2))))
% 6.82/7.04 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.82/7.04 (assert (forall ((N tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K5))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K5))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K5))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K5))))))
% 6.82/7.04 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 6.82/7.04 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.times_times_complex (@ _let_1 X2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.times_times_rat (@ _let_1 X2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.times_times_int (@ _let_1 X2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M3 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.82/7.04 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M3)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ F I4)) (@ G I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) tptp.one_one_nat)))) _let_1))))))
% 6.82/7.04 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.82/7.04 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 6.82/7.04 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arctan X2) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.82/7.04 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))))
% 6.82/7.04 (assert (forall ((W tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) (@ tptp.real_V1022390504157884413omplex A)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.82/7.04 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.82/7.04 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_complex))))
% 6.82/7.04 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.82/7.04 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.82/7.04 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X2)) (not (= X2 tptp.zero_zero_real)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2)) (not (= X2 tptp.zero_zero_complex)))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) A)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.complex)) (G (-> tptp.product_prod_nat_nat tptp.real))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6381953495645901045omplex F) S2))) (@ (@ tptp.groups4567486121110086003t_real G) S2)))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S2))) (@ (@ tptp.groups8097168146408367636l_real G) S2)))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S2))) (@ (@ tptp.groups8778361861064173332t_real G) S2)))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S2))) (@ (@ tptp.groups6591440286371151544t_real G) S2)))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S2))) (@ (@ tptp.groups5808333547571424918x_real G) S2)))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S2))) (@ (@ tptp.groups6591440286371151544t_real G) S2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I4)))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A2))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I4 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I4)))) A2))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I4)))) A2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) Y2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) Y2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2)))))
% 6.82/7.04 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))))))
% 6.82/7.04 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (N tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N) (@ (@ tptp.power_power_real Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N) (@ (@ tptp.power_power_complex Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (R tptp.real) (Y2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y2)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y2))) (@ (@ tptp.times_times_real R) S))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (R tptp.real) (Y2 tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y2)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y2))) (@ (@ tptp.times_times_real R) S))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y2))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y2))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2))) E))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2))) E))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (R tptp.real) (Y2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y2)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (R tptp.real) (Y2 tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y2)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2))) E))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2))) E))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (R tptp.real) (B tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (R tptp.real) (B tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y2))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y2) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y2))))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y2))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y2) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y2))) E))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B)))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B)))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.82/7.04 (assert (forall ((W tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D2))))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D2))))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X2) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X2) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((Z tptp.real) (W tptp.real) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z) M)) (@ (@ tptp.power_power_real W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z) W))))))))
% 6.82/7.04 (assert (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z) M)) (@ (@ tptp.power_power_complex W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W))))))))
% 6.82/7.04 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (= (@ tptp.suminf_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.82/7.04 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (= (@ tptp.suminf_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M3)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.82/7.04 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))) (@ tptp.summable_real F))))
% 6.82/7.04 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.82/7.04 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.82/7.04 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.82/7.04 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (@ tptp.power_power_real C)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (@ tptp.power_power_complex C)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ tptp.summable_real F))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))))
% 6.82/7.04 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))))
% 6.82/7.04 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 6.82/7.04 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.82/7.04 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.82/7.04 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real F)) C) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.plus_plus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (= (@ (@ tptp.plus_plus_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)) (@ tptp.suminf_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (= (@ (@ tptp.plus_plus_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)) (@ tptp.suminf_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_real)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_nat)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_int)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ F N2)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 6.82/7.04 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I4))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ tptp.summable_int F)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ tptp.summable_nat F)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ tptp.summable_real F)))))
% 6.82/7.04 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real C)))))
% 6.82/7.04 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex C)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I5)) (@ tptp.suminf_int F)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (I5 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I5)) (@ tptp.suminf_nat F)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (I5 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I5)) (@ tptp.suminf_real F)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real F) (@ (@ tptp.plus_plus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N9 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M2) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N7)))) E)))))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (E tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N9 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M2) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N7)))) E)))))))))))
% 6.82/7.04 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (=> (@ tptp.summable_real F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N7)))))) R))))))))
% 6.82/7.04 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (=> (@ tptp.summable_complex F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N7)))))) R))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I2)) tptp.one_one_real)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ (@ tptp.power_power_real Z) I4))))))))))
% 6.82/7.04 (assert (forall ((R tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_real R) R0) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N3))) (@ (@ tptp.power_power_real R0) N3))) M7)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N2))) (@ (@ tptp.power_power_real R) N2)))))))))
% 6.82/7.04 (assert (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N3)))))) (@ tptp.summable_real F)))))
% 6.82/7.04 (assert (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N3)))))) (@ tptp.summable_complex F)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))))
% 6.82/7.04 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) tptp.pi))
% 6.82/7.04 (assert (forall ((Y2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.zero_zero_real))
% 6.82/7.04 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y2))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arctan Y2))))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.bit1 tptp.one))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_1))) (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_3)))))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real _let_3)) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2))))))))) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_2)))))))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_2)))) (= (@ (@ tptp.divide_divide_real tptp.pi) _let_3) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real _let_3) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_2)))))) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))))))))))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D3))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ F (@ _let_2 _let_1))) (@ F (@ _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real F))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X2)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X2) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) Y2) (and (=> _let_5 (= Y2 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y2 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 6.82/7.04 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K2) _let_4) (@ (@ tptp.member_int L) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (not (= X2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T5 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T5))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.minus_5127226145743854075T_VEBT A2))) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) B3)) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A2))) (=> (not (@ (@ tptp.member_complex X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) B3)) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X2) B3)) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X2) B3)) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((X2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X2) B3)) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (=> (not (@ (@ tptp.member_nat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) B3)) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((X2 tptp.vEBT_VEBT) (B3 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) B3) (= (@ (@ tptp.minus_5127226145743854075T_VEBT (@ (@ tptp.insert_VEBT_VEBT X2) A2)) B3) (@ (@ tptp.minus_5127226145743854075T_VEBT A2) B3)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (B3 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ (@ tptp.member_complex X2) B3) (= (@ (@ tptp.minus_811609699411566653omplex (@ (@ tptp.insert_complex X2) A2)) B3) (@ (@ tptp.minus_811609699411566653omplex A2) B3)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (B3 tptp.set_real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X2) B3) (= (@ (@ tptp.minus_minus_set_real (@ (@ tptp.insert_real X2) A2)) B3) (@ (@ tptp.minus_minus_set_real A2) B3)))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int X2) B3) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X2) A2)) B3) (@ (@ tptp.minus_minus_set_int A2) B3)))))
% 6.82/7.04 (assert (forall ((X2 tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) B3) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) A2)) B3) (@ (@ tptp.minus_1356011639430497352at_nat A2) B3)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) B3) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X2) A2)) B3) (@ (@ tptp.minus_minus_set_nat A2) B3)))))
% 6.82/7.04 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.82/7.04 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.82/7.04 (assert (forall ((A tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT A))) (= (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))) (@ _let_1 A2)))))
% 6.82/7.04 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A2)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) (@ _let_1 A2)))))
% 6.82/7.04 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) (@ _let_1 A2)))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.minus_5127226145743854075T_VEBT A2))) (= (@ tptp.finite5795047828879050333T_VEBT (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT A) B3))) (@ tptp.finite5795047828879050333T_VEBT (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (= (@ tptp.finite_finite_real (@ _let_1 (@ (@ tptp.insert_real A) B3))) (@ tptp.finite_finite_real (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A) B3))) (@ tptp.finite_finite_int (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A2))) (= (@ tptp.finite3207457112153483333omplex (@ _let_1 (@ (@ tptp.insert_complex A) B3))) (@ tptp.finite3207457112153483333omplex (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A2))) (= (@ tptp.finite6177210948735845034at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A) B3))) (@ tptp.finite6177210948735845034at_nat (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A) B3))) (@ tptp.finite_finite_nat (@ _let_1 B3))))))
% 6.82/7.04 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.82/7.04 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.82/7.04 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.82/7.04 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.82/7.04 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.82/7.04 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.82/7.04 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.82/7.04 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.82/7.04 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.82/7.04 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real tptp.pi) X2)) (@ tptp.sin_real X2))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.04 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.82/7.04 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.82/7.04 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.82/7.04 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.82/7.04 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.82/7.04 (assert (forall ((K tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int K) tptp.bot_bot_set_int))) (= (@ (@ tptp.minus_minus_set_int _let_1) (@ tptp.set_ord_lessThan_int K)) _let_1))))
% 6.82/7.04 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat))) (= (@ (@ tptp.minus_minus_set_nat _let_1) (@ tptp.set_ord_lessThan_nat K)) _let_1))))
% 6.82/7.04 (assert (forall ((K tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real K) tptp.bot_bot_set_real))) (= (@ (@ tptp.minus_minus_set_real _let_1) (@ tptp.set_or5984915006950818249n_real K)) _let_1))))
% 6.82/7.04 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.82/7.04 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X2))) (let ((_let_2 (@ tptp.cos_complex X2))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (let ((_let_2 (@ tptp.cos_real X2))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X2)) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X2)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.int)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X2)) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X2)) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 6.82/7.04 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 6.82/7.04 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.82/7.04 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.82/7.04 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.82/7.04 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.cos_real X2))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) tptp.one_one_complex))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) tptp.one_one_complex))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 6.82/7.04 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 6.82/7.04 (assert (forall ((N tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.one_one_real)))
% 6.82/7.04 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) tptp.zero_zero_real))
% 6.82/7.04 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((N tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (exists ((R3 tptp.real) (A5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X2 (@ _let_1 (@ tptp.cos_real A5))) (= Y2 (@ _let_1 (@ tptp.sin_real A5))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (=> (= (@ tptp.cos_complex X2) tptp.one_one_complex) (= (@ tptp.sin_complex X2) tptp.zero_zero_complex))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.cos_real X2) tptp.one_one_real) (= (@ tptp.sin_real X2) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.vEBT_VEBT) (B3 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) B3))) (let ((_let_2 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_3 (@ (@ tptp.minus_5127226145743854075T_VEBT (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (B3 tptp.set_complex) (A2 tptp.set_complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (let ((_let_2 (@ tptp.insert_complex X2))) (let ((_let_3 (@ (@ tptp.minus_811609699411566653omplex (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_complex X2) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (B3 tptp.set_real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A2) B3))) (let ((_let_2 (@ tptp.insert_real X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_real (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_real X2) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (B3 tptp.set_int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (let ((_let_2 (@ tptp.insert_int X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_int X2) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B3))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat X2))) (let ((_let_3 (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat X2) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (B3 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (let ((_let_2 (@ tptp.insert_nat X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_nat X2) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X2)) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (=> (= (@ tptp.sin_complex X2) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X2)) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X2)) tptp.one_one_real))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X2)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X2))) (@ tptp.cos_complex X2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X2)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X2))) (@ tptp.cos_real X2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X2)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X2))) (@ tptp.abs_abs_real X2))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real M)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT A))) (let ((_let_2 (@ tptp.minus_5127226145743854075T_VEBT A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT (@ _let_2 B3)) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B3)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_real (@ _let_2 B3)) (@ _let_1 tptp.bot_bot_set_real)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 B3)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B3)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 6.82/7.04 (assert (forall ((A tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT A))) (=> (@ (@ tptp.member_VEBT_VEBT A) A2) (= (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))) A2)))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.insert_complex A))) (=> (@ (@ tptp.member_complex A) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))) A2)))))
% 6.82/7.04 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.member_int A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) A2)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.member_real A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) A2)))))
% 6.82/7.04 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) A2)))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.member_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) A2)))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT A))) (let ((_let_2 (@ tptp.minus_5127226145743854075T_VEBT A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_5127226145743854075T_VEBT (@ _let_2 (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))) B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_real (@ _let_2 (@ _let_1 tptp.bot_bot_set_real))) B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B3))))))
% 6.82/7.04 (assert (forall ((X2 tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ (@ tptp.minus_5127226145743854075T_VEBT (@ _let_1 A2)) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT)) A2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (=> (not (@ (@ tptp.member_complex X2) A2)) (= (@ (@ tptp.minus_811609699411566653omplex (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_complex)) A2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_int)) A2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ (@ tptp.minus_minus_set_real (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_real)) A2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X2) A2)) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)) A2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (=> (not (@ (@ tptp.member_nat X2) A2)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_nat)) A2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (= (@ tptp.uminus8041839845116263051T_VEBT (@ _let_1 A2)) (@ (@ tptp.minus_5127226145743854075T_VEBT (@ tptp.uminus8041839845116263051T_VEBT A2)) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (= (@ tptp.uminus1532241313380277803et_int (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ _let_1 tptp.bot_bot_set_int))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (= (@ tptp.uminus612125837232591019t_real (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_real (@ tptp.uminus612125837232591019t_real A2)) (@ _let_1 tptp.bot_bot_set_real))))))
% 6.82/7.04 (assert (forall ((X2 tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (= (@ tptp.uminus6524753893492686040at_nat (@ _let_1 A2)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.uminus6524753893492686040at_nat A2)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))))))
% 6.82/7.04 (assert (forall ((X2 tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (= (@ tptp.uminus5710092332889474511et_nat (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ _let_1 tptp.bot_bot_set_nat))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (C4 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.minus_5127226145743854075T_VEBT B3))) (let ((_let_2 (@ tptp.ord_le4337996190870823476T_VEBT A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_VEBT_VEBT X2) A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X2 tptp.complex) (C4 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex B3))) (let ((_let_2 (@ tptp.ord_le211207098394363844omplex A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_complex X2) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_complex X2) A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X2 tptp.real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X2) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_real X2) A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X2 tptp.int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X2) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_int X2) A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B3))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X2) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member8440522571783428010at_nat X2) A2))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X2 tptp.nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X2) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_nat X2) A2))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y2))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2))))) tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) tptp.pi) (@ _let_1 (@ tptp.sin_real X2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X2)) (@ tptp.sin_real X2)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ _let_1 (@ tptp.sin_real X2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X2))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_2 Y2) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2)) (@ _let_1 X2))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (=> (= (@ tptp.cos_real X2) (@ tptp.cos_real Y2)) (= X2 Y2)))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X2))) tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X2))) tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((S2 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X3 tptp.vEBT_VEBT) (S5 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S5) (=> (forall ((Y4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y4) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_VEBT_VEBT X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_complex X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S5) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_nat X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S5 tptp.set_int)) (=> (@ tptp.finite_finite_int S5) (=> (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_int X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X3 tptp.real) (S5 tptp.set_real)) (=> (@ tptp.finite_finite_real S5) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.member_real Y4) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_real X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.num))) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X3 tptp.vEBT_VEBT) (S5 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S5) (=> (forall ((Y4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y4) S5) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_VEBT_VEBT X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) S5) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_complex X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S5) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) S5) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_nat X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S5 tptp.set_int)) (=> (@ tptp.finite_finite_int S5) (=> (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) S5) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_int X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X3 tptp.real) (S5 tptp.set_real)) (=> (@ tptp.finite_finite_real S5) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.member_real Y4) S5) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_real X3) S5)))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B5 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A7) (@ (@ tptp.ord_less_real B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B5 tptp.rat) (A7 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A7) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) A7) (@ (@ tptp.ord_less_rat B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_rat B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B5 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) A7) (@ (@ tptp.ord_less_num B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B5 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A7) (@ (@ tptp.ord_less_nat B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B5 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A7) (@ (@ tptp.ord_less_int B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B5 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A7) (@ (@ tptp.ord_less_real X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B5 tptp.rat) (A7 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A7) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) A7) (@ (@ tptp.ord_less_rat X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_rat B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B5 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) A7) (@ (@ tptp.ord_less_num X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B5 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A7) (@ (@ tptp.ord_less_nat X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B5 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A7) (@ (@ tptp.ord_less_int X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B5) A7)))))) (@ P A2))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A2)))) (let ((_let_4 (@ (@ tptp.member_real X2) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A2)))) (let ((_let_4 (@ (@ tptp.member_int X2) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A2)))) (let ((_let_4 (@ (@ tptp.member_real X2) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A2)))) (let ((_let_4 (@ (@ tptp.member_int X2) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X2)) _let_2)))))))))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z) W)) _let_1)))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z) W)) _let_1)))))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N)))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat N))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K) N)))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N)))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N)))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ P A2) (=> (forall ((A5 tptp.vEBT_VEBT) (A7 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A7) (=> (@ (@ tptp.member_VEBT_VEBT A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_5127226145743854075T_VEBT A7) (@ (@ tptp.insert_VEBT_VEBT A5) tptp.bot_bo8194388402131092736T_VEBT))))))) (@ P tptp.bot_bo8194388402131092736T_VEBT))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ P A2) (=> (forall ((A5 tptp.complex) (A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (@ (@ tptp.member_complex A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex A5) tptp.bot_bot_set_complex))))))) (@ P tptp.bot_bot_set_complex))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P A2) (=> (forall ((A5 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (@ (@ tptp.member_int A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int A5) tptp.bot_bot_set_int))))))) (@ P tptp.bot_bot_set_int))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P A2) (=> (forall ((A5 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (@ (@ tptp.member_real A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real A5) tptp.bot_bot_set_real))))))) (@ P tptp.bot_bot_set_real))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ P A2) (=> (forall ((A5 tptp.product_prod_nat_nat) (A7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A7) (=> (@ (@ tptp.member8440522571783428010at_nat A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A7) (@ (@ tptp.insert8211810215607154385at_nat A5) tptp.bot_bo2099793752762293965at_nat))))))) (@ P tptp.bot_bo2099793752762293965at_nat))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P A2) (=> (forall ((A5 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (@ (@ tptp.member_nat A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat A5) tptp.bot_bot_set_nat))))))) (@ P tptp.bot_bot_set_nat))))))
% 6.82/7.04 (assert (forall ((X7 (-> tptp.set_VEBT_VEBT Bool)) (A2 tptp.set_VEBT_VEBT)) (=> (@ X7 A2) (=> (forall ((A7 tptp.set_VEBT_VEBT)) (=> (@ X7 A7) (exists ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A7) (@ (@ tptp.insert_VEBT_VEBT X4) tptp.bot_bo8194388402131092736T_VEBT)))) (and (@ (@ tptp.member_VEBT_VEBT X4) A7) (or (@ X7 _let_1) (not (@ tptp.finite5795047828879050333T_VEBT _let_1)))))))) (not (@ tptp.finite5795047828879050333T_VEBT A2))))))
% 6.82/7.04 (assert (forall ((X7 (-> tptp.set_complex Bool)) (A2 tptp.set_complex)) (=> (@ X7 A2) (=> (forall ((A7 tptp.set_complex)) (=> (@ X7 A7) (exists ((X4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex)))) (and (@ (@ tptp.member_complex X4) A7) (or (@ X7 _let_1) (not (@ tptp.finite3207457112153483333omplex _let_1)))))))) (not (@ tptp.finite3207457112153483333omplex A2))))))
% 6.82/7.04 (assert (forall ((X7 (-> tptp.set_int Bool)) (A2 tptp.set_int)) (=> (@ X7 A2) (=> (forall ((A7 tptp.set_int)) (=> (@ X7 A7) (exists ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int)))) (and (@ (@ tptp.member_int X4) A7) (or (@ X7 _let_1) (not (@ tptp.finite_finite_int _let_1)))))))) (not (@ tptp.finite_finite_int A2))))))
% 6.82/7.04 (assert (forall ((X7 (-> tptp.set_real Bool)) (A2 tptp.set_real)) (=> (@ X7 A2) (=> (forall ((A7 tptp.set_real)) (=> (@ X7 A7) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real)))) (and (@ (@ tptp.member_real X4) A7) (or (@ X7 _let_1) (not (@ tptp.finite_finite_real _let_1)))))))) (not (@ tptp.finite_finite_real A2))))))
% 6.82/7.04 (assert (forall ((X7 (-> tptp.set_Pr1261947904930325089at_nat Bool)) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ X7 A2) (=> (forall ((A7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ X7 A7) (exists ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A7) (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat)))) (and (@ (@ tptp.member8440522571783428010at_nat X4) A7) (or (@ X7 _let_1) (not (@ tptp.finite6177210948735845034at_nat _let_1)))))))) (not (@ tptp.finite6177210948735845034at_nat A2))))))
% 6.82/7.04 (assert (forall ((X7 (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (=> (@ X7 A2) (=> (forall ((A7 tptp.set_nat)) (=> (@ X7 A7) (exists ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat)))) (and (@ (@ tptp.member_nat X4) A7) (or (@ X7 _let_1) (not (@ tptp.finite_finite_nat _let_1)))))))) (not (@ tptp.finite_finite_nat A2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT)) (=> (not (@ tptp.finite5795047828879050333T_VEBT S2)) (not (@ tptp.finite5795047828879050333T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT S2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT)))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_complex) (A tptp.complex)) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex)))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_int) (A tptp.int)) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_real) (A tptp.real)) (=> (not (@ tptp.finite_finite_real S2)) (not (@ tptp.finite_finite_real (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat S2)) (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat S2) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat)))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_nat) (A tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_le4337996190870823476T_VEBT A2))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT X2) A2))) (let ((_let_3 (@ tptp.insert_VEBT_VEBT X2))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_3 tptp.bot_bo8194388402131092736T_VEBT))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (let ((_let_2 (@ (@ tptp.member_complex X2) A2))) (let ((_let_3 (@ tptp.insert_complex X2))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (let ((_let_2 (@ (@ tptp.member_int X2) A2))) (let ((_let_3 (@ tptp.insert_int X2))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (let ((_let_2 (@ (@ tptp.member_real X2) A2))) (let ((_let_3 (@ tptp.insert_real X2))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X2) A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X2))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (let ((_let_2 (@ (@ tptp.member_nat X2) A2))) (let ((_let_3 (@ tptp.insert_nat X2))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))) B3) (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) B3) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) B3) (@ (@ tptp.ord_less_eq_set_real A2) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B3) (@ (@ tptp.ord_le3146513528884898305at_nat A2) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) B3) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B3))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 6.82/7.04 (assert (forall ((Xs2 tptp.list_real) (I tptp.nat) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I) X2))) (@ (@ tptp.insert_real X2) (@ tptp.set_real2 Xs2)))))
% 6.82/7.04 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I) X2))) (@ (@ tptp.insert_int X2) (@ tptp.set_int2 Xs2)))))
% 6.82/7.04 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2))) (@ (@ tptp.insert_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.82/7.04 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I) X2))) (@ (@ tptp.insert_nat X2) (@ tptp.set_nat2 Xs2)))))
% 6.82/7.04 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.sin_complex W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.82/7.04 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.sin_real W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.82/7.04 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2)) (@ (@ tptp.ord_less_real Y2) X2)))))))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.pi) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.pi) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y2)) (@ tptp.cos_real X2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) tptp.pi))))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri3624122377584611663nteger N)))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.82/7.04 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.82/7.04 (assert (forall ((P (-> tptp.set_VEBT_VEBT Bool)) (B3 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (=> (not (@ tptp.finite5795047828879050333T_VEBT B3)) _let_1) (=> (forall ((A7 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A7) (=> (not (= A7 tptp.bot_bo8194388402131092736T_VEBT)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A7) B3) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A7) (@ P (@ (@ tptp.minus_5127226145743854075T_VEBT A7) (@ (@ tptp.insert_VEBT_VEBT X4) tptp.bot_bo8194388402131092736T_VEBT))))) (@ P A7)))))) _let_1))))))
% 6.82/7.04 (assert (forall ((P (-> tptp.set_complex Bool)) (B3 tptp.set_complex)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bot_set_complex) (=> (=> (not (@ tptp.finite3207457112153483333omplex B3)) _let_1) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (not (= A7 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A7) B3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))))) (@ P A7)))))) _let_1))))))
% 6.82/7.04 (assert (forall ((P (-> tptp.set_int Bool)) (B3 tptp.set_int)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B3)) _let_1) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (not (= A7 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) B3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))) (@ P A7)))))) _let_1))))))
% 6.82/7.04 (assert (forall ((P (-> tptp.set_real Bool)) (B3 tptp.set_real)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bot_set_real) (=> (=> (not (@ tptp.finite_finite_real B3)) _let_1) (=> (forall ((A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (not (= A7 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A7) B3) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))) (@ P A7)))))) _let_1))))))
% 6.82/7.04 (assert (forall ((P (-> tptp.set_Pr1261947904930325089at_nat Bool)) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (=> (not (@ tptp.finite6177210948735845034at_nat B3)) _let_1) (=> (forall ((A7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A7) (=> (not (= A7 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A7) B3) (=> (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A7) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A7) (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat))))) (@ P A7)))))) _let_1))))))
% 6.82/7.04 (assert (forall ((P (-> tptp.set_nat Bool)) (B3 tptp.set_nat)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B3)) _let_1) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (not (= A7 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) B3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))) (@ P A7)))))) _let_1))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT B3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((A7 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A7) (=> (not (= A7 tptp.bot_bo8194388402131092736T_VEBT)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A7) B3) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) A7) (@ P (@ (@ tptp.minus_5127226145743854075T_VEBT A7) (@ (@ tptp.insert_VEBT_VEBT X4) tptp.bot_bo8194388402131092736T_VEBT))))) (@ P A7)))))) (@ P B3))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (not (= A7 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A7) B3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))))) (@ P A7)))))) (@ P B3))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (not (= A7 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) B3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))) (@ P A7)))))) (@ P B3))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real B3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (not (= A7 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A7) B3) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))) (@ P A7)))))) (@ P B3))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A7) (=> (not (= A7 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A7) B3) (=> (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A7) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A7) (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat))))) (@ P A7)))))) (@ P B3))))))
% 6.82/7.04 (assert (forall ((B3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (not (= A7 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) B3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))) (@ P A7)))))) (@ P B3))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((T6 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le3480810397992357184T_VEBT T6) S2) (=> (@ P T6) (exists ((X4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT S2) T6)) (@ P (@ (@ tptp.insert_VEBT_VEBT X4) T6))))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((T6 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex T6) S2) (=> (@ P T6) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex S2) T6)) (@ P (@ (@ tptp.insert_complex X4) T6))))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T6 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T6) S2) (=> (@ P T6) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int S2) T6)) (@ P (@ (@ tptp.insert_int X4) T6))))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((T6 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real T6) S2) (=> (@ P T6) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real S2) T6)) (@ P (@ (@ tptp.insert_real X4) T6))))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat S2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((T6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat T6) S2) (=> (@ P T6) (exists ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) (@ (@ tptp.minus_1356011639430497352at_nat S2) T6)) (@ P (@ (@ tptp.insert8211810215607154385at_nat X4) T6))))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T6) S2) (=> (@ P T6) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat S2) T6)) (@ P (@ (@ tptp.insert_nat X4) T6))))))) (@ P S2))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_le3480810397992357184T_VEBT A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le3480810397992357184T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_3 tptp.bot_bo8194388402131092736T_VEBT))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) B3)))))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_complex X2))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_complex A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A2) B3)))))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X2))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B3)))))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X2))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B3)))))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X2))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3)))))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X2))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B3)))))))))))))
% 6.82/7.04 (assert (forall ((K tptp.num)) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.semiri5044797733671781792omplex (@ tptp.pred_numeral K))))))
% 6.82/7.04 (assert (forall ((K tptp.num)) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ tptp.pred_numeral K))))))
% 6.82/7.04 (assert (forall ((K tptp.num)) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int K)) (@ tptp.semiri1406184849735516958ct_int (@ tptp.pred_numeral K))))))
% 6.82/7.04 (assert (forall ((K tptp.num)) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real K)) (@ tptp.semiri2265585572941072030t_real (@ tptp.pred_numeral K))))))
% 6.82/7.04 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.semiri1408675320244567234ct_nat (@ tptp.pred_numeral K)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X2)) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N)) X2)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N)) X2)) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N)) X2)) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) tptp.pi) (= X2 (@ tptp.cos_real T5)) (= Y2 (@ tptp.sin_real T5)))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X2)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X2)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X2)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X2)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 6.82/7.04 (assert (forall ((A tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.82/7.04 (assert (forall ((A tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.82/7.04 (assert (forall ((A tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.82/7.04 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.82/7.04 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.82/7.04 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.82/7.04 (assert (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X3) tptp.zero_zero_real) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (= Y4 X3))))))
% 6.82/7.04 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.82/7.04 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y2)) (@ tptp.cos_real X2)))))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.cos_real X3) Y2) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ tptp.cos_real Y4) Y2)) (= Y4 X3)))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.int)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups769130701875090982BT_int G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (X2 tptp.int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat)) (X2 tptp.int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ tptp.groups769130701875090982BT_int G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X2) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ tptp.groups769130701875090982BT_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X2 (@ tptp.cos_real T5)) (= Y2 (@ tptp.sin_real T5)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X2 (@ tptp.cos_real T5)) (= Y2 (@ tptp.sin_real T5))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.real)) (C (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.groups2240296850493347238T_real C) (@ (@ tptp.minus_5127226145743854075T_VEBT S2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S2))) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (and (=> _let_2 (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups5808333547571424918x_real C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.rat)) (C (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ (@ tptp.groups136491112297645522BT_rat C) (@ (@ tptp.minus_5127226145743854075T_VEBT S2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S2))) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (and (=> _let_2 (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat)) (C (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups5058264527183730370ex_rat C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.nat)) (C (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ (@ tptp.groups771621172384141258BT_nat C) (@ (@ tptp.minus_5127226145743854075T_VEBT S2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S2))) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (and (=> _let_2 (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups5693394587270226106ex_nat C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.int)) (C (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ (@ tptp.groups769130701875090982BT_int C) (@ (@ tptp.minus_5127226145743854075T_VEBT S2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S2))) (=> (@ tptp.finite5795047828879050333T_VEBT S2) (and (=> _let_2 (= (@ (@ tptp.groups769130701875090982BT_int (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups769130701875090982BT_int (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.int)) (C (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.groups5690904116761175830ex_int C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups8778361861064173332t_real C) (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_2 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat)) (C (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.groups3906332499630173760nt_rat C) (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_2 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (not (forall ((T5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (=> (@ (@ tptp.ord_less_real T5) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X2 (@ tptp.cos_real T5)) (not (= Y2 (@ tptp.sin_real T5))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.82/7.04 (assert (forall ((I tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ (@ tptp.member_VEBT_VEBT I) A2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups2240296850493347238T_real F) A2)))))))
% 6.82/7.04 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))))
% 6.82/7.04 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))))
% 6.82/7.04 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))))
% 6.82/7.04 (assert (forall ((I tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ (@ tptp.member_VEBT_VEBT I) A2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups136491112297645522BT_rat F) A2)))))))
% 6.82/7.04 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))))
% 6.82/7.04 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))))
% 6.82/7.04 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))))
% 6.82/7.04 (assert (forall ((I tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.member_nat I) A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))))
% 6.82/7.04 (assert (forall ((I tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ (@ tptp.member_VEBT_VEBT I) A2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups771621172384141258BT_nat F) A2)))))))
% 6.82/7.04 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_complex (= M3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M3)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M3)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_real (= M3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M3)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M3)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri5044797733671781792omplex N) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri773545260158071498ct_rat N) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.04 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.82/7.04 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X2))) tptp.one_one_real))))))
% 6.82/7.04 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X2)))))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y2)) (@ tptp.sin_real X2))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y2)) (@ _let_1 Y2)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_1) (=> (= (@ tptp.sin_real X2) (@ tptp.sin_real Y2)) (= X2 Y2))))))))))
% 6.82/7.04 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (exists ((X tptp.int)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.82/7.04 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.cos_complex W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_complex))))))
% 6.82/7.04 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.cos_real W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_real))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.cos_real X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X2)) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T5) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y2)) (@ tptp.sin_real X2))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))))))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_eq_real X3) _let_1) (= (@ tptp.sin_real X3) Y2) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ tptp.sin_real Y4) Y2)) (= Y4 X3)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (or (exists ((X tptp.nat)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X tptp.nat)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.82/7.04 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B9 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M3)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B9) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real X2) T5) (@ (@ tptp.ord_less_real T5) tptp.zero_zero_real) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T5) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_real T5) X2) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T5) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.82/7.04 (assert (= tptp.cos_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ tptp.semiri2265585572941072030t_real N2))) tptp.zero_zero_real)))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_real T5) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T5) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T5) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X2)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T5) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T5 tptp.real)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T5) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))
% 6.82/7.04 (assert (= tptp.sin_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N2)))))))
% 6.82/7.04 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A2)))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.82/7.04 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N)))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.82/7.04 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N)))))))))
% 6.82/7.04 (assert (forall ((R tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R)))) (@ (@ tptp.power_power_nat N) R)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat N) _let_1))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.82/7.04 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.82/7.04 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (=> (@ (@ tptp.ord_less_real T5) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T5)) (@ tptp.sin_real T5)))))))))))
% 6.82/7.04 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L2))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L2) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L2)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X2) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X2)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X2) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_6 (= Y2 (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y2 (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.sin_real X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.tan_real X2))))
% 6.82/7.04 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X2))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (I tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))) (@ tptp.tan_real X2))))
% 6.82/7.04 (assert (forall ((A (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) X2) (= (@ A tptp.zero_zero_nat) X2))))
% 6.82/7.04 (assert (forall ((A (-> tptp.nat tptp.real)) (X2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) X2) (= (@ A tptp.zero_zero_nat) X2))))
% 6.82/7.04 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X2))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D2)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D2)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S) T))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S) T))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S) T))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real A) C)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) A)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_real A) B))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B) (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_nat A) B))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_int A) B))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) (@ (@ tptp.minus_minus_real A) B))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 6.82/7.04 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) C))) (@ (@ tptp.times_times_complex D2) C)) (@ (@ tptp.sums_complex F) D2)))))
% 6.82/7.04 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real D2) C)) (@ (@ tptp.sums_real F) D2)))))
% 6.82/7.04 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (@ (@ tptp.times_times_complex C) D2)) (@ (@ tptp.sums_complex F) D2)))))
% 6.82/7.04 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) D2)) (@ (@ tptp.sums_real F) D2)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.numera6690914467698888265omplex W)) (and (= A (@ tptp.numeral_numeral_real W)) (= B tptp.zero_zero_real)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2)))))
% 6.82/7.04 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 6.82/7.04 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S) (@ (@ tptp.sums_complex F) S)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L2) (@ F tptp.zero_zero_nat))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.nat)) (L2 tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L2) (@ F tptp.zero_zero_nat))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.int)) (L2 tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L2) (@ F tptp.zero_zero_nat))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ F tptp.zero_zero_nat))))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ F I2) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S) (@ (@ tptp.sums_complex F) S)))))
% 6.82/7.04 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ F I2) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (and (= A (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D2)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C)) (@ _let_1 D2))) (@ (@ tptp.plus_plus_real (@ _let_2 D2)) (@ _let_1 C))))))))
% 6.82/7.04 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N2 M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.power_power_complex Z) M))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N2 M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.power_power_real Z) M))))
% 6.82/7.04 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N2 M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N2)))) (@ (@ tptp.power_power_int Z) M))))
% 6.82/7.04 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ A tptp.zero_zero_nat))))
% 6.82/7.04 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ A tptp.zero_zero_nat))))
% 6.82/7.04 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex X)))))
% 6.82/7.04 (assert (= tptp.tan_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X)) (@ tptp.cos_real X)))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real) (N tptp.nat)) (=> (@ (@ tptp.sums_real F) S) (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.82/7.04 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.sums_real F) S))))
% 6.82/7.04 (assert (forall ((G (-> tptp.nat tptp.real)) (S2 tptp.real) (A2 tptp.set_nat) (S4 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S2) (=> (@ tptp.finite_finite_nat A2) (=> (= S4 (@ (@ tptp.plus_plus_real S2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) A2))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N2) A2)) (@ F N2)) (@ G N2)))) S4))))))
% 6.82/7.04 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))))
% 6.82/7.04 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.82/7.04 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ (@ tptp.sums_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.82/7.04 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ (@ tptp.sums_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.82/7.04 (assert (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N2)))) tptp.one_one_real))
% 6.82/7.04 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y2) (@ tptp.tan_real X3)))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 6.82/7.04 (assert (forall ((Y2 tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y2))))))
% 6.82/7.04 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2)) (@ _let_1 Y2)))))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 Y2) (=> (@ _let_1 _let_2) (=> (@ _let_3 X2) (=> (@ (@ tptp.ord_less_real X2) _let_2) (= (@ _let_1 X2) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y2)) (@ tptp.tan_real X2))))))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y2)) (@ tptp.tan_real X2))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y2) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ tptp.tan_real Y4) Y2)) (= Y4 X3)))))))))
% 6.82/7.05 (assert (= (@ tptp.tan_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y2)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y2))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X2) Y2))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y2))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) X2))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real) (F (-> tptp.nat tptp.real)) (Y2 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (=> (@ (@ tptp.sums_real F) Y2) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ F (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X2) Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X3) Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (@ _let_2 Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X2))) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (= (@ tptp.tan_real X2) Y2) (= (@ tptp.arctan Y2) X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X2)) X2))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arctan Y2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_real _let_1) _let_2) (= (@ tptp.tan_real _let_1) Y2))))))
% 6.82/7.05 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((K3 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) L4)) (=> (=> (not (and (@ (@ tptp.member_int K3) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K3) L4)))))) (@ (@ P A0) A12)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y2))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) Y2))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y2))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y2))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y2))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X2) Y2))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y2))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.minus_minus_real X2) Y2))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y2))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X2) Y2))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y2))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.plus_plus_real X2) Y2))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (exists ((Z3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z3) (@ (@ tptp.ord_less_real Z3) _let_1) (= (@ tptp.tan_real Z3) X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.cos_real X2))))
% 6.82/7.05 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.82/7.05 (assert (= tptp.tan_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.82/7.05 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((C (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2)))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ C N2))) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2))))))))
% 6.82/7.05 (assert (forall ((C (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2)))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ C N2))) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X2) (@ (@ tptp.ord_less_eq_real X2) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X2) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X2)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.82/7.05 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X5 (-> tptp.nat tptp.real))) (or (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_real (@ X5 M3)) (@ X5 N2)))) (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_real (@ X5 N2)) (@ X5 M3))))))))
% 6.82/7.05 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X5 (-> tptp.nat tptp.set_nat))) (or (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X5 M3)) (@ X5 N2)))) (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X5 N2)) (@ X5 M3))))))))
% 6.82/7.05 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X5 (-> tptp.nat tptp.rat))) (or (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_rat (@ X5 M3)) (@ X5 N2)))) (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_rat (@ X5 N2)) (@ X5 M3))))))))
% 6.82/7.05 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X5 (-> tptp.nat tptp.num))) (or (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_num (@ X5 M3)) (@ X5 N2)))) (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_num (@ X5 N2)) (@ X5 M3))))))))
% 6.82/7.05 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X5 (-> tptp.nat tptp.nat))) (or (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_nat (@ X5 M3)) (@ X5 N2)))) (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_nat (@ X5 N2)) (@ X5 M3))))))))
% 6.82/7.05 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X5 (-> tptp.nat tptp.int))) (or (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_int (@ X5 M3)) (@ X5 N2)))) (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.ord_less_eq_int (@ X5 N2)) (@ X5 M3))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (= (@ tptp.sqrt X2) (@ tptp.sqrt Y2)) (= X2 Y2))))
% 6.82/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 6.82/7.05 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sqrt X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sqrt X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 6.82/7.05 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X2) tptp.zero_zero_real))) (let ((_let_2 (= X2 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X2) A)) (not (= X2 tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X2)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) X2)) (@ tptp.abs_abs_real X2))))
% 6.82/7.05 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X2) tptp.one_one_real) (= X2 tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y2)) Y2)))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X2)) X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X2) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) K))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X2)))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X2)) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y2) A)) (@ (@ tptp.powr_real X2) A)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X2) Y2))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y2) A))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sqrt X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real A) B))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y2) A)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y2) A)) (@ (@ tptp.powr_real X2) A)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ _let_1 (@ (@ tptp.powr_real X2) Y2)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X2) (@ _let_1 Y2)) (= X2 Y2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X2) A)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y2) B))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A)) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X2) Y2)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y2) A))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X2) Y2)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y2) A))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real X2) _let_1) _let_1)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X2) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y2))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y2) Y2))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.powr_real B))) (= (@ (@ tptp.divide_divide_real A) (@ _let_1 C)) (@ (@ tptp.times_times_real A) (@ _let_1 (@ tptp.uminus_uminus_real C)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log (@ (@ tptp.powr_real A) B)) X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X2)) B)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (B tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X2 tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X2) Y2)) (@ (@ tptp.times_times_real Y2) (@ _let_1 X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X2) Y2)) (@ (@ tptp.times_times_real Y2) (@ tptp.ln_ln_real X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.82/7.05 (assert (forall ((W tptp.real) (Z1 tptp.real) (Z22 tptp.real)) (let ((_let_1 (@ tptp.powr_real W))) (= (@ _let_1 (@ (@ tptp.minus_minus_real Z1) Z22)) (@ (@ tptp.divide_divide_real (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X2)))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X2) N)))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y2)) X2))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y2)))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y2)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y2))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y2)) X2) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.log B) X2)))))))
% 6.82/7.05 (assert (= tptp.diffs_int (lambda ((C3 (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C3 _let_1))))))
% 6.82/7.05 (assert (= tptp.diffs_real (lambda ((C3 (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C3 _let_1))))))
% 6.82/7.05 (assert (= tptp.diffs_complex (lambda ((C3 (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ C3 _let_1))))))
% 6.82/7.05 (assert (= tptp.diffs_rat (lambda ((C3 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C3 _let_1))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2) (@ (@ tptp.ord_less_real X2) (@ tptp.sqrt Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)))))
% 6.82/7.05 (assert (forall ((C (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (forall ((X3 tptp.complex)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X3) N2))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2)))))))
% 6.82/7.05 (assert (forall ((C (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((X3 tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X3) N2))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real X2) (@ _let_1 Y2)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y2)))))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ tptp.sqrt _let_1))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y2)) X2) (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.log B) X2)))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y2))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y2)))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y2)) X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y2)))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (= (@ tptp.sqrt X2) Y2)))))
% 6.82/7.05 (assert (forall ((U tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) U) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) U))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) X2) (= Y2 tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) Y2) (= X2 tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B) D2)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D2) _let_1))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A)) A))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X2)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X2))))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real Y2) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y2)) X2))))))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real (@ _let_1 X2)) Y2) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) Y2)))))))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real Y2) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y2)) X2))))))))))
% 6.82/7.05 (assert (= tptp.powr_real (lambda ((X tptp.real) (A3 tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A3) (@ tptp.ln_ln_real X)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) Y2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))) (@ (@ tptp.plus_plus_real X2) Y2))))))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N) (= (@ tptp.sqrt (@ _let_3 N)) (@ _let_3 (@ (@ tptp.divide_divide_nat N) _let_2)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y2))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.sqrt X2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real (@ _let_1 X2)) Y2) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y2))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X2) Y2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) K5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) K5) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X3) N2)))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) K5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) K5) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X3) N2)))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) N) (@ (@ tptp.power_power_real X2) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (U tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y2)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))) U))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.arcosh_real X2) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (U tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X2) _let_4) (=> (@ (@ tptp.ord_less_real Y2) _let_4) (=> (@ _let_3 X2) (=> (@ _let_3 Y2) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))) U)))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.82/7.05 (assert (= tptp.arctan (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo6980174941875973593q_real X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.set_nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo7278393974255667507et_nat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo4267028734544971653eq_rat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo1459490580787246023eq_num X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo4902158794631467389eq_nat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X7 N3)) (@ X7 (@ tptp.suc N3)))) (@ tptp.topolo4899668324122417113eq_int X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo6980174941875973593q_real X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.set_nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo7278393974255667507et_nat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo4267028734544971653eq_rat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo1459490580787246023eq_num X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo4902158794631467389eq_nat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X7 (@ tptp.suc N3))) (@ X7 N3))) (@ tptp.topolo4899668324122417113eq_int X7))))
% 6.82/7.05 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X5 (-> tptp.nat tptp.real))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 6.82/7.05 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X5 (-> tptp.nat tptp.set_nat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 6.82/7.05 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X5 (-> tptp.nat tptp.rat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 6.82/7.05 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X5 (-> tptp.nat tptp.num))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 6.82/7.05 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X5 (-> tptp.nat tptp.nat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 6.82/7.05 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X5 (-> tptp.nat tptp.int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo6980174941875973593q_real X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.set_nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo7278393974255667507et_nat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_rat (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo4267028734544971653eq_rat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_num (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo1459490580787246023eq_num X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_nat (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo4902158794631467389eq_nat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_int (@ X7 M4)) (@ X7 N3)))) (@ tptp.topolo4899668324122417113eq_int X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo6980174941875973593q_real X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.set_nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo7278393974255667507et_nat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_rat (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo4267028734544971653eq_rat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_num (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo1459490580787246023eq_num X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_nat (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo4902158794631467389eq_nat X7))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_int (@ X7 N3)) (@ X7 M4)))) (@ tptp.topolo4899668324122417113eq_int X7))))
% 6.82/7.05 (assert (= tptp.arsinh_real (lambda ((X tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 6.82/7.05 (assert (= tptp.arcosh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X2) tptp.one_one_complex) (= X2 tptp.one_one_real))))
% 6.82/7.05 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 6.82/7.05 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 6.82/7.05 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.82/7.05 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X2) Y2)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X2)) N))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X2)) N))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.minus_minus_real X2) Y2)) (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y2)))))
% 6.82/7.05 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.82/7.05 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.82/7.05 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.82/7.05 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 6.82/7.05 (assert (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.82/7.05 (assert (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y2)) Y2)))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y2)) Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (B tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) _let_1))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) (@ tptp.numeral_numeral_real B))))))
% 6.82/7.05 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.05 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.05 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.82/7.05 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 6.82/7.05 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.82/7.05 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 6.82/7.05 (assert (= (@ tptp.arcsin (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y2))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real) (X2 tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (R tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X2) Y2)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X2) R)) (@ (@ tptp.times_times_real Y2) R)))))
% 6.82/7.05 (assert (forall ((R tptp.real) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X2) Y2)) (@ (@ tptp.complex2 (@ _let_1 X2)) (@ _let_1 Y2))))))
% 6.82/7.05 (assert (forall ((R tptp.real) (X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X2) Y2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R) X2)) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real) (R tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X2) Y2)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X2) R)) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) (@ tptp.arccos X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real)) (= (= (@ tptp.arccos X2) (@ tptp.arccos Y2)) (= X2 Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X2)) (@ tptp.arccos Y2)) (@ (@ tptp.ord_less_eq_real Y2) X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (= (@ tptp.arcsin X2) (@ tptp.arcsin Y2)) (= X2 Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X2))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X2))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y2)) (@ tptp.arccos X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X2)) (@ tptp.arccos Y2)) (@ (@ tptp.ord_less_real Y2) X2))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) tptp.pi)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X2)) X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y2)) (@ (@ tptp.ord_less_real X2) Y2))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y2)) Y2))))
% 6.82/7.05 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex B)) (@ tptp.real_V4546457046886955230omplex A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.82/7.05 (assert (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arccos Y2))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arccos Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X2)) tptp.zero_zero_real))))))
% 6.82/7.05 (assert (forall ((M tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.cos_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X2))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X2)))))))
% 6.82/7.05 (assert (forall ((M tptp.int) (X2 tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X2))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X2))))))
% 6.82/7.05 (assert (forall ((M tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.sin_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X2))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X2)))))))
% 6.82/7.05 (assert (forall ((M tptp.int) (X2 tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X2))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (= (@ tptp.arccos (@ tptp.cos_real X2)) (@ tptp.uminus_uminus_real X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X2)) tptp.zero_zero_real))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arccos Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.cos_real _let_1) Y2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X2))))))
% 6.82/7.05 (assert (= tptp.sin_real (lambda ((X tptp.real)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))
% 6.82/7.05 (assert (= tptp.sin_complex (lambda ((X tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))
% 6.82/7.05 (assert (= tptp.cos_real (lambda ((X tptp.real)) (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))
% 6.82/7.05 (assert (= tptp.cos_complex (lambda ((X tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))
% 6.82/7.05 (assert (= tptp.arsinh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arcsin Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X2)) X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y2) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y2)) X2))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) Y2) (@ _let_1 (@ tptp.sin_real Y2)))))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.sin_real _let_1) Y2)))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (= (@ tptp.sin_real _let_1) Y2))))))))
% 6.82/7.05 (assert (forall ((Theta tptp.real)) (not (forall ((K3 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K3)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 6.82/7.05 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 6.82/7.05 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 6.82/7.05 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.82/7.05 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I4 tptp.int)) (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))) N2) tptp.zero_zero_int))))
% 6.82/7.05 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I4 tptp.real)) (@ (@ tptp.plus_plus_real I4) tptp.one_one_real))) N2) tptp.zero_zero_real))))
% 6.82/7.05 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) N2) tptp.zero_zero_nat))))
% 6.82/7.05 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.plus_plus_complex I4) tptp.one_one_complex))) N2) tptp.zero_zero_complex))))
% 6.82/7.05 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I4 tptp.rat)) (@ (@ tptp.plus_plus_rat I4) tptp.one_one_rat))) N2) tptp.zero_zero_rat))))
% 6.82/7.05 (assert (forall ((R tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R) _let_1))))))
% 6.82/7.05 (assert (forall ((R tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R) K2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R) _let_1))))))
% 6.82/7.05 (assert (forall ((R tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R) _let_1))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X2)) X2) (exists ((N2 tptp.int)) (= X2 (@ tptp.ring_1_of_int_real N2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X2)) X2) (exists ((N2 tptp.int)) (= X2 (@ tptp.ring_1_of_int_rat N2))))))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.82/7.05 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.82/7.05 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.82/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.82/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.82/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.82/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.82/7.05 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 6.82/7.05 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 6.82/7.05 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.82/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.82/7.05 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.82/7.05 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) Z))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) Z))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat))))
% 6.82/7.05 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X2))))
% 6.82/7.05 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real V)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 6.82/7.05 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.82/7.05 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 6.82/7.05 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B)))))
% 6.82/7.05 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 6.82/7.05 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.82/7.05 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X2))))
% 6.82/7.05 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.82/7.05 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B)))))
% 6.82/7.05 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B)))))
% 6.82/7.05 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X2))))
% 6.82/7.05 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.82/7.05 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X2))) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X2))) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y2)) (@ (@ tptp.ord_less_rat X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X2) N))))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X2) N))))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X2) N))))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X2) N))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_complex)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_real)))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 6.82/7.05 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.82/7.05 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.82/7.05 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.82/7.05 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.82/7.05 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.82/7.05 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y2))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y2))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X2)))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) X2)))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L2))) (@ (@ tptp.divide_divide_int K) L2))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K)) (@ tptp.ring_1_of_int_rat L2))) (@ (@ tptp.divide_divide_int K) L2))))
% 6.82/7.05 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A3)) K2))) (@ tptp.semiri5044797733671781792omplex K2)))))
% 6.82/7.05 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A3)) K2))) (@ tptp.semiri773545260158071498ct_rat K2)))))
% 6.82/7.05 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A3)) K2))) (@ tptp.semiri2265585572941072030t_real K2)))))
% 6.82/7.05 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)) (@ tptp.semiri5044797733671781792omplex K2)))))
% 6.82/7.05 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)) (@ tptp.semiri773545260158071498ct_rat K2)))))
% 6.82/7.05 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)) (@ tptp.semiri2265585572941072030t_real K2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (=> (= X2 (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (=> (= X2 (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (= (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (@ (@ tptp.plus_plus_complex (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X2) N)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X2) N)))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X2) N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_2) (@ (@ tptp.plus_plus_complex (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_2) (@ (@ tptp.plus_plus_real (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim6058952711729229775r_real X2))) tptp.one_one_int)))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim3151403230148437115or_rat X2))) tptp.one_one_int)))
% 6.82/7.05 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ _let_1 tptp.one_one_real)) K))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ _let_1 tptp.one_one_complex)) K))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) _let_1)) K)) (@ (@ tptp.gbinomial_real A) K))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K)) (@ (@ tptp.gbinomial_rat A) K))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real A) _let_3) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex A) _let_3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real _let_3) A) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex _let_3) A) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.82/7.05 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 6.82/7.05 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 6.82/7.05 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N)))))
% 6.82/7.05 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N)))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N)))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N)))))
% 6.82/7.05 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N)))))
% 6.82/7.05 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N)))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N)))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N)))))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))))
% 6.82/7.05 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))))
% 6.82/7.05 (assert (forall ((Z tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ _let_1 N))))))
% 6.82/7.05 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N) K))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N) K))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N) K))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N) K))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N) K))))
% 6.82/7.05 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K2))))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K2))))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K2))))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat)))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) M))))))
% 6.82/7.05 (assert (forall ((Z tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) M))))))
% 6.82/7.05 (assert (forall ((Z tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) M))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) M))))))
% 6.82/7.05 (assert (forall ((Z tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) M))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I4)))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T) (@ (@ tptp.ord_less_rat T) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I4)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X2) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X2) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) Z))))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X2) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X2) Z))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.82/7.05 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_2)) (@ (@ tptp.gbinomial_real _let_1) _let_2)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.gbinomial_real A) K)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_2)) (@ (@ tptp.gbinomial_complex _let_1) _let_2)) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.gbinomial_complex A) K)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ (@ tptp.gbinomial_real A) _let_1)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) K))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ (@ tptp.gbinomial_complex A) _let_1)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) K))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K))))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A) (@ tptp.ring_1_of_int_real B))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A)) B)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.82/7.05 (assert (forall ((Q2 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q2)))) Q2)) P2))))
% 6.82/7.05 (assert (forall ((Q2 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q2)))) Q2)) P2))))
% 6.82/7.05 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A) K)))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A) K)))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.82/7.05 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K2)) A3)) tptp.one_one_real)) K2)))))
% 6.82/7.05 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K2)) A3)) tptp.one_one_complex)) K2)))))
% 6.82/7.05 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K2)) A3)) tptp.one_one_rat)) K2)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N))))))
% 6.82/7.05 (assert (forall ((R tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.82/7.05 (assert (forall ((R tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.82/7.05 (assert (forall ((R tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 6.82/7.05 (assert (forall ((R tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 6.82/7.05 (assert (forall ((R tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 6.82/7.05 (assert (forall ((Q2 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real P2) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q2)))) tptp.one_one_real)) Q2)))))
% 6.82/7.05 (assert (forall ((Q2 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_rat P2) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q2)))) tptp.one_one_rat)) Q2)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ tptp.semiri3624122377584611663nteger N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ tptp.semiri5044797733671781792omplex N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.82/7.05 (assert (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (K tptp.nat)) (= (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (K tptp.nat)) (= (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (K tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.82/7.05 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K)))))
% 6.82/7.05 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K)))))
% 6.82/7.05 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K)))))
% 6.82/7.05 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K)))))
% 6.82/7.05 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K)))))
% 6.82/7.05 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K)))))
% 6.82/7.05 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))))
% 6.82/7.05 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 6.82/7.05 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 6.82/7.05 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X2)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X2) (@ (@ tptp.ord_less_real X2) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (@ tptp.semiri5044797733671781792omplex N))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (@ tptp.semiri773545260158071498ct_rat N))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (@ tptp.semiri2265585572941072030t_real N))))))))
% 6.82/7.05 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.82/7.05 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K2))))))
% 6.82/7.05 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K2))))))
% 6.82/7.05 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K2))))))
% 6.82/7.05 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K2)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.82/7.05 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K2)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.82/7.05 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.82/7.05 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.82/7.05 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A3 tptp.complex) (N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A3) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.82/7.05 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A3) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.82/7.05 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.82/7.05 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K2))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.82/7.05 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I) K))))
% 6.82/7.05 (assert (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I) K))))
% 6.82/7.05 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I) K))))
% 6.82/7.05 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I) K))))
% 6.82/7.05 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I) K))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I) K))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.82/7.05 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 6.82/7.05 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)))
% 6.82/7.05 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)))
% 6.82/7.05 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G) tptp.bot_bot_set_real) tptp.one_one_rat)))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups73079841787564623at_rat G) A2) tptp.one_one_rat))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups1072433553688619179nt_rat G) A2) tptp.one_one_rat))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups225925009352817453ex_rat G) A2) tptp.one_one_rat))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups1707563613775114915nt_nat G) A2) tptp.one_one_nat))))
% 6.82/7.05 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X2)) (@ tptp.set_or4236626031148496127et_nat Y2)) (@ (@ tptp.ord_less_eq_set_nat X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X2)) (@ tptp.set_ord_atMost_rat Y2)) (@ (@ tptp.ord_less_eq_rat X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X2)) (@ tptp.set_ord_atMost_num Y2)) (@ (@ tptp.ord_less_eq_num X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X2)) (@ tptp.set_ord_atMost_int Y2)) (@ (@ tptp.ord_less_eq_int X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X2)) (@ tptp.set_ord_atMost_nat Y2)) (@ (@ tptp.ord_less_eq_nat X2) Y2))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S2) tptp.one_one_rat)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S2) tptp.one_one_rat)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S2) tptp.one_one_rat)))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S2) tptp.one_one_rat)))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A2)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X2) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A2)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A2))))))))
% 6.82/7.05 (assert (forall ((L2 tptp.set_nat) (H2 tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L2) H2)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L2) H2)) (@ (@ tptp.ord_less_eq_set_nat H2) H3)))))
% 6.82/7.05 (assert (forall ((L2 tptp.rat) (H2 tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L2) H2)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (@ (@ tptp.ord_less_eq_rat H2) H3)))))
% 6.82/7.05 (assert (forall ((L2 tptp.num) (H2 tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L2) H2)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L2) H2)) (@ (@ tptp.ord_less_eq_num H2) H3)))))
% 6.82/7.05 (assert (forall ((L2 tptp.nat) (H2 tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) H2)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L2) H2)) (@ (@ tptp.ord_less_eq_nat H2) H3)))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (H2 tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L2) H2)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L2) H2)) (@ (@ tptp.ord_less_eq_int H2) H3)))))
% 6.82/7.05 (assert (forall ((L2 tptp.real) (H2 tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L2) H2)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L2) H2)) (@ (@ tptp.ord_less_eq_real H2) H3)))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A2)) (@ (@ tptp.groups708209901874060359at_nat H2) A2)))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A2)) (@ (@ tptp.groups705719431365010083at_int H2) A2)))))
% 6.82/7.05 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A2)) (@ (@ tptp.groups1705073143266064639nt_int H2) A2)))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A2) tptp.one_one_nat))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A2) tptp.one_one_int))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A2) tptp.one_one_int))))
% 6.82/7.05 (assert (forall ((G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.complex)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.complex tptp.real)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.complex tptp.rat)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups225925009352817453ex_rat G) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_rat)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.rat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups4061424788464935467al_rat G) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_rat)))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.power_power_nat (@ F X)) N))) A2))))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.power_power_int (@ F X)) N))) A2))))
% 6.82/7.05 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.power_power_int (@ F X)) N))) A2))))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) A))))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A2)) A))))
% 6.82/7.05 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) A))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.82/7.05 (assert (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) U2))))))
% 6.82/7.05 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) U2))))))
% 6.82/7.05 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) U2))))))
% 6.82/7.05 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) U2))))))
% 6.82/7.05 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) U2))))))
% 6.82/7.05 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) U2))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) A2)))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) A2)))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) A2)))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int G) A2)))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int G) A2)))))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K))))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A I2) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ (@ tptp.power_power_nat X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K2)) (@ B (@ (@ tptp.minus_minus_nat R5) K2))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) N)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (R tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M)))))))))
% 6.82/7.05 (assert (forall ((R tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R)) (@ (@ tptp.power_power_nat N) R)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K))) _let_1))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial K2) M))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.binomial N) K)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.82/7.05 (assert (forall ((R tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R) K2)) K2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R) N))) N))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.minus_minus_nat M) K2)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (R tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K2)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R) K2))))) (@ tptp.set_ord_atMost_nat R)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (@ tptp.binomial N))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N)) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))))
% 6.82/7.05 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.82/7.05 (assert (= tptp.binomial (lambda ((N2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K2))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ tptp.if_nat (@ _let_2 K2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2))) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K2)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X2)) N)))))
% 6.82/7.05 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) N2)))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X2)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))))
% 6.82/7.05 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.82/7.05 (assert (= tptp.divide_divide_real (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.times_times_real X) (@ tptp.inverse_inverse_real Y)))))
% 6.82/7.05 (assert (forall ((R tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.real_V2046097035970521341omplex R) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y2)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y2) A))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.82/7.05 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2)))) (and (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real _let_1) X2) (@ tptp.inverse_inverse_real _let_1))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X2))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ _let_1 (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ _let_1 X2))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.real_V4546457046886955230omplex tptp.pi))) tptp.imaginary_unit)) tptp.one_one_complex))
% 6.82/7.05 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) tptp.one_one_complex))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y2)) (@ (@ tptp.ord_less_real X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X2)) (@ _let_1 X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X2)) (@ _let_1 X2)))))
% 6.82/7.05 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X2) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X2))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z))) _let_1)))))
% 6.82/7.05 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))))
% 6.82/7.05 (assert (= tptp.divide1717551699836669952omplex (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.times_times_complex X) (@ tptp.invers8013647133539491842omplex Y)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y2)) (@ _let_1 X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_real Y2) X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_real X2) Y2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ tptp.arcosh_real (@ tptp.cosh_real X2)) X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (= (@ (@ tptp.complex2 X2) Y2) tptp.imaginary_unit) (and (= X2 tptp.zero_zero_real) (= Y2 tptp.one_one_real)))))
% 6.82/7.05 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real A) _let_2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real B)) _let_2)))))))
% 6.82/7.05 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A))))) tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.82/7.05 (assert (= (@ tptp.arg (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.05 (assert (= (@ tptp.csqrt tptp.imaginary_unit) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.imaginary_unit)) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.82/7.05 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.82/7.05 (assert (= (@ tptp.cis (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)))
% 6.82/7.05 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.82/7.05 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.82/7.05 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.minus_minus_real A) B)))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.plus_plus_real A) B)))))
% 6.82/7.05 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X2)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X2))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K2 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X2)) tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X2))))
% 6.82/7.05 (assert (= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.tan_real X) Y))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X2) (@ tptp.the_real (lambda ((X tptp.real)) false))))))
% 6.82/7.05 (assert (= tptp.arccos (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.cos_real X) Y)))))))
% 6.82/7.05 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real))))))
% 6.82/7.05 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.cot_real X2))))
% 6.82/7.05 (assert (= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.sin_real X) Y))))))))
% 6.82/7.05 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K2)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N2))))))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real I)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I)))))))))))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.82/7.05 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.82/7.05 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))))
% 6.82/7.05 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.82/7.05 (assert (forall ((V tptp.num) (V3 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V3)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V3))))))
% 6.82/7.05 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N))))
% 6.82/7.05 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N)))))
% 6.82/7.05 (assert (forall ((Y2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) (@ tptp.nat2 Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))) A) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.82/7.05 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.82/7.05 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N)))))
% 6.82/7.05 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N))))))
% 6.82/7.05 (assert (forall ((V tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) tptp.one_one_nat) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) tptp.one_one_int)))))
% 6.82/7.05 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.82/7.05 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.82/7.05 (assert (= tptp.numeral_numeral_nat (lambda ((I4 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I4)))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y2)))))
% 6.82/7.05 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2)) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2))))))
% 6.82/7.05 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M3) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) N) (@ (@ tptp.ord_less_eq_int X2) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.82/7.05 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B))) (@ (@ tptp.plus_plus_nat A) B))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (not (@ (@ tptp.dvd_dvd_int L2) K)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.modulo_modulo_int K) L2)) (@ tptp.sgn_sgn_int L2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) M)) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))))
% 6.82/7.05 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))))))
% 6.82/7.05 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.82/7.05 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.82/7.05 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.82/7.05 (assert (= tptp.minus_minus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.82/7.05 (assert (= tptp.divide_divide_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.82/7.05 (assert (= tptp.modulo_modulo_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.82/7.05 (assert (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.82/7.05 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.82/7.05 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N2 tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N2)) (@ P N2))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z7)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))))
% 6.82/7.05 (assert (forall ((V tptp.int) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 6.82/7.05 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))
% 6.82/7.05 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z7) (=> (@ (@ tptp.ord_less_eq_int Z7) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z7)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X2) Y2)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y2))))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L2)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y2))))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L2))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L2)) N) (or (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) (@ (@ tptp.minus_minus_nat N) M)))))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_nat))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X2) Y2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y2))))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.divide_divide_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) A) (@ (@ tptp.ord_less_eq_nat X2) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.modulo_modulo_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))))
% 6.82/7.05 (assert (= tptp.divide_divide_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L) K2))))))))))))
% 6.82/7.05 (assert (= tptp.modulo_modulo_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K2) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L) K2))))) _let_2)))))))))))
% 6.82/7.05 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N2) K2) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N2)))))))
% 6.82/7.05 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.05 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M2) (= (@ _let_1 M2) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))))
% 6.82/7.05 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.suc (@ tptp.nat2 Z)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z))))))
% 6.82/7.05 (assert (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M))))))
% 6.82/7.05 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 6.82/7.05 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z7))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z7)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z7) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 6.82/7.05 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int _let_1) N2))))))))
% 6.82/7.05 (assert (forall ((R tptp.int) (L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R) (@ tptp.sgn_sgn_int L2)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R)) (@ tptp.abs_abs_int L2)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L2)) R)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R)))))))
% 6.82/7.05 (assert (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K2 tptp.int)) (and (= A1 K2) (= A22 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K2)))) (exists ((L tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A1 K2) (= A22 L) (= A32 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L tptp.zero_zero_int)) (= K2 (@ (@ tptp.times_times_int Q4) L)))) (exists ((R5 tptp.int) (L tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A1 K2) (= A22 L) (= A32 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L)) (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L)) R5))))))))
% 6.82/7.05 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A33) (=> (=> (= A23 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q3) A23)))))) (not (forall ((R3 tptp.int) (Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) A23)) R3)))))))))))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2))) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K)))))))))
% 6.82/7.05 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.nat2 K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K))))))
% 6.82/7.05 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.plus_plus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K2) N2)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.82/7.05 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.minus_minus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N2))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))))))))))))))))
% 6.82/7.05 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C))))))))
% 6.82/7.05 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 _let_2) (= L _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X2)) (@ _let_1 X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X2) X2)))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X2) (@ _let_1 Y2)) (= X2 Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X2) tptp.zero_zero_real)))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) (and (@ _let_1 K) (@ _let_1 L2))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_real X2) Y2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_real X2) Y2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.one_one_real) (= X2 tptp.one_one_real)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) tptp.one_one_real) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X2)) (@ tptp.sgn_sgn_real X2)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X2)) (@ tptp.inverse_inverse_real (@ _let_1 X2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y2)) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 Y2))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X2)) (@ _let_2 (@ _let_1 X2)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ _let_1 X2))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X2) (@ (@ tptp.root M) (@ (@ tptp.root N) X2)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y2)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ _let_1 Y2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N) X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X2) Y2)))))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L2)))))
% 6.82/7.05 (assert (= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real X) (@ tptp.abs_abs_real X)))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y2)) (@ (@ tptp.bit_se1409905431419307370or_int X2) Y2)) (@ (@ tptp.plus_plus_int X2) Y2))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N))) Y2))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.pow X2) tptp.one) X2)))
% 6.82/7.05 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X2 tptp.real)) (= (@ P (@ (@ tptp.root N) X2)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N)) X2) (@ P Y))))))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) Y2) (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y2)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X2) Y2) (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y2)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X2) K)) (@ (@ tptp.power_power_real (@ _let_1 X2)) K))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ _let_1 X2)))))))
% 6.82/7.05 (assert (= tptp.sgn_sgn_complex (lambda ((Z4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex Z4) (@ tptp.real_V4546457046886955230omplex (@ tptp.real_V1022390504157884413omplex Z4))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N) X2)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ (@ tptp.root N4) X2)) (@ (@ tptp.root N) X2)))))))
% 6.82/7.05 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.82/7.05 (assert (= tptp.sgn_sgn_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (= A3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y2) N))) (@ tptp.abs_abs_real Y2)))))
% 6.82/7.05 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N4) X2))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N4) X2)) (@ (@ tptp.root N) X2)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Y2 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (= (@ (@ tptp.power_power_real Y2) N) X2) (= (@ (@ tptp.root N) X2) Y2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Y2 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y2) N) X2) (= (@ (@ tptp.root N) X2) Y2)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2))))
% 6.82/7.05 (assert (forall ((A tptp.real) (N tptp.nat) (X2 tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X2) (=> (= X2 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N4) X2))))))))
% 6.82/7.05 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M3) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (X2 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X2)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.arg Z) X2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (B tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X2)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y2) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X2) Y2)) _let_1)))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis _let_1)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) X2) (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.82/7.05 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K2)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X2)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X2))))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 6.82/7.05 (assert (= tptp.arg (lambda ((Z4 tptp.complex)) (@ (@ (@ tptp.if_real (= Z4 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A3 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z4) (@ tptp.cis A3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A3) (@ (@ tptp.ord_less_eq_real A3) tptp.pi))))))))
% 6.82/7.05 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))))
% 6.82/7.05 (assert (forall ((Y2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.82/7.05 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.82/7.05 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 6.82/7.05 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 6.82/7.05 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 6.82/7.05 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.82/7.05 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.82/7.05 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 6.82/7.05 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.82/7.05 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.82/7.05 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.82/7.05 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.82/7.05 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X2) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y2 tptp.one))))) (let ((_let_3 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa2) Y2) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y2 (@ tptp.bit1 M4)))))) (=> (=> _let_3 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (not (= Y2 _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X2 (@ tptp.bit0 N3))) (=> _let_1 (not (= Y2 (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y2 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (=> (exists ((N3 tptp.num)) (= X2 (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (not (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))))))))))))))))))
% 6.82/7.05 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.82/7.05 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M3)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.82/7.05 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.82/7.05 (assert (forall ((S tptp.vEBT_VEBT) (M tptp.nat) (Listy tptp.list_VEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M))))) (=> (@ (@ tptp.vEBT_invar_vebt S) M) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Listy)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (= M (@ tptp.suc N)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Listy)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height X3)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))) (=> (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height S)) _let_1) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT S) (@ tptp.set_VEBT_VEBT2 Listy))))) _let_1)))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.82/7.05 (assert (forall ((Bs tptp.list_o)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) _let_1) Bs)) (@ (@ tptp.power_power_int _let_1) (@ tptp.size_size_list_o Bs))))))
% 6.82/7.05 (assert (forall ((T tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 TreeList))) (=> (@ (@ tptp.member_VEBT_VEBT T) _let_1) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_height T)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary) _let_1))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X14 tptp.vEBT_VEBT) (M tptp.nat) (X13 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_VEBT_height X14))) (let ((_let_2 (@ tptp.times_times_nat N))) (@ (@ tptp.ord_less_eq_nat (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat M) (@ _let_2 (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat _let_1) (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13)))))))))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (X13 tptp.list_VEBT_VEBT) (Foo tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT X13)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_height (@ (@ tptp.nth_VEBT_VEBT X13) I))) (@ (@ tptp.ord_max_nat Foo) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13))))))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (X13 tptp.list_VEBT_VEBT) (N tptp.nat) (X14 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT X13)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ tptp.vEBT_VEBT_height (@ (@ tptp.nth_VEBT_VEBT X13) I)))) (@ tptp.suc (@ tptp.suc (@ _let_1 (@ (@ tptp.ord_max_nat (@ tptp.vEBT_VEBT_height X14)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 6.82/7.05 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2)))))
% 6.82/7.05 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))))
% 6.82/7.05 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Uu) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary) (@ tptp.set_VEBT_VEBT2 TreeList))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X2) Y2) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= Y2 tptp.zero_zero_nat))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) Summary2)) (not (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary2) (@ tptp.set_VEBT_VEBT2 TreeList2))))))))))))))
% 6.82/7.05 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K2) N2)) M3))))))))
% 6.82/7.05 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.82/7.05 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M3)) (not (@ _let_2 N2)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.82/7.05 (assert (forall ((M7 tptp.set_nat) (N4 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N4) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N4))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) (= (@ _let_1 K) (@ _let_1 L2))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X2) Y2)))))))
% 6.82/7.05 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y2) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X2) Y2)) _let_1)))))))
% 6.82/7.05 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K2)) (not (@ _let_2 L)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.82/7.05 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L)) (@ (@ (@ tptp.if_int (= L _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L2) (@ (@ tptp.bit_se545348938243370406it_int N) L2))))
% 6.82/7.05 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.82/7.05 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_ri7919022796975470100ot_int K)) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.82/7.05 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 6.82/7.05 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.82/7.05 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ tptp.bit_ri7919022796975470100ot_int L))))))
% 6.82/7.05 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 6.82/7.05 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 6.82/7.05 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K2)) tptp.one_one_int))))
% 6.82/7.05 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.82/7.05 (assert (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)))
% 6.82/7.05 (assert (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.82/7.05 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K2 tptp.int) (L tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 6.82/7.05 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int L))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) L)))))
% 6.82/7.05 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K2 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 6.82/7.05 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 6.82/7.05 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 6.82/7.05 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_ri7919022796975470100ot_int K)) _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K) _let_1))))))
% 6.82/7.05 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int K)) (not (@ _let_1 K))))))
% 6.82/7.05 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)))
% 6.82/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.82/7.05 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) _let_1))))
% 6.82/7.05 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.82/7.05 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)))
% 6.82/7.05 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))))
% 6.82/7.05 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.times_times_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.82/7.05 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.times_times_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.82/7.05 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K2))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K2) _let_1))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) X2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (= Y2 tptp.zero_zero_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1)))))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y2 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary2) (@ tptp.set_VEBT_VEBT2 TreeList2)))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (and (=> B5 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y2 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (and (=> A5 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y2 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (=> (= (@ tptp.vEBT_T_m_i_n_t X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) X2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_1) (=> (= Y2 (@ _let_2 (@ (@ (@ tptp.if_nat A5) tptp.zero_zero_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1)))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (=> (= (@ tptp.vEBT_T_m_a_x_t X2) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) X2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_1) (=> (= Y2 (@ _let_2 (@ (@ (@ tptp.if_nat B5) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1)))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel))) (=> (= (@ tptp.vEBT_T_m_i_n_N_u_l_l X2) Y2) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y2 tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X2) Y2) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (=> Y2 (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (=> Y2 (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X2) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X2) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.82/7.05 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X5 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X5 M3)) (@ X5 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.05 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.size_size_VEBT_VEBT) X13)) (@ tptp.size_size_VEBT_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 6.82/7.05 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.82/7.05 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat N) (@ _let_1 N))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K)))) (let ((_let_3 (@ tptp.pred_numeral K))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 6.82/7.05 (assert (forall ((C tptp.nat) (Y2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X2) Y2))) (let ((_let_2 (@ (@ tptp.ord_less_nat X2) Y2))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y2))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X2) C)) (@ (@ tptp.minus_minus_nat Y2) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) tptp.one_one_nat)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ A I2)) (@ A J2))))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I2))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ B I4)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) L2))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L2))) (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 6.82/7.05 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_size_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.vEBT_size_VEBT) X13)) (@ tptp.vEBT_size_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.82/7.05 (assert (forall ((T tptp.vEBT_VEBT) (D2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D2) (@ (@ tptp.vEBT_invar_vebt T) D2))))
% 6.82/7.05 (assert (forall ((T tptp.vEBT_VEBT) (D2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D2) (@ (@ tptp.vEBT_VEBT_valid T) D2))))
% 6.82/7.05 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.82/7.05 (assert (forall ((Uu Bool) (Uv Bool) (D2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D2) (= D2 tptp.one_one_nat))))
% 6.82/7.05 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.csqrt Z)) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.82/7.05 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (N tptp.nat)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (R tptp.real)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) R))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.numeral_numeral_real W)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X2)) (@ tptp.real_V1022390504157884413omplex X2))))
% 6.82/7.05 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X2) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.re X2)) (@ tptp.re Y2)))))
% 6.82/7.05 (assert (forall ((R tptp.real) (X2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R) X2)) (@ (@ tptp.times_times_real R) (@ tptp.re X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.minus_minus_real (@ tptp.re X2)) (@ tptp.re Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X2))) (@ tptp.real_V1022390504157884413omplex X2))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.re Z))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 6.82/7.05 (assert (= tptp.csqrt (lambda ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z4))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z4))) (let ((_let_4 (@ tptp.im Z4))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.im Z))) (= (@ tptp.im (@ tptp.csqrt Z)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_1 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_1))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.re X2))) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X2) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (R tptp.real)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) R))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_real (@ tptp.re X2)) N)))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.numeral_numeral_real W)))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (N tptp.nat)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.re X2))) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X2) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.im X2))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X2)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X2)))))))
% 6.82/7.05 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X2) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.im X2)) (@ tptp.im Y2)))))
% 6.82/7.05 (assert (forall ((R tptp.real) (X2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R) X2)) (@ (@ tptp.times_times_real R) (@ tptp.im X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.minus_minus_real (@ tptp.im X2)) (@ tptp.im Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X2))) (@ tptp.real_V1022390504157884413omplex X2))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X2) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) (@ tptp.im Y2))) (@ (@ tptp.times_times_real (@ tptp.im X2)) (@ tptp.re Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (=> (= (@ tptp.im X2) (@ tptp.im Y2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X2))) (@ tptp.abs_abs_real (@ tptp.re Y2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (=> (= (@ tptp.re X2) (@ tptp.re Y2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X2))) (@ tptp.abs_abs_real (@ tptp.im Y2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X2) Y2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) (@ tptp.re Y2))) (@ (@ tptp.times_times_real (@ tptp.im X2)) (@ tptp.im Y2))))))
% 6.82/7.05 (assert (= tptp.plus_plus_complex (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y))))))
% 6.82/7.05 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X))) (@ _let_1 (@ tptp.im X)))))))
% 6.82/7.05 (assert (= tptp.minus_minus_complex (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.minus_minus_real (@ tptp.im X)) (@ tptp.im Y))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.csqrt Z))) (let ((_let_2 (@ tptp.re _let_1))) (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (and (= _let_2 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im _let_1))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.cos_real (@ tptp.im Z))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.sin_real (@ tptp.im Z))))))
% 6.82/7.05 (assert (= tptp.times_times_complex (lambda ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.re Y))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X)))) (let ((_let_3 (@ tptp.im Y))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X)))) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_4 _let_1)) (@ _let_2 _let_3))) (@ (@ tptp.plus_plus_real (@ _let_4 _let_3)) (@ _let_2 _let_1))))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X2))) (@ tptp.im X2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= Z tptp.zero_zero_complex) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)) tptp.zero_zero_real)))))
% 6.82/7.05 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z4)) _let_1)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X2))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.82/7.05 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.re W))) (=> (= (@ (@ tptp.power_power_complex W) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im W)))) (= (@ tptp.csqrt Z) W))))))
% 6.82/7.05 (assert (forall ((B tptp.complex)) (let ((_let_1 (@ tptp.re B))) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im B)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.real_V1022390504157884413omplex Z))) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.re Z)) _let_2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.im Z)) _let_2)) _let_1)) tptp.one_one_real))))))
% 6.82/7.05 (assert (= tptp.invers8013647133539491842omplex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (let ((_let_3 (@ tptp.re X))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))
% 6.82/7.05 (assert (= tptp.divide1717551699836669952omplex (lambda ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 6.82/7.05 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) R)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.re R))))))
% 6.82/7.05 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) R)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.re R))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z) (@ tptp.cnj Z)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z)))) tptp.imaginary_unit))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.divide1717551699836669952omplex X2) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cnj X2)) (@ tptp.cnj Y2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.minus_minus_complex X2) Y2)) (@ (@ tptp.minus_minus_complex (@ tptp.cnj X2)) (@ tptp.cnj Y2)))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.05 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.divide1717551699836669952omplex A) B))) (and (= (@ _let_2 (@ tptp.re _let_3)) (@ _let_2 (@ tptp.re _let_1))) (= (@ _let_2 (@ tptp.im _let_3)) (@ _let_2 (@ tptp.im _let_1)))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)))))
% 6.82/7.05 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re Z))))))
% 6.82/7.05 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A3) (@ tptp.cnj B2))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex Z) (@ tptp.cnj W)))) (= (@ (@ tptp.plus_plus_complex _let_1) (@ (@ tptp.times_times_complex (@ tptp.cnj Z)) W)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re _let_1)))))))
% 6.82/7.05 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 6.82/7.05 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.82/7.05 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I4) N)))) (@ tptp.suc N))))
% 6.82/7.05 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L2))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L2)) tptp.one_one_int)))))
% 6.82/7.05 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 6.82/7.05 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.82/7.05 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.82/7.05 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L2) (@ tptp.uminus1351360451143612070nteger L2))))
% 6.82/7.05 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 6.82/7.05 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 6.82/7.05 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 6.82/7.05 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A2))))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (= A2 _let_1)))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S2)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S2))))))
% 6.82/7.05 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N4)) N))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) S2))))
% 6.82/7.05 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C)))) N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) N))))
% 6.82/7.05 (assert (= tptp.code_integer_of_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.82/7.05 (assert (= tptp.abs_abs_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K2)) K2))))
% 6.82/7.05 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ (@ tptp.ord_less_int Xa2) X2))))
% 6.82/7.05 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.82/7.05 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa2) X2)))))
% 6.82/7.05 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.modulo_modulo_int Xa2) X2)))))
% 6.82/7.05 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int Xa2) X2)))))
% 6.82/7.05 (assert (= tptp.archim6058952711729229775r_real (lambda ((X tptp.real)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z4)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))
% 6.82/7.05 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X tptp.rat)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z4)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.82/7.05 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 6.82/7.05 (assert (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (not (forall ((S3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S3) (forall ((T5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T5) (not (= R (@ (@ tptp.plus_plus_rat S3) T5)))))))))))
% 6.82/7.05 (assert (= tptp.sgn_sgn_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (= A3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.82/7.05 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.82/7.05 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.82/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.82/7.05 (assert (forall ((Q2 tptp.int) (P2 tptp.int)) (=> (@ (@ tptp.ord_less_int Q2) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P2)) (@ tptp.uminus_uminus_int Q2)))))))
% 6.82/7.05 (assert (= tptp.code_int_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K2)))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.82/7.05 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K2) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K2)))))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 6.82/7.05 (assert (forall ((X2 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.minus_8373710615458151222nteger X2) Xa2)) (@ (@ tptp.minus_minus_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.divide6298287555418463151nteger X2) Xa2)) (@ (@ tptp.divide_divide_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.modulo364778990260209775nteger X2) Xa2)) (@ (@ tptp.modulo_modulo_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa2)))))
% 6.82/7.05 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))))
% 6.82/7.05 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer K2)) (@ tptp.code_int_of_integer L)))))
% 6.82/7.05 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))
% 6.82/7.05 (assert (forall ((R tptp.product_prod_int_int) (P2 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize R) (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.82/7.05 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K2) L)) (@ (@ tptp.modulo364778990260209775nteger K2) L)))))
% 6.82/7.05 (assert (= tptp.code_num_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K2)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (= tptp.code_nat_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.82/7.05 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.82/7.05 (assert (= tptp.code_divmod_abs (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.82/7.05 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K2)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L) S6)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L)) S6)))))) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A3) D)) (@ (@ tptp.times_times_int B2) C3))) (@ (@ tptp.times_times_int C3) D))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.82/7.05 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.82/7.05 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.82/7.05 (assert (forall ((R tptp.rat) (N tptp.int) (D2 tptp.int)) (=> (= (@ tptp.quotient_of R) (@ (@ tptp.product_Pair_int_int N) D2)) (= R (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat N)) (@ tptp.ring_1_of_int_rat D2))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 6.82/7.05 (assert (forall ((R tptp.rat) (P2 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.quotient_of R) (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M5)))) M)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M5) N)))) M)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K2 tptp.nat)) K2)) (@ _let_1 N))))))
% 6.82/7.05 (assert (= tptp.ord_less_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A3) D)) (@ (@ tptp.times_times_int C3) B2)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 6.82/7.05 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) D)) (@ (@ tptp.times_times_int C3) B2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.82/7.05 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P5 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P5)))))
% 6.82/7.05 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 6.82/7.05 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K)))))
% 6.82/7.05 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int L2))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat L2)))))
% 6.82/7.05 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.82/7.05 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M)) K)))))
% 6.82/7.05 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K))))
% 6.82/7.05 (assert (= tptp.nat_prod_decode_aux (lambda ((K2 tptp.nat) (M3 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M3) K2)) (@ (@ tptp.product_Pair_nat_nat M3) (@ (@ tptp.minus_minus_nat K2) M3))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M3) _let_1)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y2) (and (=> _let_2 (= Y2 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_2) (= Y2 (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.modulo_modulo_nat M) N))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 6.82/7.05 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.divide_divide_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_fst_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S2))) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N7) (@ tptp.finite_card_nat S2)) (@ (@ tptp.member_nat (@ R3 N7)) S2))))))))
% 6.82/7.05 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K2) (@ tptp.sgn_sgn_Code_integer L))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L)) S6)))))) _let_1))))))))))
% 6.82/7.05 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_integer K) L2)) (@ (@ tptp.modulo364778990260209775nteger K) L2))))
% 6.82/7.05 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_abs K) L2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L2)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 6.82/7.05 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R)))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N)))))))
% 6.82/7.05 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc8508995932063986495nteger (@ (@ tptp.code_divmod_integer K) L2)) (@ (@ tptp.divide6298287555418463151nteger K) L2))))
% 6.82/7.05 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc8508995932063986495nteger (@ (@ tptp.code_divmod_abs K) L2)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L2)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N))))))))
% 6.82/7.05 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.82/7.05 (assert (= tptp.adjust_mod (lambda ((L tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L) R5)))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) Y2) (and (=> _let_3 (= Y2 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y2 (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa2))))))))))))))
% 6.82/7.05 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y2) (@ (@ tptp.modulo_modulo_nat X2) Y2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y2) (= (@ (@ tptp.bezw X2) Y2) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y2)))))))))))
% 6.82/7.05 (assert (= tptp.bezw (lambda ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 6.82/7.05 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_4 (= Y2 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y2 (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa2)))))))) (not _let_1)))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ tptp.suc X2))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_3 (= Y2 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_3) (= Y2 (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.82/7.05 (assert (= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 6.82/7.05 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N)) (or (not (= M tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.gcd_gcd_int X2))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 6.82/7.05 (assert (forall ((N tptp.num) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X2) (@ (@ tptp.gcd_gcd_int _let_1) X2)))))
% 6.82/7.05 (assert (= tptp.gcd_gcd_int (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X) Y)))))
% 6.82/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) A))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) B))))
% 6.82/7.05 (assert (forall ((Y2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y2) (= (@ (@ tptp.gcd_gcd_int X2) Y2) (@ (@ tptp.gcd_gcd_int Y2) (@ (@ tptp.modulo_modulo_int X2) Y2))))))
% 6.82/7.05 (assert (= tptp.gcd_gcd_int (lambda ((K2 tptp.int) (L tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K2) (@ (@ tptp.gcd_gcd_int L) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K2)) (@ tptp.abs_abs_int L))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I3) (@ P I3))) (@ P K3)))) (@ P M)))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L2) tptp.one_one_int))))))
% 6.82/7.05 (assert (forall ((N tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N) tptp.one)) K)))))
% 6.82/7.05 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.82/7.05 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N)) (or (not (= M tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) A))))
% 6.82/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) B))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M) N)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.82/7.05 (assert (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X) Y)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 6.82/7.05 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (not (= Y2 tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X2) Y2) (@ (@ tptp.gcd_gcd_nat Y2) (@ (@ tptp.modulo_modulo_nat X2) Y2))))))
% 6.82/7.05 (assert (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ (@ tptp.if_nat (= Y tptp.zero_zero_nat)) X) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X) Y))))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa2) Y2) (and (=> _let_1 (= Y2 X2)) (=> (not _let_1) (= Y2 (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))))))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.82/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X3))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X3))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 6.82/7.05 (assert (= tptp.gcd_gcd_Code_integer (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (@ tptp.abs_abs_Code_integer (@ (@ (@ tptp.if_Code_integer (= L tptp.zero_z3403309356797280102nteger)) K2) (@ (@ tptp.gcd_gcd_Code_integer L) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K2)) (@ tptp.abs_abs_Code_integer L))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_2 (= Y2 X2)) (=> (not _let_2) (= Y2 (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2))))) (not _let_1)))))))))
% 6.82/7.05 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L2)))))
% 6.82/7.05 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X2)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.82/7.05 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) X))) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))))
% 6.82/7.05 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X2)))))
% 6.82/7.05 (assert (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y3))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X2)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X2))))
% 6.82/7.05 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.82/7.05 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))))
% 6.82/7.05 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X))) X2)))))
% 6.82/7.05 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.82/7.05 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X2))))
% 6.82/7.05 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X2))))
% 6.82/7.05 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))) Xa2) X2)))))
% 6.82/7.05 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0))) Xa2) X2)))))
% 6.82/7.05 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M7) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 6.82/7.05 (assert (forall ((N4 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N4) (= (@ tptp.gcd_Gcd_nat N4) tptp.one_one_nat))))
% 6.82/7.05 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U2) Z4)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 6.82/7.05 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U2) Z4)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 6.82/7.05 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M3) N2))) M3)))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.82/7.05 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.82/7.05 (assert (= tptp.nat2 (lambda ((X tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X)))))
% 6.82/7.05 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M))))
% 6.82/7.05 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 6.82/7.05 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.82/7.05 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N))))))))
% 6.82/7.05 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.82/7.05 (assert (= tptp.minus_minus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0))))))
% 6.82/7.05 (assert (= tptp.plus_plus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit1 Y2)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y2))) X2)))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.82/7.05 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.82/7.05 (assert (= tptp.sqr (lambda ((X tptp.num)) (@ (@ tptp.times_times_num X) X))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit0 Y2)) (@ tptp.sqr (@ _let_1 Y2))))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.82/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 6.82/7.05 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D2)) (@ (@ tptp.times_times_int B) C)))))
% 6.82/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.82/7.05 (assert (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D2))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D2)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.82/7.05 (assert (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D2)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D2)))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (@ P (@ (@ tptp.fract A5) B5)))) (@ P Q2))))
% 6.82/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.gcd_gcd_int A) B))) (= (@ (@ tptp.fract (@ (@ tptp.divide_divide_int A) _let_1)) (@ (@ tptp.divide_divide_int B) _let_1)) (@ (@ tptp.fract A) B)))))
% 6.82/7.05 (assert (= tptp.fract (lambda ((K2 tptp.int) (L tptp.int)) (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K2)) (@ tptp.ring_1_of_int_rat L)))))
% 6.82/7.05 (assert (= tptp.numeral_numeral_rat (lambda ((K2 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K2)) tptp.one_one_int))))
% 6.82/7.05 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ _let_1 A))))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.82/7.05 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.82/7.05 (assert (forall ((K tptp.num)) (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.82/7.05 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) tptp.one_one_int) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q4)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))))
% 6.82/7.05 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.82/7.05 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.82/7.05 (assert (forall ((R tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.82/7.05 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num tptp.one))) N))))
% 6.82/7.05 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.82/7.05 (assert (= tptp.ord_less_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))))))
% 6.82/7.05 (assert (= tptp.ord_less_eq_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))))))
% 6.82/7.05 (assert (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))))
% 6.82/7.05 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M3 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M3)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 6.82/7.05 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 6.82/7.05 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M)))))
% 6.82/7.05 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R)) M))))))
% 6.82/7.05 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R)) M)))))
% 6.82/7.05 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.82/7.05 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.82/7.05 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit0 M))) (= (@ (@ tptp.bit_and_not_num _let_1) tptp.one) (@ tptp.some_num _let_1)))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N2) M)))) N))))
% 6.82/7.05 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int Q2)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))) N))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M)))))
% 6.82/7.05 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M3 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 tptp.nat) (X tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P5 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num O) P5)))) (lambda ((P5 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P5))))) X))) A3))) (@ (@ tptp.product_Pair_nat_num N2) M3)))))
% 6.82/7.05 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B)))))
% 6.82/7.05 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y) X)))))
% 6.82/7.05 (assert (= tptp.positive (lambda ((X tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 tptp.none_num)))) (let ((_let_2 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X2) Xa2) Y2) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) (not (= Y2 (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num _let_1))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M4) N3)))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))))))))))))))))))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.82/7.05 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y2 tptp.none_num)))) (let ((_let_5 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X2) Xa2) Y2) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) _let_4)) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (=> (exists ((M4 tptp.num)) (= X2 (@ tptp.bit0 M4))) (=> _let_2 _let_4)) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))) (=> (=> (exists ((M4 tptp.num)) (= X2 (@ tptp.bit1 M4))) _let_3) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))))))))))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X2) Xa2) Y2) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y2 tptp.none_num)))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ tptp.some_num (@ tptp.bit1 N3))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 N3))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit1 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))))))))))))))))))))
% 6.82/7.05 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.82/7.05 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))))
% 6.82/7.05 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 6.82/7.05 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))))
% 6.82/7.05 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))))
% 6.82/7.05 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.82/7.05 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 6.82/7.05 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.82/7.05 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (exists ((Q3 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q3))) (and (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real _let_1) Y2)))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) (@ tptp.pred_numeral K))))))
% 6.82/7.05 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N)) Q2) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q2)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I)) (@ (@ tptp.minus_minus_nat N) I)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N)) I))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int) (R tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) R) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N)) L2) R)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) L2)))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M5) N)))) M))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M5)))) M))))
% 6.82/7.05 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.82/7.05 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)))
% 6.82/7.05 (assert (= tptp.comple4887499456419720421f_real (lambda ((X5 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X5))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X7) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X7 I2))) (= (@ tptp.suminf_real X7) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X7) (@ tptp.set_ord_lessThan_nat I4)))) tptp.top_top_set_nat)))))))
% 6.82/7.05 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.82/7.05 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.82/7.05 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.82/7.05 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.image_real_real (@ tptp.times_times_real A)) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ (@ tptp.insert_real tptp.zero_zero_real) tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))))
% 6.82/7.05 (assert (= tptp.root (lambda ((N2 tptp.nat) (X tptp.real)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2)))) X)))))
% 6.82/7.05 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.82/7.05 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 6.82/7.05 (assert (= (@ tptp.finite_card_char tptp.top_top_set_char) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))
% 6.82/7.05 (assert (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))))
% 6.82/7.05 (assert (forall ((X1 Bool) (X23 Bool) (X33 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X8 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X23) X33) X42) X52) X62) X72) X8)) tptp.zero_zero_nat)))
% 6.82/7.05 (assert (forall ((C tptp.char)) (@ (@ tptp.ord_less_nat (@ tptp.comm_s629917340098488124ar_nat C)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.82/7.05 (assert (= (@ (@ tptp.image_char_nat tptp.comm_s629917340098488124ar_nat) tptp.top_top_set_char) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.82/7.05 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger B72)) _let_1)) (@ tptp.zero_n356916108424825756nteger B62))) _let_1)) (@ tptp.zero_n356916108424825756nteger B52))) _let_1)) (@ tptp.zero_n356916108424825756nteger B42))) _let_1)) (@ tptp.zero_n356916108424825756nteger B32))) _let_1)) (@ tptp.zero_n356916108424825756nteger B22))) _let_1)) (@ tptp.zero_n356916108424825756nteger B1))) _let_1)) (@ tptp.zero_n356916108424825756nteger B0))))))
% 6.82/7.05 (assert (forall ((C tptp.char)) (= (@ tptp.comm_s629917340098488124ar_nat (@ tptp.ascii_of C)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one)))) (@ tptp.comm_s629917340098488124ar_nat C)))))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K))) (@ (@ tptp.cons_nat K) tptp.nil_nat)))))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.nat)) (=> (= (@ tptp.nat_list_encode X2) Y2) (=> (=> (= X2 tptp.nil_nat) (not (= Y2 tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X2 (@ (@ tptp.cons_nat X3) Xs3)) (not (= Y2 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.82/7.05 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X2) Xs2)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X2) (@ tptp.nat_list_encode Xs2)))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.82/7.05 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 6.82/7.05 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 6.82/7.05 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 6.82/7.05 (assert (forall ((I tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I)) tptp.one_one_int)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.82/7.05 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 6.82/7.05 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.82/7.05 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 6.82/7.05 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.82/7.05 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) S2)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) S2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) S2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) S2)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real) (Y2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.member_real X2) _let_1) (=> (@ (@ tptp.member_real Y2) _let_1) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (= (@ F X2) (@ F Y2)))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.plus_plus_real X2) H4))))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X2) H4))) (@ F X2)))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X2) H4))) (@ F X2)))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.minus_minus_real X2) H4))))))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ (@ tptp.minus_minus_real B) A)) K)))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ G A)) (@ G B)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real) (D2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D2) (= (@ F X2) (@ F Y3)))) (= L2 tptp.zero_zero_real))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F3 Z3)))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B))) _let_1)))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real) (D2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D2) (@ (@ tptp.ord_less_eq_real (@ F X2)) (@ F Y3)))) (= L2 tptp.zero_zero_real))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X2 tptp.real) (D2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D2) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X2)))) (= L2 tptp.zero_zero_real))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X2) S))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ G X)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X2)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 6.82/7.05 (assert (forall ((Z tptp.real) (R tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z4 tptp.real)) (@ (@ tptp.powr_real Z4) R))) (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X2))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) R))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real)) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (let ((_let_3 (@ F X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) (@ F X)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F3 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F3 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ F X) N3))) (@ (@ F3 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X3)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N3 tptp.nat) (X3 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X3) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X3) N3)) (@ (@ F Y3) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (@ F X)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A2))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) A2)))))
% 6.82/7.05 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X3) N2)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X) (@ tptp.suc N2))))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X0) N2))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 6.82/7.05 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M4 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 6.82/7.05 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X2 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 6.82/7.05 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real H2) T5) (@ (@ tptp.ord_less_eq_real T5) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T5) (@ (@ tptp.ord_less_real T5) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.82/7.05 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 6.82/7.05 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_real T5) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.82/7.05 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (forall ((M4 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T5 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T5))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))))
% 6.82/7.05 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X2))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T5) (@ (@ tptp.ord_less_eq_real T5) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real A) T5) (@ (@ tptp.ord_less_real T5) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T5) (@ (@ tptp.ord_less_eq_real T5) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real C) T5) (@ (@ tptp.ord_less_real T5) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T5) (@ (@ tptp.ord_less_eq_real T5) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) B) (=> (not (= X2 C)) (exists ((T5 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T5))) (let ((_let_2 (@ tptp.ord_less_real X2))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T5) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T5) (@ _let_1 X2))) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T5)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) N))))))))))))))))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B3 tptp.real)) (=> (forall ((M4 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M2 tptp.nat) (T7 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M2) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real U2) P5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T7)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T7) P5)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T7) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F))) (exists ((L6 tptp.real) (M9 tptp.real)) (and (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y4) (@ (@ tptp.ord_less_eq_real Y4) M9)) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B) (= (@ F X3) Y4)))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R3)) (@ (@ tptp.ord_less_real (@ F X4)) tptp.zero_zero_real)))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L2 tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R3)) (not (= (@ F X4) tptp.zero_zero_real))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X4))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.sqrt)))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (@ tptp.root N))))
% 6.82/7.05 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (= (@ G (@ F Z3)) Z3)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.top_top_set_real)))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X2)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y3) (=> (@ (@ tptp.ord_less_real Y3) B) (= (@ F (@ G Y3)) Y3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arccos)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.82/7.05 (assert (forall ((B tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real B) X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.82/7.05 (assert (forall ((D2 tptp.real) (X2 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X2))) D2) (= (@ G (@ F Z3)) Z3))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X2))) D2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) G)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (exists ((C2 tptp.real)) (and (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F3 C2))))))))))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.82/7.05 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C)) tptp.at_top_nat) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X7) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X7 I2))) B3)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X7) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N3))) (@ G N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N7)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N7))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_real R3) (@ X7 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X7 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.82/7.05 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.82/7.05 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) L2)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N7)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X2)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X2) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((C tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real C))) (=> (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real _let_1)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.82/7.05 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real C)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real C)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X2) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N2)))) N2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_nat)))
% 6.82/7.05 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2))))))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2)))))))))
% 6.82/7.05 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K3 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.82/7.05 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K3 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))))))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 6.82/7.05 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 6.82/7.05 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F4 (-> tptp.real tptp.real))) (exists ((C3 tptp.real)) (= F4 (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C3)))))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X2) Y))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.82/7.05 (assert (= tptp.real_V3694042436643373181omplex (lambda ((X tptp.complex) (Y tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y)))))
% 6.82/7.05 (assert (= tptp.real_V975177566351809787t_real (lambda ((X tptp.real) (Y tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y)))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.82/7.05 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.82/7.05 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.82/7.05 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N))) tptp.at_bot_real) F5))))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) tptp.at_bot_real))
% 6.82/7.05 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N))) tptp.at_top_real) F5))))))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K)) (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat)))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) K)) (@ tptp.exp_real X)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) Y))) Y))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_real)))
% 6.82/7.05 (assert (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))
% 6.82/7.05 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X3) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.82/7.05 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.at_top_real))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5849166863359141190n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_2) _let_1))))))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real X2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_2) _let_1))))))))))
% 6.82/7.05 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real B) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ P (@ (@ tptp.plus_plus_real X) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real A) B)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_top_real) _let_1)))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_top_real) _let_1)))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) F5) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5984915006950818249n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) F5) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_top_real) _let_1)))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_bot_real) _let_1)))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_bot_real) _let_1)))))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_2) _let_1))))))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (X2 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) _let_1) tptp.at_top_real) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_1) tptp.at_top_real)))))))))
% 6.82/7.05 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5984915006950818249n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_2) _let_1))))))))))
% 6.82/7.05 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F0) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G0) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G0 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F0) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G0) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X)) (@ G0 X)))) F5) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5849166863359141190n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) F5) _let_1))))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X)) (@ G2 X)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_bot_real) _let_1)))))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N2) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N6)) F5)))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P N2)))))))
% 6.82/7.05 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (@ P X3))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I4) K)))) tptp.at_top_nat))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X2)) tptp.at_top_nat)))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X7) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X7 I2))) (@ (@ tptp.bfun_nat_real X7) tptp.at_top_nat)))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X7) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X7 I2))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X7) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X7 I3)))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (not (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))
% 6.82/7.05 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima2)))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y2 (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (= Y2 (not (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Y2 (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X2 _let_1) (=> (= Y2 (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) G))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C2) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.arcosh_real))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ _let_1 (lambda ((X tptp.real)) (@ tptp.arcosh_real (@ F X)))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (exists ((C2 tptp.real) (D3 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C2) D3)) (@ (@ tptp.ord_less_eq_real C2) D3)))))))
% 6.82/7.05 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.82/7.05 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.82/7.05 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.artanh_real))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.member_real (@ F X3)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X tptp.real)) (@ tptp.artanh_real (@ F X)))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F3 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ F3 Z3) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F3 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F3 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (= (@ F B) (@ F A)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F B)) (@ F A)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F A)) (@ F B)))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X2) (=> (@ (@ tptp.ord_less_eq_real X2) B) (= (@ F X2) (@ F A)))))))))
% 6.82/7.05 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))))))))
% 6.82/7.05 (assert (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X) Y)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.82/7.05 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X) Y)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.82/7.05 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X7) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X7 I2)) B3)) (@ (@ tptp.bfun_nat_real X7) tptp.at_top_nat)))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X7) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X7 I2)) B3)) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X7) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X7 I3)) L6))))))))))
% 6.82/7.05 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M3)) M3))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N6 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) M3) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P (@ (@ tptp.product_Pair_nat_nat N2) M3))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (=> (@ tptp.order_mono_nat_real F) (=> (@ tptp.order_5726023648592871131at_nat G) (= (@ (@ tptp.bfun_nat_real (lambda ((X tptp.nat)) (@ F (@ G X)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 6.82/7.05 (assert (forall ((D2 tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) D2))) (= (@ (@ tptp.filtermap_real_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real X) D2))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1))))))
% 6.82/7.05 (assert (forall ((A tptp.real)) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) A))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N)))) tptp.top_top_set_real))))
% 6.82/7.05 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.82/7.05 (assert (forall ((F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F3 X3))) (@ tptp.order_7092887310737990675l_real F)))))
% 6.82/7.05 (assert (forall ((N4 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N4) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) K))) N4))))
% 6.82/7.05 (assert (forall ((N4 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N4)))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (@ tptp.summable_real (@ (@ tptp.comp_nat_real_nat F) G)))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G))) (@ tptp.suminf_real F)))))))
% 6.82/7.05 (assert (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.82/7.05 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (=> (forall ((X3 tptp.nat)) (=> (not (@ (@ tptp.member_nat X3) (@ (@ tptp.image_nat_nat G) tptp.top_top_set_nat))) (= (@ F X3) tptp.zero_zero_real))) (= (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G)) (@ tptp.suminf_real F))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (or (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X2) N))))))
% 6.82/7.05 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M3 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M3)))))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.82/7.05 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.82/7.05 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.82/7.05 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (N2 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X2)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X2) tptp.field_5140801741446780682s_real))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X2) X3)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X3) X2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y2) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X2) X3) (@ (@ tptp.ord_less_real X3) Y2))))))
% 6.82/7.05 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) M)) J))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 6.82/7.05 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K) _let_1)))))
% 6.82/7.05 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 6.82/7.05 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q2))))))
% 6.82/7.05 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M3))))))
% 6.82/7.05 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M3)))))
% 6.82/7.05 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M3))))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.upt M) N))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat) (X2 tptp.nat) (Xs2 tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X2) Xs2)) (and (@ (@ tptp.ord_less_nat I) J) (= I X2) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs2)))))
% 6.82/7.05 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J3)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J3))) tptp.nil_nat))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 6.82/7.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N4))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L) N4)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L)) tptp.one_one_nat) N4))))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N4 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N4))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N4) M)) tptp.one_one_nat)) N4))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 6.82/7.05 (assert (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.nth_nat Ns) I))))))
% 6.82/7.05 (assert (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))))
% 6.82/7.05 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X2) Y2) (=> (@ _let_1 X2) (=> (=> (= X2 tptp.nil_nat) (=> (= Y2 tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X3) Xs3))) (=> (= X2 _let_1) (=> (= Y2 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 6.82/7.05 (assert (= tptp.quotient_of (lambda ((X tptp.rat)) (@ tptp.the_Pr4378521158711661632nt_int (lambda ((Pair tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Pair))) (let ((_let_2 (@ tptp.product_fst_int_int Pair))) (and (= X (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)))))))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.algebr932160517623751201me_int K))) (= (@ _let_1 (@ tptp.abs_abs_int L2)) (@ _let_1 L2)))))
% 6.82/7.05 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.algebr932160517623751201me_int (@ tptp.abs_abs_int K)) L2) (@ (@ tptp.algebr932160517623751201me_int K) L2))))
% 6.82/7.05 (assert (forall ((Q2 tptp.int) (P2 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P2) Q2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2) (=> (@ (@ tptp.algebr932160517623751201me_int P2) Q2) (= (@ tptp.normalize _let_1) _let_1))))))
% 6.82/7.05 (assert (forall ((A tptp.int) (B tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (=> (@ (@ tptp.algebr932160517623751201me_int A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ tptp.abs_abs_int X2) tptp.one_one_int)))))))
% 6.82/7.05 (assert (forall ((Q2 tptp.rat)) (not (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= Q2 (@ (@ tptp.fract A5) B5)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (not (@ (@ tptp.algebr932160517623751201me_int A5) B5))))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.algebr932160517623751201me_int A5) B5) (@ P (@ (@ tptp.fract A5) B5))))) (@ P Q2))))
% 6.82/7.05 (assert (forall ((Q2 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= Q2 (@ (@ tptp.fract A5) B5)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (not (= A5 tptp.zero_zero_int)) (not (@ (@ tptp.algebr932160517623751201me_int A5) B5)))))) (= Q2 tptp.zero_zero_rat))))
% 6.82/7.05 (assert (forall ((R tptp.rat)) (exists ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X3))) (let ((_let_2 (@ tptp.product_fst_int_int X3))) (and (= R (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1) (forall ((Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y4))) (let ((_let_2 (@ tptp.product_fst_int_int Y4))) (=> (and (= R (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)) (= Y4 X3)))))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.algebr932160517623751201me_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.algebr934650988132801477me_nat M) N))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.algebr932160517623751201me_int (@ tptp.semiri1314217659103216013at_int N)) K))))
% 6.82/7.05 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ (@ tptp.algebr932160517623751201me_int K) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.82/7.05 (assert (forall ((A tptp.nat) (D2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.algebr934650988132801477me_nat A) D2) (=> (@ (@ tptp.algebr934650988132801477me_nat B) C) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) D2)) (and (= A B) (= C D2)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc tptp.zero_zero_nat))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc N))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc N)) N)))
% 6.82/7.05 (assert (forall ((A tptp.nat) (B tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X2))) (=> (@ (@ tptp.algebr934650988132801477me_nat A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= X2 tptp.one_one_nat)))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.field_5140801741446780682s_real) (not (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X2) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M4)) (@ tptp.semiri5074537144036343181t_real N3))) (not (@ (@ tptp.algebr934650988132801477me_nat M4) N3)))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (exists ((A8 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A8) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N3))) A8)))) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N2)) (@ Y6 N2))))))))
% 6.82/7.05 (assert (forall ((C tptp.rat)) (= (@ tptp.vanishes (lambda ((N2 tptp.nat)) C)) (= C tptp.zero_zero_rat))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X7) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X7 N2)) (@ Y6 N2))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N2)))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X7) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N2)) (@ Y6 N2))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (R tptp.rat)) (=> (@ tptp.vanishes X7) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N7))) R))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N3))) R3)))))) (@ tptp.vanishes X7))))
% 6.82/7.05 (assert (= tptp.vanishes (lambda ((X5 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X5 N2))) R5)))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X2) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num _let_1)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.82/7.05 (assert (forall ((R tptp.real) (A tptp.real)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.rcis R) A)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real tptp.one_one_real) R)) (@ tptp.uminus_uminus_real A)))))
% 6.82/7.05 (assert (forall ((R tptp.real) (A tptp.real)) (= (@ tptp.re (@ (@ tptp.rcis R) A)) (@ (@ tptp.times_times_real R) (@ tptp.cos_real A)))))
% 6.82/7.05 (assert (forall ((R tptp.real) (A tptp.real)) (= (@ tptp.im (@ (@ tptp.rcis R) A)) (@ (@ tptp.times_times_real R) (@ tptp.sin_real A)))))
% 6.82/7.05 (assert (= tptp.cis (@ tptp.rcis tptp.one_one_real)))
% 6.82/7.05 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B)) (@ (@ tptp.rcis (@ (@ tptp.times_times_real R1) R22)) (@ (@ tptp.plus_plus_real A) B)))))
% 6.82/7.05 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real R1) R22)) (@ (@ tptp.minus_minus_real A) B)))))
% 6.82/7.05 (assert (forall ((R tptp.real) (A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.rcis R) A)) N) (@ (@ tptp.rcis (@ (@ tptp.power_power_real R) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X2) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X2) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ tptp.bit1 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit1 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bit1 M4)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))))
% 6.82/7.05 (assert (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))
% 6.82/7.05 (assert (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y)))))) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N))))))
% 6.82/7.05 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.82/7.05 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat) (M tptp.nat)) (let ((_let_1 (@ tptp.produc457027306803732586at_nat A2))) (= (@ _let_1 (lambda ((Uu3 tptp.nat)) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 (lambda ((I4 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) I4))))) (@ _let_1 (lambda ((I4 tptp.nat)) (@ (@ tptp.set_or6659071591806873216st_nat (@ (@ tptp.minus_minus_nat M) I4)) M))))))))
% 6.82/7.05 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 6.82/7.05 (assert (forall ((F5 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F5)) (@ tptp.finite_finite_nat F5))))
% 6.82/7.05 (assert (forall ((N tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N)) A2)) (@ (@ tptp.insert_nat N) (@ _let_1 A2))))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A2)) (@ _let_1 A2)))))
% 6.82/7.05 (assert (forall ((X2 tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X2)))))
% 6.82/7.05 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.nat_set_encode (@ (@ tptp.vimage_nat_nat tptp.suc) A2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat_set_encode A2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (R tptp.rat)) (=> (@ tptp.cauchy X7) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M2) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X7 M2)) (@ X7 N7)))) R))))))))))
% 6.82/7.05 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 6.82/7.05 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ (@ tptp.minus_1356011639430497352at_nat tptp.bNF_Ca8665028551170535155natLeq) tptp.id_nat2)))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (not (@ tptp.vanishes X7)) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N2))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.rat)) (@ tptp.cauchy (lambda ((N2 tptp.nat)) X2))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N2)) (@ Y6 N2))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N2)))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N2)) (@ Y6 N2))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X7 N2)) (@ Y6 N2))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (exists ((B5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B5) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N7))) B5)))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (not (@ tptp.vanishes X7)) (=> (@ tptp.cauchy Y6) (=> (not (@ tptp.vanishes Y6)) (=> (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X7 N2)) (@ Y6 N2)))) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ tptp.inverse_inverse_rat (@ X7 N2))) (@ tptp.inverse_inverse_rat (@ Y6 N2))))))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (not (@ tptp.vanishes X7)) (exists ((B5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B5) (exists ((K3 tptp.nat)) (or (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat B5) (@ tptp.uminus_uminus_rat (@ X7 N7))))) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat B5) (@ X7 N7))))))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (not (@ tptp.vanishes X7)) (exists ((B5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B5) (exists ((K3 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat B5) (@ tptp.abs_abs_rat (@ X7 N7))))))))))))
% 6.82/7.05 (assert (= tptp.cauchy (lambda ((X5 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) M3) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X5 M3)) (@ X5 N2)))) R5)))))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) M4) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X7 M4)) (@ X7 N3)))) R3)))))))) (@ tptp.cauchy X7))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)) (lambda ((Uu3 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X7)) (@ tptp.real2 Y6)) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_eq_rat (@ X7 N2)) (@ (@ tptp.plus_plus_rat (@ Y6 N2)) R5))))))))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((X10 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X10) (@ P (@ tptp.real2 X10)))) (@ P X2))))
% 6.82/7.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N))))))
% 6.82/7.05 (assert (= tptp.one_one_real (@ tptp.real2 (lambda ((N2 tptp.nat)) tptp.one_one_rat))))
% 6.82/7.05 (assert (= tptp.zero_zero_real (@ tptp.real2 (lambda ((N2 tptp.nat)) tptp.zero_zero_rat))))
% 6.82/7.05 (assert (= tptp.field_7254667332652039916t_real (lambda ((X tptp.rat)) (@ tptp.real2 (lambda ((N2 tptp.nat)) X)))))
% 6.82/7.05 (assert (= tptp.semiri5074537144036343181t_real (lambda ((X tptp.nat)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat X))))))
% 6.82/7.05 (assert (= tptp.ring_1_of_int_real (lambda ((X tptp.int)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.ring_1_of_int_rat X))))))
% 6.82/7.05 (assert (forall ((Y6 (-> tptp.nat tptp.rat)) (X2 tptp.real)) (=> (@ tptp.cauchy Y6) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.real2 Y6)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.field_7254667332652039916t_real (@ Y6 N3))))))))
% 6.82/7.05 (assert (forall ((Y6 (-> tptp.nat tptp.rat)) (X2 tptp.real)) (=> (@ tptp.cauchy Y6) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.field_7254667332652039916t_real (@ Y6 N3)))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.real2 Y6))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y2 tptp.real)) (=> (@ tptp.cauchy X7) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.field_7254667332652039916t_real (@ X7 N3))) Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X7)) Y2)))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X7)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N2))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 X7)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N2)) (@ Y6 N2)))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.times_times_real (@ tptp.real2 X7)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N2)) (@ Y6 N2)))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.minus_minus_real (@ tptp.real2 X7)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X7 N2)) (@ Y6 N2)))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y6) (= (= (@ tptp.real2 X7) (@ tptp.real2 Y6)) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X7 N2)) (@ Y6 N2)))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.real2 X7)))) (let ((_let_2 (@ tptp.vanishes X7))) (=> (@ tptp.cauchy X7) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N2))))))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (= (not (@ tptp.positive2 (@ tptp.real2 X7))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_eq_rat (@ X7 N2)) R5))))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (= (@ tptp.positive2 (@ tptp.real2 X7)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_rat R5) (@ X7 N2)))))))))))
% 6.82/7.05 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (@ tptp.positive2 (@ (@ tptp.minus_minus_real Y) X)))))
% 6.82/7.05 (assert (forall ((X2 tptp.real)) (=> (not (@ tptp.positive2 X2)) (=> (not (= X2 tptp.zero_zero_real)) (@ tptp.positive2 (@ tptp.uminus_uminus_real X2))))))
% 6.82/7.05 (assert (not (@ tptp.positive2 tptp.zero_zero_real)))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ tptp.positive2 X2) (=> (@ tptp.positive2 Y2) (@ tptp.positive2 (@ (@ tptp.plus_plus_real X2) Y2))))))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (=> (@ tptp.positive2 X2) (=> (@ tptp.positive2 Y2) (@ tptp.positive2 (@ (@ tptp.times_times_real X2) Y2))))))
% 6.82/7.05 (assert (= tptp.positive2 (lambda ((X tptp.real)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_rat R5) (@ (@ tptp.rep_real X) N2))))))))))
% 6.82/7.05 (assert (= tptp.positive2 (@ (@ (@ tptp.map_fu1856342031159181835at_o_o tptp.rep_real) tptp.id_o) (lambda ((X5 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_rat R5) (@ X5 N2)))))))))))
% 6.82/7.05 (assert (= tptp.inverse_inverse_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X5 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X5)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X5 N2)))) __flatten_var_0)))))
% 6.82/7.05 (assert (= tptp.uminus_uminus_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X5 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X5 N2))))))
% 6.82/7.05 (assert (= tptp.times_times_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X5 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X5 N2)) (@ Y7 N2))))))
% 6.82/7.05 (assert (= tptp.plus_plus_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X5 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X5 N2)) (@ Y7 N2))))))
% 6.82/7.05 (assert (forall ((X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X2) X2) (= (@ tptp.inverse_inverse_real (@ tptp.real2 X2)) (@ tptp.real2 (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X2)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X2 N2)))))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((Y3 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Y3) Y3) (@ P (@ tptp.real2 Y3)))) (@ P X2))))
% 6.82/7.05 (assert (@ (@ tptp.realrel (lambda ((N2 tptp.nat)) tptp.one_one_rat)) (lambda ((N2 tptp.nat)) tptp.one_one_rat)))
% 6.82/7.05 (assert (@ (@ tptp.realrel (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S2) N)))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (@ (@ tptp.realrel X7) X7))))
% 6.82/7.05 (assert (forall ((X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X2) X2) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X2)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X2 N2))))))))
% 6.82/7.05 (assert (forall ((Xa2 (-> tptp.nat tptp.rat)) (X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa2) Xa2) (=> (@ (@ tptp.realrel X2) X2) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 Xa2)) (@ tptp.real2 X2)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ Xa2 N2)) (@ X2 N2)))))))))
% 6.82/7.05 (assert (forall ((Xa2 (-> tptp.nat tptp.rat)) (X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa2) Xa2) (=> (@ (@ tptp.realrel X2) X2) (= (@ (@ tptp.times_times_real (@ tptp.real2 Xa2)) (@ tptp.real2 X2)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ Xa2 N2)) (@ X2 N2)))))))))
% 6.82/7.05 (assert (forall ((X7 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X7) (=> (@ tptp.cauchy Y6) (=> (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X7 N2)) (@ Y6 N2)))) (@ (@ tptp.realrel X7) Y6))))))
% 6.82/7.05 (assert (= tptp.realrel (lambda ((X5 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (and (@ tptp.cauchy X5) (@ tptp.cauchy Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X5 N2)) (@ Y7 N2))))))))
% 6.82/7.05 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S2)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S2) N))))))
% 6.82/7.05 (assert (forall ((X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X2) X2) (= (@ tptp.positive2 (@ tptp.real2 X2)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_rat R5) (@ X2 N2)))))))))))
% 6.82/7.05 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5))) (lambda ((X5 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_rat R5) (@ X5 N2))))))))) (lambda ((X5 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_rat R5) (@ X5 N2))))))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (Q (-> tptp.nat Bool)) (M tptp.nat)) (=> (@ P N) (=> (@ Q M) (=> (not (@ P tptp.zero_zero_nat)) (=> (forall ((K3 tptp.nat)) (= (@ P (@ tptp.suc K3)) (@ Q K3))) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))))
% 6.82/7.05 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M3 tptp.nat)) (@ P (@ tptp.suc M3))))))))))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ (@ tptp.if_int false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ (@ tptp.if_int true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ (@ tptp.if_num false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (@ (@ (@ tptp.if_num true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ (@ tptp.if_real false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.real) (Y2 tptp.real)) (= (@ (@ (@ tptp.if_real true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X5 tptp.real)) (@ P X5)))))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.complex) (Y2 tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.extended_enat) (Y2 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.vEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.list_int) (Y2 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.list_int) (Y2 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y2 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y2 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.option_nat) (Y2 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.option_nat) (Y2 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.option_num) (Y2 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.option_num) (Y2 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.product_prod_int_int) (Y2 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.product_prod_int_int) (Y2 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X2) Y2) X2)))
% 6.82/7.05 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X2) Y2) Y2)))
% 6.82/7.05 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y2 /export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 17614 Alarm clock ( read result; case "$result" in
% 299.91/300.16 unsat)
% 299.91/300.16 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.91/300.16 ;;
% 299.91/300.16 sat)
% 299.91/300.16 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.91/300.16 ;;
% 299.91/300.16 esac; exit 1 )
% 299.91/300.17 Alarm clock
% 299.91/300.17 % cvc5---1.0.5 exiting
% 299.91/300.17 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------